diff --git "a/raw/mathlib-v4.33.0/declarations-47.jsonl" "b/raw/mathlib-v4.33.0/declarations-47.jsonl"
new file mode 100644--- /dev/null
+++ "b/raw/mathlib-v4.33.0/declarations-47.jsonl"
@@ -0,0 +1,10000 @@
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.isLoop_tfae._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.isLoop_tfae","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.isLoop_tfae._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.isLoop_tfae","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopless_iff_forall_isCircuit.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopless_iff_forall_isCircuit","reducibility":"abbrev","statement_dag_size":113,"type_refs":["And","And.intro","Exists","Exists.intro","Matroid","Matroid.E","Matroid.IsLoop","Membership.mem","Set","Set.instMembership"],"value_dag_size":175,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.E","Matroid.IsLoop","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopless_iff_forall_isCircuit.match_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopless_iff_forall_isCircuit","reducibility":"abbrev","statement_dag_size":80,"type_refs":["And","And.intro","Exists","Exists.intro","Matroid","Matroid.IsCircuit","Set","Set.Subsingleton"],"value_dag_size":131,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsCircuit","Set","Set.Subsingleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoop_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoop_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsLoop","Matroid.loops","Membership.mem","Set","Set.instMembership"],"value_dag_size":34,"value_refs":["Matroid","Matroid.IsLoop","Matroid.isLoop_iff","Matroid.loops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoopless_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoopless_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Matroid","Matroid.E","Matroid.IsLoop","Matroid.Loopless","Membership.mem","Not","Set","Set.instMembership"],"value_dag_size":40,"value_refs":["Matroid","Matroid.E","Matroid.IsLoop","Matroid.Loopless","Matroid.loopless_iff_forall_not_isLoop","Membership.mem","Not","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoopless_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoopless_iff","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.mapEmbedding_isLoop_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.mapEmbedding_isLoop_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsLoop","Matroid.loops","Membership.mem","Set","Set.instMembership"],"value_dag_size":34,"value_refs":["Matroid","Matroid.IsLoop","Matroid.isLoop_iff","Matroid.loops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.mapEmbedding_isLoop_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.mapEmbedding_isLoop_iff","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Matroid","Matroid.closure","Matroid.loops","Set","Set.instEmptyCollection"],"value_dag_size":29,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Matroid","Matroid.closure","Matroid.closure_empty","Matroid.loops","Set","Set.instEmptyCollection"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.not_isNonloop_iff_closure._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.not_isNonloop_iff_closure","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Matroid","Matroid.E","Matroid.IsLoop","Matroid.closure","Matroid.loops","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":55,"value_refs":["And","Eq","Matroid","Matroid.E","Matroid.IsLoop","Matroid.closure","Matroid.isLoop_iff_closure_eq_loops_and_mem_ground","Matroid.loops","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.not_isNonloop_iff_closure._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.not_isNonloop_iff_closure","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.closure","Set","Set.instInter"],"value_dag_size":36,"value_refs":["Eq.symm","Inter.inter","Matroid","Matroid.E","Matroid.closure","Matroid.closure_inter_ground","Set","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.removeLoops_loopless._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.removeLoops_loopless","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Matroid","Matroid.E","Matroid.IsNonloop","Matroid.Loopless","Membership.mem","Set","Set.instMembership"],"value_dag_size":38,"value_refs":["Matroid","Matroid.E","Matroid.IsNonloop","Matroid.Loopless","Matroid.loopless_iff_forall_isNonloop","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsLoop","Matroid.loops","Membership.mem","Set","Set.instMembership"],"value_dag_size":34,"value_refs":["Matroid","Matroid.IsLoop","Matroid.isLoop_iff","Matroid.loops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.restrict_isLoop_iff","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Matroid","Matroid.closure","Matroid.loops","Set","Set.instEmptyCollection"],"value_dag_size":29,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Matroid","Matroid.closure","Matroid.closure_empty","Matroid.loops","Set","Set.instEmptyCollection"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Loop","name":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.uniqueBaseOn_isLoop_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.uniqueBaseOn_isLoop_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsLoop","Matroid.loops","Membership.mem","Set","Set.instMembership"],"value_dag_size":34,"value_refs":["Matroid","Matroid.IsLoop","Matroid.isLoop_iff","Matroid.loops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Insert.insert","Set","Set.image","Set.instInsert"],"value_dag_size":52,"value_refs":["Eq.symm","Insert.insert","Set","Set.image","Set.image_insert_eq","Set.instInsert"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.IsBasis.map","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap._simp_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","Matroid","Matroid.Indep","Matroid.restrict","Set","Set.instLE"],"value_dag_size":44,"value_refs":["And","LE.le","Matroid","Matroid.Indep","Matroid.restrict","Matroid.restrict_indep_iff","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap._simp_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage"],"value_dag_size":53,"value_refs":["LE.le","Set","Set.image","Set.image_subset_iff","Set.instLE","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap._simp_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":51,"value_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap._simp_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap._simp_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","LE.le","Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.comapOn","Set","Set.InjOn","Set.image","Set.instLE"],"value_dag_size":70,"value_refs":["And","LE.le","Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.comapOn","Matroid.comapOn_isBase_iff","Set","Set.InjOn","Set.image","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Set","Set.instInter"],"value_dag_size":44,"value_refs":["Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Matroid.isBasis'_iff_isBasis_inter_ground","Set","Set.instInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Matroid","Matroid.E","Matroid.IsBase","Matroid.IsBasis","Set"],"value_dag_size":31,"value_refs":["Matroid","Matroid.E","Matroid.IsBase","Matroid.IsBasis","Matroid.isBasis_ground_iff","Set","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_dep_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_dep_iff","reducibility":null,"statement_dag_size":82,"type_refs":["And","LE.le","Matroid","Matroid.E","Matroid.Indep","Not","Or","Set","Set.InjOn","Set.image","Set.instLE","Set.preimage"],"value_dag_size":409,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq.mp","Eq.symm","Eq.trans","False","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","Matroid","Matroid.E","Matroid.Indep","Not","Or","Set","Set.InjOn","Set.image","Set.instLE","Set.preimage","True","True.intro","congr","congrArg","congrFun'","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_emptyOn._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_emptyOn","reducibility":null,"statement_dag_size":32,"type_refs":["EmptyCollection.emptyCollection","Eq","Matroid","Matroid.E","Matroid.emptyOn","Set","Set.instEmptyCollection"],"value_dag_size":40,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Matroid","Matroid.E","Matroid.emptyOn","Matroid.ground_eq_empty_iff","Set","Set.instEmptyCollection","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_finitary._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_finitary","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE"],"value_dag_size":64,"value_refs":["LE.le","Set","Set.forall_subset_image_iff","Set.image","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Set","Set.instInter"],"value_dag_size":44,"value_refs":["Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Matroid.isBasis'_iff_isBasis_inter_ground","Set","Set.instInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Inter.inter","LE.le","Set","Set.instInter","Set.instLE"],"value_dag_size":42,"value_refs":["And","Inter.inter","LE.le","Set","Set.instInter","Set.instLE","Set.subset_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","Eq.symm","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis'_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_10","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage"],"value_dag_size":59,"value_refs":["Eq.symm","LE.le","Set","Set.image","Set.image_subset_iff","Set.instLE","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","Not","Or"],"value_dag_size":19,"value_refs":["Classical.or_iff_not_imp_right","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff.match_1_8","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff","reducibility":"abbrev","statement_dag_size":84,"type_refs":["And.intro","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":104,"value_refs":["And.casesOn","And.intro","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_map","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Iff","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE"],"value_dag_size":58,"value_refs":["And","Eq","Iff","LE.le","Matroid","Matroid.E","Matroid.Indep","Matroid.ext_iff_indep","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFinitaryMapEmbedding._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFinitaryMapEmbedding","reducibility":null,"statement_dag_size":28,"type_refs":["Function.Embedding","Matroid","Matroid.Finitary","Matroid.mapEmbedding"],"value_dag_size":58,"value_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.injective","Function.Injective.injOn","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.Finitary","Matroid.instFinitaryMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFinitaryMapEquiv._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFinitaryMapEquiv","reducibility":null,"statement_dag_size":28,"type_refs":["Equiv","Matroid","Matroid.Finitary","Matroid.mapEquiv"],"value_dag_size":57,"value_refs":["DFunLike.coe","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Function.Injective.injOn","Matroid","Matroid.E","Matroid.Finitary","Matroid.instFinitaryMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFiniteMapEmbedding._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFiniteMapEmbedding","reducibility":null,"statement_dag_size":28,"type_refs":["Function.Embedding","Matroid","Matroid.Finite","Matroid.mapEmbedding"],"value_dag_size":58,"value_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.injective","Function.Injective.injOn","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.Finite","Matroid.instFiniteMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFiniteMapEquiv._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instFiniteMapEquiv","reducibility":null,"statement_dag_size":28,"type_refs":["Equiv","Matroid","Matroid.Finite","Matroid.mapEquiv"],"value_dag_size":57,"value_refs":["DFunLike.coe","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Function.Injective.injOn","Matroid","Matroid.E","Matroid.Finite","Matroid.instFiniteMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instNonemptyMapEmbedding._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instNonemptyMapEmbedding","reducibility":null,"statement_dag_size":28,"type_refs":["Function.Embedding","Matroid","Matroid.Nonempty","Matroid.mapEmbedding"],"value_dag_size":58,"value_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.injective","Function.Injective.injOn","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.Nonempty","Matroid.instNonemptyMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instNonemptyMapEquiv._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instNonemptyMapEquiv","reducibility":null,"statement_dag_size":28,"type_refs":["Equiv","Matroid","Matroid.Nonempty","Matroid.mapEquiv"],"value_dag_size":57,"value_refs":["DFunLike.coe","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Function.Injective.injOn","Matroid","Matroid.E","Matroid.Nonempty","Matroid.instNonemptyMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMap.match_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMap","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBase","Set"],"value_dag_size":70,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMapEmbedding._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMapEmbedding","reducibility":null,"statement_dag_size":28,"type_refs":["Function.Embedding","Matroid","Matroid.RankFinite","Matroid.mapEmbedding"],"value_dag_size":58,"value_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.injective","Function.Injective.injOn","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.RankFinite","Matroid.instRankFiniteMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMapEquiv._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankFiniteMapEquiv","reducibility":null,"statement_dag_size":28,"type_refs":["Equiv","Matroid","Matroid.RankFinite","Matroid.mapEquiv"],"value_dag_size":57,"value_refs":["DFunLike.coe","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Function.Injective.injOn","Matroid","Matroid.E","Matroid.RankFinite","Matroid.instRankFiniteMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankPosMapEmbedding._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankPosMapEmbedding","reducibility":null,"statement_dag_size":28,"type_refs":["Function.Embedding","Matroid","Matroid.RankPos","Matroid.mapEmbedding"],"value_dag_size":58,"value_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.injective","Function.Injective.injOn","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.RankPos","Matroid.instRankPosMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankPosMapEquiv._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.instRankPosMapEquiv","reducibility":null,"statement_dag_size":28,"type_refs":["Equiv","Matroid","Matroid.RankPos","Matroid.mapEquiv"],"value_dag_size":57,"value_refs":["DFunLike.coe","Equiv","Equiv.injective","Equiv.instEquivLike","EquivLike.toFunLike","Function.Injective.injOn","Matroid","Matroid.E","Matroid.RankPos","Matroid.instRankPosMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map","reducibility":null,"statement_dag_size":107,"type_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.Indep","Matroid.mapSetEmbedding","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","Subtype","Subtype.val"],"value_dag_size":112,"value_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","Matroid","Matroid.E","Matroid.Indep","Matroid.mapSetEmbedding","Matroid.mapSetEmbedding_indep_iff'","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","Subtype","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map.match_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map","reducibility":"abbrev","statement_dag_size":171,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.image","Set.instLE"],"value_dag_size":254,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.image","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map.match_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map","reducibility":"abbrev","statement_dag_size":105,"type_refs":["And","Eq","Exists","Exists.intro","Matroid","Matroid.Indep","Set","Set.image"],"value_dag_size":133,"value_refs":["And","Eq","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.Indep","Set","Set.image"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_indep_iff.match_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_indep_iff","reducibility":"abbrev","statement_dag_size":163,"type_refs":["And","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.Indep","Set","Set.instLE","Set.preimage","Set.range"],"value_dag_size":183,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.Indep","Set","Set.instLE","Set.preimage","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_isBase_iff.match_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_isBase_iff","reducibility":"abbrev","statement_dag_size":163,"type_refs":["And","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE","Set.preimage","Set.range"],"value_dag_size":183,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE","Set.preimage","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_isBasis_iff.match_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapEmbedding_isBasis_iff","reducibility":"abbrev","statement_dag_size":198,"type_refs":["And","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.IsBasis","Set","Set.instLE","Set.preimage","Set.range"],"value_dag_size":288,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Matroid","Matroid.IsBasis","Set","Set.instLE","Set.preimage","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding","reducibility":null,"statement_dag_size":29,"type_refs":["EmptyCollection.emptyCollection","Eq","LE.le","Set","Set.instEmptyCollection","Set.instLE"],"value_dag_size":31,"value_refs":["EmptyCollection.emptyCollection","Eq","LE.le","Set","Set.instEmptyCollection","Set.instLE","Set.subset_empty_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","Eq.symm","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Exists","LE.le","Set","Set.image","Set.instLE","Set.range"],"value_dag_size":51,"value_refs":["Eq","Exists","LE.le","Set","Set.image","Set.instLE","Set.range","Set.subset_range_iff_exists_image_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":40,"value_refs":["Eq","Subtype","Subtype.val","Subtype.val_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_comap._proof_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_comap","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","Exists","Matroid","Matroid.Indep","Set","Set.InjOn","Set.image"],"value_dag_size":316,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Lean.Grind._simp_1","Lean.Grind.intro_with_eq","Matroid","Matroid.Indep","Not","Set","Set.InjOn","Set.image","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","funext","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_comap._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_comap","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage","Set.range"],"value_dag_size":48,"value_refs":["Eq","LE.le","Set","Set.image","Set.image_preimage_eq_iff","Set.instLE","Set.preimage","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dep_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","LE.le","Set","Set.image","Set.instLE"],"value_dag_size":66,"value_refs":["And","Eq","Exists","LE.le","Set","Set.image","Set.instLE","Set.subset_image_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","LE.le","Set","Set.image","Set.instLE"],"value_dag_size":66,"value_refs":["And","Eq","Exists","LE.le","Set","Set.image","Set.instLE","Set.subset_image_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual","reducibility":null,"statement_dag_size":37,"type_refs":["Eq"],"value_dag_size":43,"value_refs":["Eq","forall_apply_eq_imp_iff₂","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","LE.le","Matroid","Matroid.E","Matroid.IsBase","Matroid.dual","SDiff.sdiff","Set","Set.instLE","Set.instSDiff"],"value_dag_size":49,"value_refs":["And","LE.le","Matroid","Matroid.E","Matroid.IsBase","Matroid.dual","Matroid.dual_isBase_iff'","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_emptyOn._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_emptyOn","reducibility":null,"statement_dag_size":32,"type_refs":["EmptyCollection.emptyCollection","Eq","Matroid","Matroid.E","Matroid.emptyOn","Set","Set.instEmptyCollection"],"value_dag_size":40,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Matroid","Matroid.E","Matroid.emptyOn","Matroid.ground_eq_empty_iff","Set","Set.instEmptyCollection","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_id._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_id","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Iff","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE"],"value_dag_size":58,"value_refs":["And","Eq","Iff","LE.le","Matroid","Matroid.E","Matroid.Indep","Matroid.ext_iff_indep","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_image_indep_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_image_indep_iff","reducibility":"abbrev","statement_dag_size":126,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Matroid","Matroid.Indep","Set","Set.image"],"value_dag_size":187,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.Indep","Set","Set.image"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_image_isBase_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_image_isBase_iff","reducibility":"abbrev","statement_dag_size":126,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Matroid","Matroid.IsBase","Set","Set.image"],"value_dag_size":187,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Set","Set.image"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_loopyOn._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_loopyOn","reducibility":null,"statement_dag_size":63,"type_refs":["And","EmptyCollection.emptyCollection","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Matroid.loopyOn","Set","Set.instEmptyCollection","Set.instLE"],"value_dag_size":66,"value_refs":["And","EmptyCollection.emptyCollection","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Matroid.eq_loopyOn_iff","Matroid.loopyOn","Set","Set.instEmptyCollection","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.restrictSubtype_isBase_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.restrictSubtype_isBase_iff","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.IsBasis","Matroid.restrict","Set","Set.instInter","Set.instLE"],"value_dag_size":60,"value_refs":["And","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.IsBasis","Matroid.isBasis_restrict_iff'","Matroid.restrict","Set","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Map","name":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.restrictSubtype_isBase_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.restrictSubtype_isBase_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Set","Set.instInter"],"value_dag_size":44,"value_refs":["Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Matroid.isBasis'_iff_isBasis_inter_ground","Set","Set.instInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","Exists","LE.le","Matroid","Matroid.Indep","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":44,"value_refs":["And","Exists","LE.le","Matroid","Matroid.Indep","Matroid.IsBase","Matroid.indep_iff","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","Set","Set.instLE","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["And","LE.le","Set","Set.instLE","Set.instUnion","Set.union_subset_iff","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff","reducibility":"abbrev","statement_dag_size":267,"type_refs":["And","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instUnion","Union.union"],"value_dag_size":455,"value_refs":["And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.casesOn","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.contract_indep_iff","reducibility":"abbrev","statement_dag_size":243,"type_refs":["And","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"],"value_dag_size":517,"value_refs":["And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.casesOn","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff","Set.subset_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":51,"value_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.Indep.union_isBasis_union_of_contract_isBasis","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Set","Set.instInter"],"value_dag_size":44,"value_refs":["Inter.inter","Matroid","Matroid.E","Matroid.IsBasis","Matroid.IsBasis'","Matroid.isBasis'_iff_isBasis_inter_ground","Set","Set.instInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Inter.inter","SDiff.sdiff","Set","Set.instInter","Set.instSDiff"],"value_dag_size":44,"value_refs":["Eq.symm","Inter.inter","SDiff.sdiff","Set","Set.instInter","Set.instSDiff","Set.sdiff_inter_distrib_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff","Set.subset_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":51,"value_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset","reducibility":null,"statement_dag_size":56,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instSDiff","True"],"value_dag_size":57,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.disjoint_sdiff_left","Set.instBooleanAlgebra","Set.instSDiff","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","Set.instUnion","Union.union"],"value_dag_size":46,"value_refs":["LE.le","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","Set.instUnion","Set.sdiff_subset_iff","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subset","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","UsesSetNotationForOrder"],"value_dag_size":45,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","UsesSetNotationForOrder","propext","subset_antisymm_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis.contract_isBasis_of_isBasis'","reducibility":null,"statement_dag_size":64,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE"],"value_dag_size":67,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_iff","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit","reducibility":null,"statement_dag_size":59,"type_refs":["And","Eq","Matroid","Matroid.Dep","Matroid.Indep","Matroid.IsCircuit","Membership.mem","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":62,"value_refs":["And","Matroid","Matroid.Dep","Matroid.Indep","Matroid.IsCircuit","Matroid.isCircuit_iff_dep_forall_sdiff_singleton_indep","Membership.mem","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","Matroid","Matroid.Dep","Matroid.E","Matroid.Indep","Not","Set","Set.instLE"],"value_dag_size":43,"value_refs":["And","LE.le","Matroid","Matroid.Dep","Matroid.E","Matroid.Indep","Matroid.dep_iff","Not","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsCircuit.contract_isCircuit","reducibility":null,"statement_dag_size":56,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instSDiff","True"],"value_dag_size":57,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.disjoint_sdiff_left","Set.instBooleanAlgebra","Set.instSDiff","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Inter.inter","LE.le","Set","Set.instInter","Set.instLE"],"value_dag_size":42,"value_refs":["And","Inter.inter","LE.le","Set","Set.instInter","Set.instLE","Set.subset_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Inter.inter","LE.le","Set","Set.instInter","Set.instLE","True"],"value_dag_size":32,"value_refs":["Inter.inter","LE.le","Set","Set.instInter","Set.instLE","Set.inter_subset_right","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq.match_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq","reducibility":"abbrev","statement_dag_size":111,"type_refs":["And.intro","Inter.inter","Matroid","Matroid.closure","Matroid.contract","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":137,"value_refs":["And.casesOn","And.intro","Inter.inter","Matroid","Matroid.closure","Matroid.contract","Membership.mem","Set","Set.instInter","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq.match_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_closure_eq","reducibility":"abbrev","statement_dag_size":157,"type_refs":["And.intro","Inter.inter","Matroid","Matroid.closure","Membership.mem","Not","SDiff.sdiff","Set","Set.instInter","Set.instMembership","Set.instSDiff","Set.instUnion","Union.union"],"value_dag_size":232,"value_refs":["And.casesOn","And.intro","Inter.inter","Matroid","Matroid.closure","Membership.mem","Not","SDiff.sdiff","Set","Set.instInter","Set.instMembership","Set.instSDiff","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_contract._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_contract","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Matroid","Matroid.dual"],"value_dag_size":35,"value_refs":["Eq","Eq.symm","Matroid","Matroid.dual","Matroid.dual_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_delete_comm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_delete_comm","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff","Set.subset_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary._simp_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary._simp_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary._simp_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary._simp_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_finitary","reducibility":null,"statement_dag_size":64,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE"],"value_dag_size":67,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_iff","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isColoop_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isColoop_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsColoop","Matroid.coloops","Membership.mem","Set","Set.instMembership"],"value_dag_size":34,"value_refs":["Matroid","Matroid.IsColoop","Matroid.coloops","Matroid.isColoop_iff_mem_coloops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isLoop_iff_mem_closure._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isLoop_iff_mem_closure","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isNonloop_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_isNonloop_iff","reducibility":"abbrev","statement_dag_size":132,"type_refs":["And.intro","Matroid","Matroid.E","Matroid.closure","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":153,"value_refs":["And.casesOn","And.intro","Matroid","Matroid.E","Matroid.closure","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_loops_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_loops_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.IsLoop","Matroid.loops","Membership.mem","Set","Set.instMembership"],"value_dag_size":40,"value_refs":["Eq.symm","Matroid","Matroid.IsLoop","Matroid.isLoop_iff","Matroid.loops","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Contract","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_rankFinite.match_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.contract_rankFinite","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBase","Matroid.contract","Set"],"value_dag_size":89,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Matroid.contract","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_isBase_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_isBase_iff","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff","Set.subset_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","Exists","LE.le","Matroid","Matroid.E","Matroid.IsBase","Matroid.Spanning","Set","Set.instLE"],"value_dag_size":54,"value_refs":["And","Exists","LE.le","Matroid","Matroid.E","Matroid.IsBase","Matroid.Spanning","Matroid.spanning_iff_exists_isBase_subset'","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instLE","Set.instSDiff","Set.subset_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff.match_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":"abbrev","statement_dag_size":239,"type_refs":["And","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"],"value_dag_size":413,"value_refs":["And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","Exists","Exists.casesOn","Exists.intro","HeytingAlgebra.toOrderBot","LE.le","Matroid","Matroid.IsBase","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff.match_1_8","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.Coindep.delete_spanning_iff","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":158,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Delete","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.delete_finitary._proof_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Delete.0.Matroid.delete_finitary","reducibility":null,"statement_dag_size":22,"type_refs":["Matroid","Matroid.Finitary","Matroid.delete","Set"],"value_dag_size":32,"value_refs":["Matroid","Matroid.E","Matroid.Finitary","Matroid.restrict_finitary","SDiff.sdiff","Set","Set.instSDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Order","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Order.0.Matroid.IsMinor.exists_eq_contract_delete_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Order.0.Matroid.IsMinor.exists_eq_contract_delete_disjoint","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.delete","Set","Set.instInter"],"value_dag_size":49,"value_refs":["Eq","Inter.inter","Matroid","Matroid.E","Matroid.delete","Matroid.delete_eq_delete_iff","Set","Set.instInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Order","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Order.0.Matroid.isStrictMinor_iff_isMinor_ssubset.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Order.0.Matroid.isStrictMinor_iff_isMinor_ssubset","reducibility":"abbrev","statement_dag_size":140,"type_refs":["And","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","LT.lt","Matroid","Matroid.E","Matroid.IsMinor","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra"],"value_dag_size":156,"value_refs":["And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","LT.lt","Matroid","Matroid.E","Matroid.IsMinor","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","Matroid","Matroid.Dep","Matroid.E","Matroid.Indep","Not","Set","Set.instLE"],"value_dag_size":43,"value_refs":["And","LE.le","Matroid","Matroid.Dep","Matroid.E","Matroid.Indep","Matroid.dep_iff","Not","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","Insert.insert","LE.le","Membership.mem","Set","Set.instInsert","Set.instLE","Set.instMembership"],"value_dag_size":50,"value_refs":["And","Insert.insert","LE.le","Membership.mem","Set","Set.insert_subset_iff","Set.instInsert","Set.instLE","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment_finset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment_finset","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment_finset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Indep.augment_finset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Matroidᵣ.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.Matroidᵣ.ext","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Matroid","Matroid.Matroidᵣ","Matroid.Matroidᵣ.ofMatroid"],"value_dag_size":32,"value_refs":["Matroid","Matroid.Matroidᵣ","Matroid.Matroidᵣ.casesOn","Matroid.Matroidᵣ.ofMatroid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.Indep","Matroid.IsBase","Maximal","Set","Set.instLE"],"value_dag_size":34,"value_refs":["Matroid","Matroid.Indep","Matroid.IsBase","Matroid.isBase_iff_maximal_indep","Maximal","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff'","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":57,"value_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","maximal_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Matroid","Matroid.Indep","Matroid.IsBase","Maximal","Set","Set.instLE"],"value_dag_size":34,"value_refs":["Matroid","Matroid.Indep","Matroid.IsBase","Matroid.isBase_iff_maximal_indep","Maximal","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBase_restrict_iff","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":57,"value_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","maximal_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBasis'_restrict_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBasis'_restrict_iff","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":57,"value_refs":["And","Eq","LE.le","Maximal","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","maximal_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBasis'_restrict_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.isBasis'_restrict_iff","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Inter.inter","LE.le","Set","Set.instInter","Set.instLE"],"value_dag_size":42,"value_refs":["And","Inter.inter","LE.le","Set","Set.instInter","Set.instLE","Set.subset_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid._simp_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid._simp_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":51,"value_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid._simp_8","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_rankFinite.match_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_rankFinite","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBase","Matroid.restrict","Set"],"value_dag_size":89,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Matroid.restrict","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_restrict_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_restrict_eq","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Minor.Restrict","name":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_restrict_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrict_restrict_eq","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_cRank.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_cRank","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":155,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_cRk_of_subset.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_cRk_of_subset","reducibility":"abbrev","statement_dag_size":110,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBasis'","Set","Set.instLE"],"value_dag_size":167,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBasis'","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_isBase.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_isBase","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":155,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_isBasis'.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Indep.cardinalMk_le_isBasis'","reducibility":"abbrev","statement_dag_size":109,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBasis'","Set","Set.instLE"],"value_dag_size":166,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBasis'","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.cRank_le_cardinalMk.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.cRank_le_cardinalMk","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":158,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.isBase_of_le_cRank.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.isBase_of_le_cRank","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":158,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.isBase_of_le_cRank_of_finite.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.Spanning.isBase_of_le_cRank_of_finite","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"],"value_dag_size":158,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRank_eq_iSup_cardinalMk_indep.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRank_eq_iSup_cardinalMk_indep","reducibility":"abbrev","statement_dag_size":146,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.Indep","Matroid.IsBase","Set","Set.instLE","Subtype","Subtype.val"],"value_dag_size":207,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.Indep","Matroid.IsBase","Set","Set.instLE","Subtype","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRank_le_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRank_le_iff","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Matroid","Matroid.IsBase","Set","Subtype","Subtype.mk"],"value_dag_size":70,"value_refs":["Matroid","Matroid.IsBase","Set","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.mk"],"value_dag_size":39,"value_refs":["Subtype","Subtype.forall","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.restrict","Set"],"value_dag_size":36,"value_refs":["Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.isBase_restrict_iff'","Matroid.restrict","Set","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","LE.le","Matroid","Matroid.IsBasis'","Matroid.comap","Set","Set.InjOn","Set.image","Set.instLE"],"value_dag_size":70,"value_refs":["And","LE.le","Matroid","Matroid.IsBasis'","Matroid.comap","Matroid.comap_isBasis'_iff","Set","Set.InjOn","Set.image","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_comap_lift","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_cardinalMk.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_cardinalMk","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Matroid","Matroid.IsBase","Matroid.restrict","Set","Subtype","Subtype.mk"],"value_dag_size":89,"value_refs":["Matroid","Matroid.IsBase","Matroid.restrict","Set","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_iff","reducibility":null,"statement_dag_size":41,"type_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","Eq","LE.le","Matroid","Matroid.IsBase","Matroid.cRank","Set","Set.Elem"],"value_dag_size":44,"value_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","LE.le","Matroid","Matroid.IsBase","Matroid.cRank","Matroid.cRank_le_iff","Set","Set.Elem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_le_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.restrict","Set"],"value_dag_size":36,"value_refs":["Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.isBase_restrict_iff'","Matroid.restrict","Set","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_map_image_lift._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_map_image_lift","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.mk"],"value_dag_size":39,"value_refs":["Subtype","Subtype.forall","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_map_image_lift._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_map_image_lift","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.restrict","Set"],"value_dag_size":36,"value_refs":["Matroid","Matroid.IsBase","Matroid.IsBasis'","Matroid.isBase_restrict_iff'","Matroid.restrict","Set","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_mono._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_mono","reducibility":null,"statement_dag_size":46,"type_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","Eq","LE.le","Matroid","Matroid.IsBasis'","Matroid.cRk","Set","Set.Elem"],"value_dag_size":50,"value_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","LE.le","Matroid","Matroid.IsBasis'","Matroid.cRk","Matroid.cRk_le_iff","Set","Set.Elem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Inter.inter","LE.le","Matroid","Matroid.IsBasis'","Matroid.restrict","Set","Set.instInter","Set.instLE"],"value_dag_size":57,"value_refs":["And","Inter.inter","LE.le","Matroid","Matroid.IsBasis'","Matroid.isBasis'_restrict_iff","Matroid.restrict","Set","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","iff_self_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.cRk_restrict_subset","reducibility":null,"statement_dag_size":46,"type_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","Eq","LE.le","Matroid","Matroid.IsBasis'","Matroid.cRk","Set","Set.Elem"],"value_dag_size":50,"value_refs":["Cardinal","Cardinal.instLE","Cardinal.mk","LE.le","Matroid","Matroid.IsBasis'","Matroid.cRk","Matroid.cRk_le_iff","Set","Set.Elem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary._simp_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder"],"value_dag_size":52,"value_refs":["And","LE.le","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","propext","sup_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary._simp_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary.match_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.invariantCardinalRank_of_finitary","reducibility":"abbrev","statement_dag_size":235,"type_refs":["And","And.intro","Exists","Exists.intro","Insert.insert","Inter.inter","Matroid","Matroid.Indep","Membership.mem","SDiff.sdiff","Set","Set.instInsert","Set.instInter","Set.instMembership","Set.instSDiff","Set.instUnion","Union.union"],"value_dag_size":324,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Insert.insert","Inter.inter","Matroid","Matroid.Indep","Membership.mem","SDiff.sdiff","Set","Set.instInsert","Set.instInter","Set.instMembership","Set.instSDiff","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Finite","Set","Set.Elem","Set.Finite"],"value_dag_size":28,"value_refs":["Eq.symm","Finite","Set","Set.Elem","Set.Finite","Set.finite_coe_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0","reducibility":null,"statement_dag_size":26,"type_refs":["Cardinal","Cardinal.aleph0","Cardinal.mk","Cardinal.partialOrder","Eq","Finite","LT.lt","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":33,"value_refs":["Cardinal","Cardinal.aleph0","Cardinal.lt_aleph0_iff_finite","Cardinal.mk","Cardinal.partialOrder","Eq.symm","Finite","LT.lt","PartialOrder.toPreorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0","reducibility":"abbrev","statement_dag_size":66,"type_refs":["And","And.intro","Exists.intro","Matroid","Matroid.IsBase","Matroid.RankFinite","Matroid.RankFinite.mk","Set","Set.Finite"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Matroid.RankFinite","Matroid.RankFinite.casesOn","Matroid.RankFinite.mk","Set","Set.Finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Cardinal","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0.match_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Cardinal.0.Matroid.rankFinite_iff_cRank_lt_aleph0","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBase","Set"],"value_dag_size":70,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBase","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRank_lt_top_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRank_lt_top_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank._simp_1_8","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_dual_add_eRank","reducibility":null,"statement_dag_size":64,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE"],"value_dag_size":67,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_iff","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_eq_one_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_eq_one_iff","reducibility":"abbrev","statement_dag_size":190,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsNonloop","Matroid.closure","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":343,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsNonloop","Matroid.closure","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_le_one_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_le_one_iff","reducibility":"abbrev","statement_dag_size":171,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.E","Matroid.closure","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":248,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.E","Matroid.closure","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_loops._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eRk_loops","reducibility":null,"statement_dag_size":63,"type_refs":["CommSemiring.toSemiring","ENat","Eq","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.eRk","Matroid.loops","MulZeroClass.toZero","OfNat.ofNat","Set","Set.instInter","Set.instLE","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":67,"value_refs":["CommSemiring.toSemiring","ENat","Eq","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.eRk","Matroid.eRk_eq_zero_iff'","Matroid.loops","MulZeroClass.toZero","OfNat.ofNat","Set","Set.instInter","Set.instLE","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eq_eRk_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eq_eRk_iff","reducibility":"abbrev","statement_dag_size":103,"type_refs":["And","And.intro","ENat","Eq","Exists","Exists.intro","Matroid","Matroid.IsBasis","Set","Set.encard"],"value_dag_size":165,"value_refs":["And","And.casesOn","And.intro","ENat","Eq","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis","Set","Set.encard"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eq_loopyOn_iff_eRank.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.eq_loopyOn_iff_eRank","reducibility":"abbrev","statement_dag_size":98,"type_refs":["And","And.intro","CommSemiring.toSemiring","ENat","Eq","Matroid","Matroid.E","Matroid.eRank","MulZeroClass.toZero","OfNat.ofNat","Set","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":115,"value_refs":["And","And.casesOn","And.intro","CommSemiring.toSemiring","ENat","Eq","Matroid","Matroid.E","Matroid.eRank","MulZeroClass.toZero","OfNat.ofNat","Set","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.exists_of_eRank_eq_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.exists_of_eRank_eq_zero","reducibility":null,"statement_dag_size":48,"type_refs":["CommSemiring.toSemiring","ENat","Eq","Matroid","Matroid.E","Matroid.eRank","Matroid.loopyOn","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":51,"value_refs":["CommSemiring.toSemiring","ENat","Eq","Matroid","Matroid.E","Matroid.eRank","Matroid.eRank_eq_zero_iff","Matroid.loopyOn","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.isBasis'_iff_indep_encard_eq_of_finite.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.isBasis'_iff_indep_encard_eq_of_finite","reducibility":"abbrev","statement_dag_size":121,"type_refs":["And","And.intro","ENat","Eq","LE.le","Matroid","Matroid.Indep","Matroid.eRk","Set","Set.encard","Set.instLE"],"value_dag_size":187,"value_refs":["And","And.casesOn","And.intro","ENat","Eq","LE.le","Matroid","Matroid.Indep","Matroid.eRk","Set","Set.encard","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.le_eRk_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.le_eRk_iff","reducibility":"abbrev","statement_dag_size":141,"type_refs":["And","And.intro","ENat","Eq","Exists","Exists.intro","LE.le","Matroid","Matroid.Indep","Set","Set.encard","Set.instLE"],"value_dag_size":264,"value_refs":["And","And.casesOn","And.intro","ENat","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.Indep","Set","Set.encard","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.ENat","name":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.spanning_iff_eRk_le'.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.ENat.0.Matroid.spanning_iff_eRk_le'","reducibility":"abbrev","statement_dag_size":104,"type_refs":["And","And.intro","ENat","LE.le","Matroid","Matroid.E","Matroid.eRank","Matroid.eRk","Set","Set.instLE","instLEENat"],"value_dag_size":124,"value_refs":["And","And.casesOn","And.intro","ENat","LE.le","Matroid","Matroid.E","Matroid.eRank","Matroid.eRk","Set","Set.instLE","instLEENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.IsRkFinite.closure.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.IsRkFinite.closure","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set"],"value_dag_size":78,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.IsRkFinite.exists_finset_isBasis'.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.IsRkFinite.exists_finset_isBasis'","reducibility":"abbrev","statement_dag_size":88,"type_refs":["And","And.intro","Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set","Set.Finite"],"value_dag_size":142,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set","Set.Finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_iff","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","Exists","Matroid","Matroid.IsBasis'","Matroid.IsRkFinite","Set","Set.Finite"],"value_dag_size":40,"value_refs":["And","Exists","Matroid","Matroid.IsBasis'","Matroid.IsRkFinite","Matroid.isRkFinite_iff_exists_isBasis'","Set","Set.Finite","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_iff_exists_isBasis'.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_iff_exists_isBasis'","reducibility":"abbrev","statement_dag_size":89,"type_refs":["And","And.intro","Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set","Set.Finite"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set","Set.Finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_inter_ground_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_inter_ground_iff","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set"],"value_dag_size":78,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_of_finite.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_of_finite","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set"],"value_dag_size":78,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Rank.Finite","name":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_set.match_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_set","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Exists","Exists.intro","Matroid","Matroid.IsBasis'","Set"],"value_dag_size":78,"value_refs":["Exists","Exists.casesOn","Exists.intro","Matroid","Matroid.IsBasis'","Set"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1","reducibility":null,"statement_dag_size":69,"type_refs":["Bool","Bool.false","Bool.true","Eq","Equiv.sumEquivSigmaBool.match_1","Sigma","Sigma.mk","cond"],"value_dag_size":67,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Equiv.sumEquivSigmaBool.match_1","Sigma","Sigma.mk","cond"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1","reducibility":null,"statement_dag_size":68,"type_refs":["Bool","Bool.false","Bool.true","Eq","Equiv.sumEquivSigmaBool.match_1","Sigma","Sigma.mk","cond"],"value_dag_size":66,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Equiv.sumEquivSigmaBool.match_1","Sigma","Sigma.mk","cond"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Equiv.sumEquivSigmaBool.match_1","reducibility":"abbrev","statement_dag_size":57,"type_refs":["Bool","Bool.false","Bool.true","Sigma","Sigma.mk","cond"],"value_dag_size":1,"value_refs":["Equiv.sumEquivSigmaBool.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_comm.match_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_comm","reducibility":"abbrev","statement_dag_size":168,"type_refs":["And","And.intro","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instInter","Set.instLE","Set.instUnion","Union.union"],"value_dag_size":249,"value_refs":["And","And.casesOn","And.intro","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instInter","Set.instLE","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_comm.match_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_comm","reducibility":"abbrev","statement_dag_size":168,"type_refs":["And","And.intro","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instInter","Set.instLE","Set.instUnion","Union.union"],"value_dag_size":249,"value_refs":["And","And.casesOn","And.intro","Inter.inter","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instInter","Set.instLE","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_indep_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_indep_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_isBase_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_isBase_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_isBasis_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.disjointSum_isBasis_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_10","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":52,"value_refs":["And","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_11","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.univ","True"],"value_dag_size":23,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_univ","Set.univ","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_6","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Exists","Sigma","Sigma.mk"],"value_dag_size":49,"value_refs":["Exists","Sigma","Sigma.exists","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma._simp_8","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Sigma","Sigma.mk"],"value_dag_size":40,"value_refs":["Sigma","Sigma.forall","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma.match_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma","reducibility":"abbrev","statement_dag_size":187,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE","Set.preimage","Sigma","Sigma.mk"],"value_dag_size":267,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","Matroid","Matroid.IsBase","Set","Set.instLE","Set.preimage","Sigma","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE"],"value_dag_size":51,"value_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","maximal_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_10","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage"],"value_dag_size":53,"value_refs":["LE.le","Set","Set.image","Set.image_subset_iff","Set.instLE","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_11","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","LE.le","Set","Set.instLE","Set.instUnion","True","Union.union"],"value_dag_size":32,"value_refs":["LE.le","Set","Set.instLE","Set.instUnion","Set.subset_union_left","Union.union","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff._simp_1_9","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","LE.le","Set","Set.instLE","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["And","LE.le","Set","Set.instLE","Set.instUnion","Set.union_subset_iff","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff.match_1_12","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":"abbrev","statement_dag_size":86,"type_refs":["Membership.mem","Set","Set.instMembership","Sigma","Sigma.mk"],"value_dag_size":118,"value_refs":["Membership.mem","Set","Set.instMembership","Sigma","Sigma.casesOn","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":"abbrev","statement_dag_size":294,"type_refs":["And","And.intro","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE","Set.preimage","Set.sigma","Set.univ","Sigma","Sigma.mk"],"value_dag_size":403,"value_refs":["And","And.casesOn","And.intro","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE","Set.preimage","Set.sigma","Set.univ","Sigma","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff.match_1_7","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sigma_isBasis_iff","reducibility":"abbrev","statement_dag_size":380,"type_refs":["And","And.intro","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE","Set.preimage","Sigma","Sigma.mk"],"value_dag_size":538,"value_refs":["And","And.casesOn","And.intro","Eq","LE.le","Matroid","Matroid.E","Matroid.Indep","Set","Set.instLE","Set.preimage","Sigma","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_indep_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_indep_iff","reducibility":null,"statement_dag_size":65,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.Indep","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":70,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.Indep","Matroid.mapEquiv","Matroid.mapEquiv_indep_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_isBase_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_isBase_iff","reducibility":null,"statement_dag_size":65,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBase","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":70,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBase","Matroid.mapEquiv","Matroid.mapEquiv_isBase_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_isBasis_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_isBasis_iff","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBasis","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":77,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBasis","Matroid.mapEquiv","Matroid.mapEquiv_isBasis_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_ground._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_ground","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff","reducibility":null,"statement_dag_size":65,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.Indep","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":70,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.Indep","Matroid.mapEquiv","Matroid.mapEquiv_indep_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Bool","Bool.false","Bool.true","Eq"],"value_dag_size":21,"value_refs":["And","Bool","Bool.false","Bool.forall_bool","Bool.true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_indep_iff","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff","reducibility":null,"statement_dag_size":65,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBase","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":70,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBase","Matroid.mapEquiv","Matroid.mapEquiv_isBase_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Bool","Bool.false","Bool.true","Eq"],"value_dag_size":21,"value_refs":["And","Bool","Bool.false","Bool.forall_bool","Bool.true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBase_iff","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBasis_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBasis_iff","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBasis","Matroid.mapEquiv","Set","Set.image"],"value_dag_size":77,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Matroid","Matroid.IsBasis","Matroid.mapEquiv","Matroid.mapEquiv_isBasis_iff","Set","Set.image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Matroid.Sum","name":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBasis_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum_isBasis_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Bool","Bool.false","Bool.true","Eq"],"value_dag_size":21,"value_refs":["And","Bool","Bool.false","Bool.forall_bool","Bool.true","propext"]}
+{"definition_height":18,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon","reducibility":"regular","statement_dag_size":23,"type_refs":["CommRing","CommRing.toCommSemiring","Finset","MvPolynomial"],"value_dag_size":147,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.commRing","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","CommRing","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Finset","Finset.prod","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","HSub.hSub","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P.eq_1","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","reducibility":null,"statement_dag_size":157,"type_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.commRing","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","CommRing","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Eq","Finset","Finset.prod","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","HSub.hSub","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","SubNegMonoid.toSub","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","instHSub"],"value_dag_size":32,"value_refs":["CommRing","CommRing.toCommSemiring","Eq.refl","Finset","MvPolynomial","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.degree_P","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon","reducibility":null,"statement_dag_size":61,"type_refs":["CommRing","CommRing.toCommSemiring","Eq","Finset","Finset.card","Finsupp","Finsupp.single","MonomialOrder","MonomialOrder.degree","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nontrivial","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P"],"value_dag_size":743,"value_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidAlgebra.commRing","AddMonoidAlgebra.commSemiring","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","AddMonoidWithOne.toOne","CommRing","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toCommMonoid","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DistribSMul.toSMulZeroClass","Eq","Eq.mpr","Eq.trans","Finset","Finset.card","Finset.instSetLike","Finset.prod","Finset.sum","Finset.sum_congr","Finset.sum_const","Finsupp","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.instZero","Finsupp.single","Finsupp.smulZeroClass","Finsupp.smul_single","HSMul.hSMul","HSub.hSub","IsRegular","Membership.mem","MonomialOrder","MonomialOrder.degree","MonomialOrder.degree_X_sub_C","MonomialOrder.degree_prod_of_regular","MonomialOrder.leadingCoeff","MonomialOrder.monic_X_sub_C","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MvPolynomial","MvPolynomial.C","MvPolynomial.X","NSMul.toSMul","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulOneClass","Nat.instMulZeroClass","Nat.instNonUnitalNonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Nontrivial","OfNat.ofNat","One.toOfNat1","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","SMulZeroClass.toSMul","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","True","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","congrArg","congrFun'","eq_self","id","instDistribOfSemiring","instDistribSMul","instHSMul","instHSub","instMulZeroOneClassOfSemiring","instOfNatNat","isRegular_one","mul_one","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.monic_P","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon","reducibility":null,"statement_dag_size":35,"type_refs":["CommRing","CommRing.toCommSemiring","Finset","MonomialOrder","MonomialOrder.Monic","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P"],"value_dag_size":157,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","CommRing","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","HSub.hSub","Membership.mem","MonomialOrder","MonomialOrder.Monic.prod","MonomialOrder.monic_X_sub_C","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon","reducibility":null,"statement_dag_size":89,"type_refs":["And","CommRing","CommRing.toCommSemiring","Eq","Exists","Finset","Finset.card","Finset.instSetLike","Finsupp","Finsupp.single","LE.le","Membership.mem","MulZeroClass.toZero","MvPolynomial.support","Nat","Nat.instMulZeroClass","SetLike.instMembership","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","instLENat"],"value_dag_size":2190,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddMonoid.toAddZeroClass","AddMonoidAlgebra.addCommGroup","AddMonoidAlgebra.algebra","AddMonoidAlgebra.commRing","AddMonoidAlgebra.nonAssocSemiring","AddMonoidAlgebra.ring","AddMonoidAlgebra.semiring","AddZero.toZero","AddZeroClass.toAddZero","AlgHom","AlgHom.algHomClass","AlgHom.funLike","AlgHom.instNonUnitalAlgHomClassOfAlgHomClass","AlgHomClass.toRingHomClass","Algebra.id","Algebra.toModule","And","And.casesOn","And.intro","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.propDecidable","CommRing","CommRing.toCommMonoid","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","CompleteBooleanAlgebra.toCompleteLattice","DFunLike.coe","DistribLattice.toLattice","DistribMulActionSemiHomClass.toAddMonoidHomClass","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","EquivLike.toFunLike","Exists","Exists.casesOn","Exists.intro","False","Finite.of_fintype","Finite.to_wellFoundedGT","Finset","Finset.card","Finset.image","Finset.instSetLike","Finset.prod","Finset.prod_congr","Finsupp","Finsupp.ext","Finsupp.instAdd","Finsupp.instAddCommMonoid","Finsupp.instAddMonoid","Finsupp.instAddZeroClass","Finsupp.instDecidableEq","Finsupp.instFunLike","Finsupp.mapDomain","Finsupp.mapDomain_apply","Finsupp.mapDomain_of_notMem_range","Finsupp.single","Finsupp.single_eq_of_ne","Finsupp.single_eq_same","Function.injective_of_subsingleton","HSub.hSub","Inhabited.default","IsWellOrder.toIsWellFounded","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Membership.mem","Module.toDistribMulAction","Monoid.toMulOneClass","MonoidHom","MonoidHom.id","MonoidHom.instFunLike","MonoidWithZeroHomClass.toMonoidHomClass","MonomialOrder.addCommMonoidSyn","MonomialOrder.degree","MonomialOrder.le_degree","MonomialOrder.lex","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulOneClass.toMulOne","MulZeroClass.toZero","MvPolynomial","MvPolynomial.C","MvPolynomial.X","MvPolynomial.algHom_C","MvPolynomial.coeff","MvPolynomial.mem_support_iff","MvPolynomial.rename","MvPolynomial.rename_X","MvPolynomial.support","MvPolynomial.support_rename_of_injective","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Ne","NonAssocSemiring.toMulZeroOneClass","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass","NonUnitalNonAssocSemiring.toAddCommMonoid","Nontrivial","Not","OfNat.ofNat","PUnit.fintype","PUnit.instCompleteBooleanAlgebra","PUnit.instLinearOrder","PUnit.instUnique","PUnit.unit","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","RingHom","RingHom.instFunLike","RingHomClass.toMonoidWithZeroHomClass","SemilatticeInf.toPartialOrder","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff._simp_1","Set.range","Set.range_const","SetLike.instMembership","Singleton.singleton","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","True","Unique.fintype","Unique.instInhabited","Unit","Unit.unit","Zero.toOfNat0","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.P","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.degree_P","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_2","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_3","_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_4","congr","congrArg","congrFun'","dite","eq_false","eq_self","funext","ge_iff_le._simp_1","id","instDecidableEqNat","instDistribLatticeOfLinearOrder","instHSub","instInhabitedPUnit","instLENat","instMulZeroClassOfSemiring","instNonemptyOfInhabited","instSubsingletonPUnit","isWellOrder_gt","map_prod","map_sub","nontrivial_of_ne","not_false_eq_true","of_eq_true","outParam","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support","reducibility":null,"statement_dag_size":81,"type_refs":["CommSemiring","CommSemiring.toSemiring","Eq","Finset","Finset.instSetLike","Finsupp","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.support","Nat","Nat.instMulZeroClass","Ne","OfNat.ofNat","SetLike.instMembership","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dag_size":86,"value_refs":["CommSemiring","CommSemiring.toSemiring","Finset","Finset.instSetLike","Finsupp","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.mem_support_iff","MvPolynomial.support","Nat","Nat.instMulZeroClass","Ne","OfNat.ofNat","SetLike.instMembership","Zero.toOfNat0","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support","reducibility":null,"statement_dag_size":263,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","Eq","EquivLike.toFunLike","Finite.of_fintype","Finite.to_wellFoundedGT","Finsupp","Finsupp.instAdd","Finsupp.instFunLike","Inhabited.default","IsWellOrder.toIsWellFounded","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toPartialOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Unique","Unique.fintype","Unique.instInhabited","instDistribLatticeOfLinearOrder","instLENat","isWellOrder_gt"],"value_dag_size":268,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","EquivLike.toFunLike","Finite.of_fintype","Finite.to_wellFoundedGT","Finsupp","Finsupp.instAdd","Finsupp.instFunLike","Inhabited.default","IsWellOrder.toIsWellFounded","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toPartialOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.lex_le_iff_of_unique","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Unique","Unique.fintype","Unique.instInhabited","instDistribLatticeOfLinearOrder","instLENat","isWellOrder_gt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.Alon.of_mem_P_support","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","IsRegular","MulOne.toMul","MulOne.toOne","MulOneClass","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","True"],"value_dag_size":34,"value_refs":["IsRegular","MulOne.toMul","MulOne.toOne","MulOneClass","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","eq_true","isRegular_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero","reducibility":null,"statement_dag_size":73,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd"],"value_dag_size":78,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.HasAntidiagonal.mem_antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","NoZeroDivisors","OfNat.ofNat","Or","Zero.toOfNat0","instHMul"],"value_dag_size":66,"value_refs":["Eq","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","NoZeroDivisors","OfNat.ofNat","Or","Zero.toOfNat0","instHMul","mul_eq_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","Not","Or"],"value_dag_size":19,"value_refs":["Classical.or_iff_not_imp_right","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","IsUnit","Monoid","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","True"],"value_dag_size":34,"value_refs":["IsUnit","Monoid","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","eq_true","isUnit_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset","reducibility":null,"statement_dag_size":86,"type_refs":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","CommSemiring","CommSemiring.toSemiring","DFunLike.coe","Eq","Finsupp","Finsupp.instAddZeroClass","Finsupp.instZero","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.constantCoeff","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0"],"value_dag_size":91,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidAlgebra.nonAssocSemiring","CommSemiring","CommSemiring.toSemiring","DFunLike.coe","Eq.symm","Finsupp","Finsupp.instAddZeroClass","Finsupp.instZero","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.constantCoeff","MvPolynomial.constantCoeff_eq","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","RingHom","RingHom.instFunLike","Semiring.toNonAssocSemiring","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset","reducibility":null,"statement_dag_size":28,"type_refs":["And","Eq","Option","Option.none","Option.some"],"value_dag_size":31,"value_refs":["And","Option","Option.forall","Option.none","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Nullstellensatz","name":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Nullstellensatz.0.MvPolynomial.eq_zero_of_eval_zero_at_prod_finset","reducibility":null,"statement_dag_size":81,"type_refs":["CommSemiring","CommSemiring.toSemiring","Eq","Finset","Finset.instSetLike","Finsupp","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.support","Nat","Nat.instMulZeroClass","Ne","OfNat.ofNat","SetLike.instMembership","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dag_size":86,"value_refs":["CommSemiring","CommSemiring.toSemiring","Finset","Finset.instSetLike","Finsupp","Membership.mem","MulZeroClass.toZero","MvPolynomial","MvPolynomial.coeff","MvPolynomial.mem_support_iff","MvPolynomial.support","Nat","Nat.instMulZeroClass","Ne","OfNat.ofNat","SetLike.instMembership","Zero.toOfNat0","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Optimization.ValuedCSP","name":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Optimization.ValuedCSP","name":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutPropertyAt.rows_lt_aux._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutPropertyAt.rows_lt_aux","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Fin","List","List.ofFn","Nat"],"value_dag_size":47,"value_refs":["Eq","Eq.symm","Fin","List","List.ofFn","List.ofFn_inj","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Optimization.ValuedCSP","name":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutPropertyAt.rows_lt_aux._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Optimization.ValuedCSP.0.Function.HasMaxCutPropertyAt.rows_lt_aux","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","List.cons","True"],"value_dag_size":31,"value_refs":["List","List.Perm","List.Perm.swap","List.cons","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Finset.exists_mem_exists_mem_inf'_card_lt._proof_1_2","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Finset.exists_mem_exists_mem_inf'_card_lt","reducibility":null,"statement_dag_size":230,"type_refs":["And","DecidableEq","DistribLattice.toLattice","Finset","Finset.Nonempty","Finset.biUnion","Finset.card","Finset.decidableMem","Finset.filter","Finset.inf'","Finset.instSetLike","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.instLinearOrder","Nat.instPreorder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instDecidableAnd","instDistribLatticeNat"],"value_dag_size":845,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.biUnion","Finset.card","Finset.decidableMem","Finset.filter","Finset.inf'","Finset.instSetLike","Finset.mem_biUnion","Finset.univ","Fintype","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instLinearOrder","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","eagerReduce","eq_true","id","instAddNat","instDecidableAnd","instDistribLatticeNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Finset.exists_mem_exists_mem_inf'_card_lt._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Finset.exists_mem_exists_mem_inf'_card_lt","reducibility":null,"statement_dag_size":51,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toNSMul","Eq","Finset","Finset.card","Finset.sum","HSMul.hSMul","NSMul.toSMul","Nat","instHSMul"],"value_dag_size":58,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toNSMul","Eq.symm","Finset","Finset.card","Finset.sum","Finset.sum_const","HSMul.hSMul","NSMul.toSMul","Nat","instHSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_card_fiber_le_of_card_le_nsmul.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_card_fiber_le_of_card_le_nsmul","reducibility":"abbrev","statement_dag_size":382,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":522,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_card_fiber_lt_of_card_lt_nsmul.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_card_fiber_lt_of_card_lt_nsmul","reducibility":"abbrev","statement_dag_size":382,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":522,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_le_card_fiber_of_nsmul_le_card.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_le_card_fiber_of_nsmul_le_card","reducibility":"abbrev","statement_dag_size":382,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":519,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_le_sum_fiber_of_nsmul_le_sum.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_le_sum_fiber_of_nsmul_le_sum","reducibility":"abbrev","statement_dag_size":336,"type_refs":["AddCommMonoid","And","And.intro","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.filter","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":464,"value_refs":["AddCommMonoid","And","And.casesOn","And.intro","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.filter","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_lt_card_fiber_of_nsmul_lt_card.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_lt_card_fiber_of_nsmul_lt_card","reducibility":"abbrev","statement_dag_size":382,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":519,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","CommSemiring","CommSemiring.toSemiring","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring.toNonAssocSemiring","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Pigeonhole","name":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_lt_sum_fiber_of_nsmul_lt_sum.match_1_1","namespace":"_private.Mathlib.Combinatorics.Pigeonhole.0.Fintype.exists_lt_sum_fiber_of_nsmul_lt_sum","reducibility":"abbrev","statement_dag_size":336,"type_refs":["AddCommMonoid","And","And.intro","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.filter","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":464,"value_refs":["AddCommMonoid","And","And.casesOn","And.intro","DecidableEq","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.filter","Finset.instSetLike","Finset.sum","Finset.univ","Fintype","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Arborescence","name":"_private.Mathlib.Combinatorics.Quiver.Arborescence.0.Quiver.geodesicArborescence._simp_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Arborescence.0.Quiver.geodesicArborescence","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Cast","name":"_private.Mathlib.Combinatorics.Quiver.Cast.0.Quiver.eq_nil_of_length_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Cast.0.Quiver.eq_nil_of_length_zero","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","False","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":21,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_ne_zero","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Covering","name":"_private.Mathlib.Combinatorics.Quiver.Covering.0.Prefunctor.pathStar_injective._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Covering.0.Prefunctor.pathStar_injective","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","HEq","Sigma","Sigma.mk"],"value_dag_size":56,"value_refs":["And","Eq","HEq","Sigma","Sigma.mk","Sigma.mk.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Covering","name":"_private.Mathlib.Combinatorics.Quiver.Covering.0.Prefunctor.pathStar_surjective._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Covering.0.Prefunctor.pathStar_surjective","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","HEq","Sigma","Sigma.mk"],"value_dag_size":56,"value_refs":["And","Eq","HEq","Sigma","Sigma.mk","Sigma.mk.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Prefunctor.mapPath_comp.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Prefunctor.mapPath_comp","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Prefunctor.mapPath_id.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Prefunctor.mapPath_id","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.comp_assoc.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.comp_assoc","reducibility":"abbrev","statement_dag_size":117,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil"],"value_dag_size":320,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.decidableEqBddPathsOfDecidableEq._proof_7","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.decidableEqBddPathsOfDecidableEq","reducibility":null,"statement_dag_size":42,"type_refs":["LE.le","Nat","Quiver","Quiver.Path","Quiver.Path.length","instLENat"],"value_dag_size":242,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.instSubsingletonBddPaths.match_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.instSubsingletonBddPaths","reducibility":"abbrev","statement_dag_size":307,"type_refs":["LE.le","Nat","OfNat.ofNat","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.BoundedPaths","Quiver.Path.cons","Quiver.Path.length","Quiver.Path.nil","instLENat","instOfNatNat"],"value_dag_size":860,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","LE.le","Nat","OfNat.ofNat","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.BoundedPaths","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.length","Quiver.Path.nil","eq_of_heq","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.instSubsingletonBddPaths.match_3","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.instSubsingletonBddPaths","reducibility":"abbrev","statement_dag_size":78,"type_refs":["LE.le","Nat","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.BoundedPaths","Quiver.Path.length","Subtype.mk","instLENat","instOfNatNat"],"value_dag_size":106,"value_refs":["LE.le","Nat","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.BoundedPaths","Quiver.Path.length","Subtype.casesOn","Subtype.mk","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.isChain_cons_toList_nonempty.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.isChain_cons_toList_nonempty","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.isChain_toList_nonempty.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.isChain_toList_nonempty","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":532,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.length.match_1","Quiver.Path.nil","Unit","Unit.unit"],"value_dag_size":76,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.length.match_1","Quiver.Path.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.length.match_1","Quiver.Path.nil","Unit"],"value_dag_size":97,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.length.match_1","Quiver.Path.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":1,"value_refs":["Quiver.Path.length.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_comp.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_comp","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_ne_zero_iff_eq_comp._proof_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_ne_zero_iff_eq_comp","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","Ne","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.length","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":834,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Quiver","Quiver.Path","Quiver.Path.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_ne_zero_iff_eq_comp._proof_1_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_ne_zero_iff_eq_comp","reducibility":null,"statement_dag_size":133,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","Quiver","Quiver.Hom","Quiver.Hom.toPath","Quiver.Path","Quiver.Path.comp","Quiver.Path.length","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Quiver","Quiver.Hom","Quiver.Hom.toPath","Quiver.Path","Quiver.Path.comp","Quiver.Path.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.nil_comp.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.nil_comp","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_comp.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_comp","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":269,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_injective._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_injective","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path","name":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_injective.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.toList_injective","reducibility":"abbrev","statement_dag_size":253,"type_refs":["Eq","List","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.toList"],"value_dag_size":1044,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.casesOn","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.toList","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Decomposition","name":"_private.Mathlib.Combinatorics.Quiver.Path.Decomposition.0.Quiver.Path.exists_mem_notMem_hom_path_path_of_notMem_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Decomposition.0.Quiver.Path.exists_mem_notMem_hom_path_path_of_notMem_mem","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Decomposition","name":"_private.Mathlib.Combinatorics.Quiver.Path.Decomposition.0.Quiver.Path.exists_mem_notMem_hom_path_path_of_notMem_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Decomposition.0.Quiver.Path.exists_mem_notMem_hom_path_path_of_notMem_mem","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.comp_eq_nil_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.comp_eq_nil_iff","reducibility":"abbrev","statement_dag_size":108,"type_refs":["And","And.intro","Eq","Nat","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.length","instOfNatNat"],"value_dag_size":126,"value_refs":["And","And.casesOn","And.intro","Eq","Nat","OfNat.ofNat","Quiver","Quiver.Path","Quiver.Path.length","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices._proof_1_3","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices","reducibility":null,"statement_dag_size":186,"type_refs":["And","Eq","Exists","List","List.instMembership","List.tail","Membership.mem","Ne","Not","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.comp","Quiver.Path.cons","Quiver.Path.end","Quiver.Path.vertices"],"value_dag_size":836,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.instMembership","List.isEmpty","List.mem_append","List.mem_cons","List.nil","List.not_mem_nil","List.tail","List.tail_append","List.tail_cons","Membership.mem","Ne","Not","Or","Or.casesOn","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.comp","Quiver.Path.cons","Quiver.Path.end","Quiver.Path.end_cons","Quiver.Path.vertices","Quiver.Path.vertices_cons","True","True.intro","congrArg","eq_false","eq_true","id","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.exists_eq_comp_and_notMem_tail_of_mem_vertices","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.mem_vertices_cons","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Vertices","name":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.vertices_ne_nil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.vertices_ne_nil","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":44,"value_refs":["Eq.symm","LT.lt","List","List.length","List.length_pos_iff_ne_nil","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Weight","name":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Weight","name":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1._arg_pusher","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1","reducibility":null,"statement_dag_size":203,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1"],"value_dag_size":858,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1","_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1.splitter","eq_of_heq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Weight","name":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1"],"value_dag_size":82,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Path.Weight","name":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1"],"value_dag_size":102,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.weight.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Path.Weight","name":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Quiver.Path.Weight.0.Quiver.Path.weight.match_1","reducibility":"abbrev","statement_dag_size":74,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil"],"value_dag_size":1,"value_refs":["Quiver.Path.weight.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Schreier","name":"_private.Mathlib.Combinatorics.Quiver.Schreier.0.Quiver.SchreierGraph.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Schreier.0.Quiver.SchreierGraph.ext","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Quiver.SchreierGraph","Quiver.SchreierGraph.ofVertex","SMul"],"value_dag_size":63,"value_refs":["Quiver.SchreierGraph","Quiver.SchreierGraph.casesOn","Quiver.SchreierGraph.ofVertex","SMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.SingleObj","name":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","Quiver.SingleObj.listToPath.match_1","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","Quiver.SingleObj.listToPath.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.SingleObj","name":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","Quiver.SingleObj.listToPath.match_1","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","Quiver.SingleObj.listToPath.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.SingleObj","name":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.listToPath.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["Quiver.SingleObj.listToPath.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.SingleObj","name":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.toPrefunctor_symm_comp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.toPrefunctor_symm_comp","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_eq","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Subquiver","name":"_private.Mathlib.Combinatorics.Quiver.Subquiver.0.Quiver.Total.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Subquiver.0.Quiver.Total.ext","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Quiver","Quiver.Hom","Quiver.Total","Quiver.Total.mk"],"value_dag_size":57,"value_refs":["Quiver","Quiver.Hom","Quiver.Total","Quiver.Total.casesOn","Quiver.Total.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.reverse.match_1","Unit","Unit.unit"],"value_dag_size":76,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.reverse.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.reverse.match_1","Unit"],"value_dag_size":97,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Quiver.Path.reverse.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Path.reverse.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Path","Quiver.Path.cons","Quiver.Path.nil","Unit"],"value_dag_size":1,"value_refs":["Quiver.Path.reverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Symmetrify","Quiver.Symmetrify.lift.match_1","Quiver.symmetrifyQuiver","Sum.inl","Sum.inr"],"value_dag_size":81,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Symmetrify","Quiver.Symmetrify.lift.match_1","Quiver.symmetrifyQuiver","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","Quiver","Quiver.Hom","Quiver.Symmetrify","Quiver.Symmetrify.lift.match_1","Quiver.symmetrifyQuiver","Sum.inl","Sum.inr"],"value_dag_size":79,"value_refs":["Eq.refl","Quiver","Quiver.Hom","Quiver.Symmetrify","Quiver.Symmetrify.lift.match_1","Quiver.symmetrifyQuiver","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Quiver.Symmetric","name":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Quiver.Symmetric.0.Quiver.Symmetrify.lift.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Quiver","Quiver.Hom","Quiver.Symmetrify","Quiver.symmetrifyQuiver","Sum.inl","Sum.inr"],"value_dag_size":1,"value_refs":["Quiver.Symmetrify.lift.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._proof_1_11","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":95,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Ne","OfNat.ofNat","Set","Set.add","Set.instMembership","Sum","Sum.inl","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":146,"value_refs":["Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Ne","OfNat.ofNat","Set","Set.add","Set.instMembership","Sum","Sum.inl","True","True.intro","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","congrArg","eq_false","eq_true","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._proof_1_12","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":108,"type_refs":["And","Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Membership.mem","Nat","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Preorder.toLT","Set","Set.instMembership","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":914,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.cast","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instMembership","Sum","Sum.inl","Sum.inr","True","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._proof_1_13","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":109,"type_refs":["And","Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Membership.mem","Nat","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Preorder.toLT","Set","Set.instMembership","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":981,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.cast","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instMembership","Sum","Sum.inl","Sum.inr","True","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._proof_1_14","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":199,"type_refs":["And","DecidablePred","Eq","Finset.Ioc","Finset.card","Finset.disjSum","Finset.filter","Finset.image","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","Ne","OfNat.ofNat","Preorder.toLE","Preorder.toLT","Set","Set.add","Set.instMembership","Sum","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1709,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.Ioc","Finset.card","Finset.card_image_iff","Finset.disjSum","Finset.filter","Finset.image","Finset.instSetLike","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.InjOn","Set.add","Set.instMembership","SetLike.coe","Sum","Sum.inr","True","True.intro","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._proof_1_6","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":141,"type_refs":["DecidablePred","Finset","Finset.Ioc","Finset.Ioo","Finset.disjSum","Finset.filter","Finset.image","Finset.instPartialOrder","HAdd.hAdd","HSub.hSub","LE.le","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","Sum","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","instAddNat","instDecidableEqNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":3780,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.Ioc","Finset.Ioo","Finset.disjSum","Finset.filter","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_Ioc","Finset.mem_Ioo","Finset.mem_disjSum","Finset.mem_filter","Finset.mem_image","Finset.subset_iff","HAdd.hAdd","HEq","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.decLe","Nat.instLocallyFiniteOrder","Nat.instPreorder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inl.inj","Sum.inr","Sum.inr.inj","True","True.intro","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.congr_eq_1","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.congr_eq_2","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.splitter","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","heq_eq_eq","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._simp_1_10","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Finset","Finset.disjSum","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sum","Sum.inr"],"value_dag_size":65,"value_refs":["Finset","Finset.disjSum","Finset.inr_mem_disjSum","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sum","Sum.inr","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Finset","Finset.disjSum","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sum","Sum.inl"],"value_dag_size":65,"value_refs":["Finset","Finset.disjSum","Finset.inl_mem_disjSum","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sum","Sum.inl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._simp_1_8","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity._simp_1_9","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Nat","Sum","Sum.inl","Sum.inr"],"value_dag_size":40,"value_refs":["Nat","Sum","Sum.casesOn","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.congr_eq_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HEq","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"],"value_dag_size":102,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","Nat","Sum","Sum.casesOn","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.congr_eq_2","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HEq","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"],"value_dag_size":102,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","Nat","Sum","Sum.casesOn","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"],"value_dag_size":36,"value_refs":["Eq.refl","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"],"value_dag_size":36,"value_refs":["Eq.refl","Nat","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1.splitter","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Nat","Sum","Sum.inl","Sum.inr"],"value_dag_size":1,"value_refs":["_private.Mathlib.Combinatorics.Schnirelmann.0.add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensity.match_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.le_schnirelmannDensity_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.le_schnirelmannDensity_iff","reducibility":"abbrev","statement_dag_size":158,"type_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"],"value_dag_size":189,"value_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.casesOn","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Exists","LE.le","Membership.mem","Not","Set","Set.instLE","Set.instMembership"],"value_dag_size":48,"value_refs":["And","Exists","LE.le","Membership.mem","Not","Set","Set.instLE","Set.instMembership","Set.not_subset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":83,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftStrictMono","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LT","LT.lt","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub"],"value_dag_size":89,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftStrictMono","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LT","LT.lt","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub","propext","sub_lt_self_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":86,"type_refs":["DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","GroupWithZero","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","Inv.inv","InvOneClass.toInv","LT.lt","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","PosMulReflectLT","Preorder.toLT","Zero.toOfNat0"],"value_dag_size":91,"value_refs":["DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","GroupWithZero","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","Inv.inv","InvOneClass.toInv","LT.lt","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","PosMulReflectLT","Preorder.toLT","Zero.toOfNat0","inv_pos","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":82,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","IsOrderedRing","LT.lt","MulZeroClass.toZero","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","Nontrivial","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLTNat","instMulZeroClassOfSemiring","instOfNatNat"],"value_dag_size":88,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","IsOrderedRing","LT.lt","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_pos","NonAssocSemiring.toAddCommMonoidWithOne","Nontrivial","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLTNat","instMulZeroClassOfSemiring","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff._simp_1_8","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff.match_1_9","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_eq_one_iff","reducibility":"abbrev","statement_dag_size":36,"type_refs":["LT.lt","Nat","OfNat.ofNat","Subtype","Subtype.mk","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["LT.lt","Nat","OfNat.ofNat","Subtype","Subtype.casesOn","Subtype.mk","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_finset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_finset","reducibility":null,"statement_dag_size":125,"type_refs":["And","DecidablePred","DivInvMonoid.toDiv","Eq","Exists","Finset.Ioc","Finset.card","Finset.filter","HAdd.hAdd","HDiv.hDiv","LE.le","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instNatCast","Real.instZero","Set","Set.instMembership","Zero.toOfNat0","instHAdd","instHDiv","instLTNat","instOfNatNat","schnirelmannDensity"],"value_dag_size":128,"value_refs":["And","DecidablePred","DivInvMonoid.toDiv","Exists","Finset.Ioc","Finset.card","Finset.filter","HAdd.hAdd","HDiv.hDiv","LE.le","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instNatCast","Real.instZero","Set","Set.instMembership","Zero.toOfNat0","instHAdd","instHDiv","instLTNat","instOfNatNat","propext","schnirelmannDensity","schnirelmannDensity_le_iff_forall"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_finset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_finset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_div.match_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_div","reducibility":"abbrev","statement_dag_size":158,"type_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"],"value_dag_size":189,"value_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.casesOn","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_iff_forall._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_iff_forall","reducibility":null,"statement_dag_size":97,"type_refs":["And","DecidablePred","DivInvMonoid.toDiv","Eq","Exists","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLT","Real.instNatCast","Set","Set.instMembership","instHDiv","instLTNat","instOfNatNat","schnirelmannDensity"],"value_dag_size":100,"value_refs":["And","DecidablePred","DivInvMonoid.toDiv","Exists","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLT","Real.instNatCast","Set","Set.instMembership","instHDiv","instLTNat","instOfNatNat","propext","schnirelmannDensity","schnirelmannDensity_lt_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_of_subset.match_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_le_of_subset","reducibility":"abbrev","statement_dag_size":158,"type_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"],"value_dag_size":189,"value_refs":["DecidablePred","DivInvMonoid.toDiv","Eq","Exists.casesOn","Exists.intro","Finset.Ioc","Finset.card","Finset.filter","HDiv.hDiv","LT.lt","Membership.mem","Nat","Nat.cast","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.instMembership","Set.range","Subtype","Subtype.val","instHDiv","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_10","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Icc","Finset.instSetLike","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_11","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":88,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HAdd.hAdd","LT.lt","OfNat.ofNat","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instHAdd"],"value_dag_size":94,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","HAdd.hAdd","LT.lt","OfNat.ofNat","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","add_pos_iff","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_12","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","LT.lt","NeZero","OfNat.ofNat","One","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","True","Zero","Zero.toOfNat0","ZeroLEOneClass"],"value_dag_size":73,"value_refs":["LT.lt","NeZero","OfNat.ofNat","One","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","ZeroLEOneClass","eq_true","zero_lt_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["Exists","Finset","Finset.card","Finset.card_le_one_iff_subset_singleton","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_8","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one._simp_1_9","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_mod_eq_one","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_modeq_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_modeq_one","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nat","Nat.ModEq","OfNat.ofNat","True","instOfNatNat"],"value_dag_size":22,"value_refs":["Nat","Nat.ModEq","Nat.modEq_one","OfNat.ofNat","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Schnirelmann","name":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_prime._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Schnirelmann.0.schnirelmannDensity_setOfPred_prime","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","False","Nat","Nat.Prime","OfNat.ofNat","instOfNatNat"],"value_dag_size":14,"value_refs":["Nat","Nat.Prime","Nat.not_prime_one","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum","reducibility":null,"statement_dag_size":91,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","Compl.compl","DecidableLE","Eq","Finset","Finset.compls","Finset.truncatedInf","Finset.truncatedSup","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"],"value_dag_size":98,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","Compl.compl","DecidableLE","Eq.symm","Finset","Finset.compl_truncatedSup","Finset.compls","Finset.truncatedInf","Finset.truncatedSup","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum","reducibility":null,"statement_dag_size":75,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Finset","Finset.sum","HAdd.hAdd","instHAdd"],"value_dag_size":83,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","Finset","Finset.sum","Finset.sum_add_distrib","HAdd.hAdd","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum","reducibility":null,"statement_dag_size":61,"type_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","instDistribOfSemiring","instHAdd","instHDiv"],"value_dag_size":68,"value_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","add_div","instDistribOfSemiring","instHAdd","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_union_add_infSum_sups._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_union_add_infSum_sups","reducibility":null,"statement_dag_size":61,"type_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","instDistribOfSemiring","instHAdd","instHDiv"],"value_dag_size":68,"value_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","add_div","instDistribOfSemiring","instHAdd","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_union_add_infSum_sups._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_union_add_infSum_sups","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_of_univ_notMem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_of_univ_notMem","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton","reducibility":null,"statement_dag_size":62,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":67,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","eq_sub_iff_add_eq","instHAdd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton","reducibility":null,"statement_dag_size":65,"type_refs":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":76,"value_refs":["AddCommGroup","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Eq.symm","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","eq_sub_iff_add_eq'","instHAdd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.sum","HSub.hSub","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHSub"],"value_dag_size":81,"value_refs":["Eq.symm","Finset","Finset.sum","Finset.sum_sub_distrib","HSub.hSub","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_singleton","reducibility":null,"statement_dag_size":64,"type_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","DivInvMonoid.toDiv","DivisionRing","DivisionRing.toDivInvMonoid","DivisionRing.toRing","Eq","HDiv.hDiv","HSub.hSub","Ring.toAddGroupWithOne","SubNegMonoid.toSub","instHDiv","instHSub"],"value_dag_size":71,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","DivInvMonoid.toDiv","DivisionRing","DivisionRing.toDivInvMonoid","DivisionRing.toRing","Eq.symm","HDiv.hDiv","HSub.hSub","Ring.toAddGroupWithOne","SubNegMonoid.toSub","instHDiv","instHSub","sub_div"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_union_add_supSum_infs._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_union_add_supSum_infs","reducibility":null,"statement_dag_size":61,"type_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","instDistribOfSemiring","instHAdd","instHDiv"],"value_dag_size":68,"value_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","add_div","instDistribOfSemiring","instHAdd","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_union_add_supSum_infs._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.supSum_union_add_supSum_infs","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.inf_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":87,"type_refs":["DecidableLE","Finset","Finset.Nonempty","Finset.filter","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instSetLike","upperClosure"],"value_dag_size":240,"value_refs":["And","And.intro","DecidableLE","Exists.intro","Finset","Finset.Nonempty","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff.mpr","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instSetLike","_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.inf_aux.match_1_1","upperClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.inf_aux.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.inf_aux","reducibility":"abbrev","statement_dag_size":179,"type_refs":["And","And.intro","Exists.intro","Finset","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instSetLike","upperClosure"],"value_dag_size":277,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instSetLike","upperClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.infs_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","DistribLattice","DistribLattice.toLattice","Finset","Finset.hasInfs","Finset.instSetLike","HasInfs.infs","Iff","Lattice.toSemilatticeInf","LowerSet","LowerSet.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.coe","SetLike.instMembership","lowerClosure"],"value_dag_size":238,"value_refs":["And","DecidableEq","DistribLattice","DistribLattice.toLattice","Eq","Eq.mpr","Finset","Finset.coe_infs","Finset.hasInfs","Finset.instSetLike","HasInfs.infs","Iff","Iff.rfl","Lattice.toSemilatticeInf","LowerSet","LowerSet.instMin","LowerSet.instSetLike","LowerSet.mem_inf_iff","Membership.mem","Min.min","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.hasInfs","SetLike.coe","SetLike.instMembership","congrArg","id","lowerClosure","lowerClosure_infs","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.lower_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Iff","LowerSet","LowerSet.instSetLike","Membership.mem","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.coe","SetLike.instMembership","Union.union","lowerClosure"],"value_dag_size":225,"value_refs":["DecidableEq","Eq","Eq.mpr","Finset","Finset.coe_union","Finset.instSetLike","Finset.instUnion","Iff","Iff.rfl","LowerSet","LowerSet.instMax","LowerSet.instSetLike","LowerSet.mem_sup_iff","Max.max","Membership.mem","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","Set","Set.instUnion","SetLike.coe","SetLike.instMembership","Union.union","congrArg","id","lowerClosure","lowerClosure_union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.map_truncatedInf._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.map_truncatedInf","reducibility":null,"statement_dag_size":58,"type_refs":["DFunLike.coe","Eq","LE","LE.le","OrderIso","instFunLikeOrderIso"],"value_dag_size":65,"value_refs":["DFunLike.coe","LE","LE.le","OrderIso","OrderIso.le_iff_le","instFunLikeOrderIso","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.map_truncatedSup._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.map_truncatedSup","reducibility":null,"statement_dag_size":58,"type_refs":["DFunLike.coe","Eq","LE","LE.le","OrderIso","instFunLikeOrderIso"],"value_dag_size":65,"value_refs":["DFunLike.coe","LE","LE.le","OrderIso","OrderIso.le_iff_le","instFunLikeOrderIso","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sup_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":85,"type_refs":["DecidableLE","Finset","Finset.Nonempty","Finset.filter","Finset.instSetLike","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.coe","SetLike.instMembership","lowerClosure"],"value_dag_size":233,"value_refs":["And","And.intro","DecidableLE","Exists.intro","Finset","Finset.Nonempty","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff.mpr","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sup_aux.match_1_1","lowerClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sup_aux.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sup_aux","reducibility":"abbrev","statement_dag_size":179,"type_refs":["And","And.intro","Exists.intro","Finset","Finset.instSetLike","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","lowerClosure"],"value_dag_size":274,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","lowerClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.sups_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":89,"type_refs":["And","DecidableEq","DistribLattice","DistribLattice.toLattice","Finset","Finset.hasSups","Finset.instSetLike","HasSups.sups","Iff","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instSetLike","upperClosure"],"value_dag_size":265,"value_refs":["And","DecidableEq","DistribLattice","DistribLattice.toLattice","Eq","Eq.mpr","Finset","Finset.coe_sups","Finset.hasSups","Finset.instSetLike","HasSups.sups","Iff","Iff.rfl","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Max.max","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","Set","Set.hasSups","SetLike.coe","SetLike.instMembership","UpperSet","UpperSet.instMax","UpperSet.instSetLike","UpperSet.mem_sup_iff","congrArg","id","propext","upperClosure","upperClosure_sups"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_of_isAntichain._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_of_isAntichain","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.inf'","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership"],"value_dag_size":84,"value_refs":["Finset","Finset.Nonempty","Finset.inf'","Finset.instSetLike","Finset.le_inf'_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_of_isAntichain._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_of_isAntichain","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_singleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_singleton","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","LE.le","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","UpperSet","UpperSet.Ici","UpperSet.instSetLike"],"value_dag_size":48,"value_refs":["LE.le","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","UpperSet","UpperSet.Ici","UpperSet.instSetLike","UpperSet.mem_Ici_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_sups._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_sups","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Eq","Finset","Finset.hasSups","Finset.image","Finset.instSProd","Function.uncurry","HasSups.sups","Max.max","Prod","SProd.sprod","SemilatticeSup","SemilatticeSup.toMax"],"value_dag_size":76,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.hasSups","Finset.image","Finset.image_sup_product","Finset.instSProd","Function.uncurry","HasSups.sups","Max.max","Prod","SProd.sprod","SemilatticeSup","SemilatticeSup.toMax"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Exists","LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","SetLike.instMembership","UpperSet","UpperSet.instSetLike","upperClosure"],"value_dag_size":68,"value_refs":["And","Exists","LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","SetLike.instMembership","UpperSet","UpperSet.instSetLike","mem_upperClosure","propext","upperClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedInf_union_left","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_infs._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_infs","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Eq","Finset","Finset.hasInfs","Finset.image","Finset.instSProd","Function.uncurry","HasInfs.infs","Min.min","Prod","SProd.sprod","SemilatticeInf","SemilatticeInf.toMin"],"value_dag_size":76,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.hasInfs","Finset.image","Finset.image_inf_product","Finset.instSProd","Function.uncurry","HasInfs.infs","Min.min","Prod","SProd.sprod","SemilatticeInf","SemilatticeInf.toMin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_of_isAntichain._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_of_isAntichain","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.sup'","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":84,"value_refs":["Finset","Finset.Nonempty","Finset.instSetLike","Finset.sup'","Finset.sup'_le_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_of_isAntichain._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_of_isAntichain","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Exists","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","SetLike.instMembership","lowerClosure"],"value_dag_size":68,"value_refs":["And","Exists","LE.le","LowerSet","LowerSet.instSetLike","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","SetLike.instMembership","lowerClosure","mem_lowerClosure","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.upper_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Iff","Membership.mem","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.coe","SetLike.instMembership","Union.union","UpperSet","UpperSet.instSetLike","upperClosure"],"value_dag_size":225,"value_refs":["DecidableEq","Eq","Eq.mpr","Finset","Finset.coe_union","Finset.instSetLike","Finset.instUnion","Iff","Iff.rfl","Membership.mem","Min.min","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instUnion","SetLike.coe","SetLike.instMembership","Union.union","UpperSet","UpperSet.instMin","UpperSet.instSetLike","UpperSet.mem_inf_iff","congrArg","id","propext","upperClosure","upperClosure_union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype","reducibility":null,"statement_dag_size":121,"type_refs":["Eq","Finset","Finset.card","Finset.fintype","Finset.range","Finset.sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Inv.inv","Nat","Nat.cast","Nat.choose","Nonempty","OfNat.ofNat","Rat","Rat.addCommMonoid","Rat.instAdd","Rat.instDiv","Rat.instInv","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.instSub","instHAdd","instHDiv","instHMul","instHSub"],"value_dag_size":2024,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommRing.toNonUnitalCommRing","Disjoint","Distrib.leftDistribClass","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","Eq","Eq.casesOn","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finset","Finset.card","Finset.card_powersetCard","Finset.disjiUnion","Finset.fintype","Finset.instInsert","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powersetCard_univ","Finset.mem_range_succ_iff","Finset.mul_sum","Finset.notMem_range_self","Finset.pairwise_disjoint_powersetCard","Finset.powerset","Finset.powersetCard","Finset.powerset_card_disjiUnion","Finset.powerset_univ","Finset.range","Finset.range_add_one","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.sum_disjiUnion","Finset.sum_insert","Finset.sum_range_reflect","Finset.univ","Fintype","Fintype.card","Fintype.card_ne_zero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mp","Iff.mpr","Insert.insert","Inv.inv","InvOneClass.toInv","IsCancelMulZero.toIsLeftCancelMulZero","IsDomain.toIsCancelMulZero","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","LE.le","LT.lt.ne'","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NSMul.toSMul","Nat","Nat.cast","Nat.cast_ne_zero","Nat.cast_sub","Nat.choose","Nat.choose_pos","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instIsOrderedAddMonoid","Nat.instLinearOrder","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.succ","Ne","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Nonempty","OfNat.ofNat","One.toOfNat1","Or","Or.inl","Pairwise.set_pairwise","Rat","Rat.addCommMonoid","Rat.addCommSemigroup","Rat.commRing","Rat.instAdd","Rat.instCharZero","Rat.instDiv","Rat.instDivisionRing","Rat.instField","Rat.instInv","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.instSub","Rat.isDomain","Rat.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.coe","SetLike.instMembership","SubNegMonoid.toSub","Zero.toOfNat0","_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_1","_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_2","_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_3","add_comm","add_tsub_cancel_right","congrArg","congrFun'","contravariant_lt_of_covariant_le","div_mul_cancel_right₀","eq_of_heq","id","instAddNat","instDecidableEqNat","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSMul","instHSub","instLENat","instMulZeroClassOfSemiring","instOfNatNat","instSubNat","mul_add","mul_comm","mul_div","mul_inv_cancel₀","nsmul_eq_mul","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card","reducibility":null,"statement_dag_size":55,"type_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul"],"value_dag_size":62,"value_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq.symm","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul","mul_div"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HMul.hMul","IsLeftCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul"],"value_dag_size":70,"value_refs":["Eq","HMul.hMul","IsLeftCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul","mul_eq_mul_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Fintype.sum_div_mul_card_choose_card","reducibility":null,"statement_dag_size":60,"type_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","Nat","Nat.cast","OfNat.ofNat","Zero.toOfNat0","instOfNatNat"],"value_dag_size":65,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","Nat","Nat.cast","Nat.cast_eq_zero","OfNat.ofNat","Zero.toOfNat0","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","Finset.range","Finset.sum","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.cast","Nat.choose","OfNat.ofNat","Rat","Rat.addCommMonoid","Rat.instDiv","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.instSub","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dag_size":2857,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","Decidable.decide","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionMonoid.toInvolutiveInv","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Field.toSemifield","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.sum","Finset.sum_congr","Finset.sum_range_sub'","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","GroupWithZero.toNontrivial","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Iff.mpr","Int","Int.instDecidableEq","Int.instNegInt","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","IsCancelMulZero.toIsLeftCancelMulZero","LE.le","LE.le.trans_lt","LT.lt","LT.lt.le","LT.lt.ne'","List.nil","Mathlib.Tactic.FieldSimp.NF.atom_eq_eval","Mathlib.Tactic.FieldSimp.NF.cons","Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div","Mathlib.Tactic.FieldSimp.NF.cons_ne_zero","Mathlib.Tactic.FieldSimp.NF.div_eq_eval","Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁","Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃","Mathlib.Tactic.FieldSimp.NF.eval","Mathlib.Tactic.FieldSimp.NF.eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval","Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg","Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons","Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero","Mathlib.Tactic.FieldSimp.NF.inv_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂","Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃","Mathlib.Tactic.FieldSimp.NF.one_eq_eval","Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst","Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq","Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul","Mathlib.Tactic.FieldSimp.subst_add","Mathlib.Tactic.FieldSimp.subst_sub","Mathlib.Tactic.FieldSimp.zpow'","Mathlib.Tactic.FieldSimp.zpow'_one","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast","Nat.cast_add","Nat.cast_add_one_ne_zero","Nat.cast_lt","Nat.cast_mul","Nat.cast_ne_zero","Nat.cast_one","Nat.cast_sub","Nat.cast_zero","Nat.choose","Nat.choose_pos","Nat.choose_succ_right_eq","Nat.choose_succ_self","Nat.choose_zero_right","Nat.instPreorder","Nat.le_of_lt_succ","Ne","NeZero.one","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","Rat","Rat.addCommGroup","Rat.addCommMonoid","Rat.addGroup","Rat.commGroupWithZero","Rat.instAdd","Rat.instAddLeftMono","Rat.instCharZero","Rat.instDiv","Rat.instDivisionRing","Rat.instField","Rat.instInv","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.instPartialOrder","Rat.instSub","Rat.instZeroLEOneClass","Rat.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","congr","congrArg","congrFun'","congr_arg","congr_arg₂","div_one","eq_mul_inv_iff_mul_eq₀","eq_self","id","inferInstance","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instIsCancelMulZero","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNat","instOfNatNat","instSubNat","inv_inv","inv_one","mul_inv_rev","mul_one","of_decide_eq_true","of_eq_true","one_mul","one_ne_zero","propext","rfl","sub_ne_zero_of_ne","sub_sub_sub_cancel_right","sub_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","two_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instOfNatNat","three_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","False","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq","Nat","NeZero","OfNat","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","four_ne_zero","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","False","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","instHMul"],"value_dag_size":76,"value_refs":["Eq","HMul.hMul","Mul","Ne","NoZeroDivisors","OfNat.ofNat","Zero","Zero.toOfNat0","eq_false","instHMul","mul_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","False","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","instHPow"],"value_dag_size":98,"value_refs":["Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","OfNat.ofNat","Zero.toOfNat0","eq_false","instHPow","pow_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":81,"type_refs":["DivInvMonoid.toZPow","Eq","False","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","instHPow"],"value_dag_size":84,"value_refs":["DivInvMonoid.toZPow","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HPow.hPow","Int","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","ZPow.toPow","Zero.toOfNat0","eq_false","instHPow","zpow_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.AhlswedeZhang","name":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.binomial_sum_eq","reducibility":null,"statement_dag_size":77,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","False","HAdd.hAdd","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHAdd"],"value_dag_size":79,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add_one_ne_zero","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","eq_false","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression","reducibility":null,"statement_dag_size":69,"type_refs":["And","DecidableEq","Down.compression","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":74,"value_refs":["And","DecidableEq","Down.compression","Down.mem_compression","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression","reducibility":null,"statement_dag_size":10,"type_refs":["And","Eq"],"value_dag_size":12,"value_refs":["And","and_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression_of_mem_compression._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.erase_mem_compression_of_mem_compression","reducibility":null,"statement_dag_size":69,"type_refs":["And","DecidableEq","Down.compression","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":74,"value_refs":["And","DecidableEq","Down.compression","Down.mem_compression","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":60,"value_refs":["Disjoint","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjUnion","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Down.mem_compression","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily.match_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.image_insert_memberSubfamily","reducibility":"abbrev","statement_dag_size":120,"type_refs":["And","And.intro","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.mem_memberSubfamily._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.mem_memberSubfamily","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.mem_memberSubfamily._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.mem_memberSubfamily","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberFamily_induction_on._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberFamily_induction_on","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberFamily_induction_on._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberFamily_induction_on","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_image_erase._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_image_erase","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_image_insert._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_image_insert","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_union_nonMemberSubfamily._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_union_nonMemberSubfamily","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_union_nonMemberSubfamily._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.memberSubfamily_union_nonMemberSubfamily","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.Down","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.nonMemberSubfamily_image_insert._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.Down.0.Finset.nonMemberSubfamily_image_insert","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.Set.Sized.uvCompression._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.Set.Sized.uvCompression","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.Set.Sized.uvCompression._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.Set.Sized.uvCompression","reducibility":null,"statement_dag_size":141,"type_refs":["And","DecidableEq","DecidableLE","DecidableRel","Disjoint","Eq","Exists","Finset","Finset.instSetLike","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","UV.compress","UV.compression"],"value_dag_size":150,"value_refs":["And","DecidableEq","DecidableLE","DecidableRel","Disjoint","Eq","Exists","Finset","Finset.instSetLike","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","UV.compress","UV.compression","UV.mem_compression","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV","reducibility":null,"statement_dag_size":114,"type_refs":["And","DecidableEq","EmptyCollection.emptyCollection","Eq","Exists","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.erase","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Membership.mem","SetLike.instMembership","UV.IsCompressed"],"value_dag_size":104,"value_refs":["And","DecidableEq","Exists","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.erase","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Membership.mem","SetLike.instMembership","UV.IsCompressed","_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.aux._proof_1_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.aux._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.aux","reducibility":null,"statement_dag_size":114,"type_refs":["And","DecidableEq","EmptyCollection.emptyCollection","Eq","Exists","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.erase","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Membership.mem","SetLike.instMembership","UV.IsCompressed"],"value_dag_size":558,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.erase","Finset.ext","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Finset.notMem_empty","Iff","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","UV.IsCompressed","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.compression_self._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.compression_self","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","DecidableLE","DecidableRel","Disjoint","Eq","Finset","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","UV.compression"],"value_dag_size":781,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidableLE","DecidableRel","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSetLike","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedCoheytingAlgebra.toLattice","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","UV.compress","UV.compress_self","UV.compression","UV.mem_compression","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.mem_compression","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.shadow_compression_subset_compression_shadow._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.shadow_compression_subset_compression_shadow","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSDiff","SDiff.sdiff"],"value_dag_size":45,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.erase","Finset.erase_sdiff_comm","Finset.instSDiff","SDiff.sdiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Compression.UV","name":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.shadow_compression_subset_compression_shadow._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Compression.UV.0.UV.shadow_compression_subset_compression_shadow","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":81,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_shadow_iff_insert_mem","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.card_le_card_diffs._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.card_le_card_diffs","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instHMul","instHPow","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instHMul","instHPow","instOfNatNat","sq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.four_functions_theorem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.four_functions_theorem","reducibility":null,"statement_dag_size":48,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton"],"value_dag_size":51,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","Finset.subset_singleton_iff","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.le_card_diffs_mul_card_diffs._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.le_card_diffs_mul_card_diffs","reducibility":null,"statement_dag_size":62,"type_refs":["DFunLike.coe","Eq","FunLike","Max","Max.max","SupHomClass"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq.symm","FunLike","Max","Max.max","SupHomClass","SupHomClass.map_sup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.le_card_diffs_mul_card_diffs._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.Finset.le_card_diffs_mul_card_diffs","reducibility":null,"statement_dag_size":62,"type_refs":["DFunLike.coe","Eq","FunLike","InfHomClass","Min","Min.min"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq.symm","FunLike","InfHomClass","InfHomClass.map_inf","Min","Min.min"]}
+{"definition_height":9,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0","reducibility":"regular","statement_dag_size":25,"type_refs":["CommSemiring","DecidableEq","Finset"],"value_dag_size":66,"value_refs":["CommSemiring","CommSemiring.toSemiring","DecidableEq","Eq","Finset","Finset.decidableEq","Finset.erase","Finset.filter","Finset.sum","Semiring.toAddCommMonoid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse.congr_simp","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse","reducibility":null,"statement_dag_size":89,"type_refs":["CommSemiring","DecidableEq","Eq","Finset","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse"],"value_dag_size":274,"value_refs":["CommSemiring","Decidable","DecidableEq","Eq","Eq.ndrec","Eq.rec","Eq.refl","Finset","Pi.instSubsingleton","Subsingleton.elim","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse","instSubsingletonDecidable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse.eq_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse","reducibility":null,"statement_dag_size":79,"type_refs":["CommSemiring","CommSemiring.toSemiring","DecidableEq","Eq","Finset","Finset.decidableEq","Finset.erase","Finset.filter","Finset.sum","Semiring.toAddCommMonoid","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse"],"value_dag_size":40,"value_refs":["CommSemiring","DecidableEq","Eq.refl","Finset","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.collapse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0","reducibility":null,"statement_dag_size":61,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Iff","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":40,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff._proof_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff","reducibility":null,"statement_dag_size":61,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Iff","Insert.insert","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":1761,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.filter_collapse_eq","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0","reducibility":null,"statement_dag_size":127,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.decidableEq","Finset.decidableMem","Finset.erase","Finset.filter","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Not","SetLike.instMembership","Singleton.singleton","ite"],"value_dag_size":1464,"value_refs":["Aesop.BuiltinRules.not_intro","And","And.casesOn","And.intro","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.decidableEq","Finset.decidableMem","Finset.erase","Finset.ext","Finset.filter","Finset.filter_congr","Finset.insert_eq_self._simp_1","Finset.instEmptyCollection","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter._simp_1","Finset.mem_insert._simp_1","Finset.mem_singleton._simp_1","Finset.notMem_empty._simp_1","Iff","Iff.intro","Iff.of_eq","Insert.insert","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.erase_eq_iff","and_iff_right_iff_imp._simp_1","and_self","congr","congrArg","congrFun'","dite","eq_false","eq_self","eq_true","id","if_neg","if_pos","iff_false","implies_congr","instDecidableOr","ite","not_and._simp_1","not_or._simp_1","not_true_eq_false","of_eq_true","or_true","propext","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":47,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.filter_eq_self","Finset.instSetLike","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":111,"type_refs":["DFunLike.coe","DecidableEq","Eq","Finset","Finset.hasSups","Finset.map","FunLike","Function.Embedding.mk","Function.Injective","HasSups.sups","SemilatticeSup","SemilatticeSup.toMax","SupHomClass"],"value_dag_size":126,"value_refs":["DFunLike.coe","DecidableEq","Eq.symm","Finset","Finset.hasSups","Finset.map","Finset.map_sups","FunLike","Function.Embedding.mk","Function.Injective","HasSups.sups","SemilatticeSup","SemilatticeSup.toMax","SupHomClass"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":111,"type_refs":["DFunLike.coe","DecidableEq","Eq","Finset","Finset.hasInfs","Finset.map","FunLike","Function.Embedding.mk","Function.Injective","HasInfs.infs","InfHomClass","SemilatticeInf","SemilatticeInf.toMin"],"value_dag_size":126,"value_refs":["DFunLike.coe","DecidableEq","Eq.symm","Finset","Finset.hasInfs","Finset.map","Finset.map_infs","FunLike","Function.Embedding.mk","Function.Injective","HasInfs.infs","InfHomClass","SemilatticeInf","SemilatticeInf.toMin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.instLattice","Finset.instUnion","Lattice.toSemilatticeSup","Max.max","SemilatticeSup.toMax","Union.union"],"value_dag_size":47,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.instLattice","Finset.instUnion","Finset.sup_eq_union","Lattice.toSemilatticeSup","Max.max","SemilatticeSup.toMax","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instLattice","Inter.inter","Lattice.toSemilatticeInf","Min.min","SemilatticeInf.toMin"],"value_dag_size":47,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.inf_eq_inter","Finset.instInter","Finset.instLattice","Inter.inter","Lattice.toSemilatticeInf","Min.min","SemilatticeInf.toMin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":62,"type_refs":["DFunLike.coe","Eq","FunLike","Max","Max.max","SupHomClass"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq.symm","FunLike","Max","Max.max","SupHomClass","SupHomClass.map_sup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem","reducibility":null,"statement_dag_size":62,"type_refs":["DFunLike.coe","Eq","FunLike","InfHomClass","Min","Min.min"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq.symm","FunLike","InfHomClass","InfHomClass.map_inf","Min","Min.min"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.four_functions_theorem_aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0","reducibility":null,"statement_dag_size":417,"type_refs":["CommSemiring","CommSemiring.toSemiring","DecidableEq","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ExistsAddOfLE","Finite","Finset","Finset.decidableEq","Finset.hasInfs","Finset.hasSups","Finset.instInter","Finset.instLattice","Finset.instUnion","Finset.sum","HMul.hMul","HasInfs.infs","HasSups.sups","Inter.inter","IsStrictOrderedRing","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","MulZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Pi.hasLe","Pi.instZero","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toAddCommMonoid","Union.union","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring"],"value_dag_size":697,"value_refs":["CommSemiring","CommSemiring.toSemiring","DecidableEq","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq.trans","ExistsAddOfLE","Finite","Finset","Finset.fintype","Finset.four_functions_theorem","Finset.instInter","Finset.instPartialOrder","Finset.instUnion","Finset.powerset","Finset.powerset_univ","Finset.subset_univ._simp_1","Finset.univ","Fintype","Fintype.ofFinite","HMul.hMul","Inter.inter","IsStrictOrderedRing","LE.le","Lattice.toSemilatticeInf","LinearOrder","MulZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Pi.hasLe","Pi.instZero","Preorder.toLE","SemilatticeInf.toPartialOrder","True","Union.union","Zero.toOfNat0","congrArg","eq_true","forall_congr","imp_self._simp_1","implies_congr","implies_true","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.holley._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.holley","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.ineq","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0","reducibility":null,"statement_dag_size":503,"type_refs":["CommSemiring","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ExistsAddOfLE","HAdd.hAdd","HMul.hMul","IsStrictOrderedRing","LE.le","Lattice.toSemilatticeInf","LinearOrder","MulZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instMulZeroClassOfSemiring"],"value_dag_size":3275,"value_refs":["AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","ExistsAddOfLE","HAdd.hAdd","HMul.hMul","HPow.hPow","IsCancelAdd.toIsLeftCancelAdd","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toIsCancelAdd","IsOrderedRing.toIsOrderedAddMonoid","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing","IsStrictOrderedRing.toIsOrderedCancelAddMonoid","IsStrictOrderedRing.toIsOrderedRing","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LE.le.antisymm","LE.le.eq_or_lt'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring.toAddCommMonoid","Semiring.toMonoid","Semiring.toNonAssocSemiring","Trans.trans","Zero.toOfNat0","add_le_add","add_le_add_three","add_nonneg","add_zero","congrArg","contravariant_lt_of_covariant_le","covariant_swap_add_of_covariant_add","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instMulZeroClassOfSemiring","instTransEq","instTransEq_1","instTransLE","le_of_mul_le_mul_right","le_refl","mul_add_mul_le_mul_add_mul","mul_le_mul","mul_nonneg","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powerset","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.FourFunctions","name":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.FourFunctions.0.sum_collapse","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":56,"value_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Finset.subset_insert_iff","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton"],"value_dag_size":65,"value_refs":["Eq","Eq.symm","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.subset_singleton_iff'","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'","reducibility":null,"statement_dag_size":48,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton"],"value_dag_size":51,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","Finset.subset_singleton_iff","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.le_card_inter_finset'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.memberSubfamily._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.memberSubfamily","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.memberSubfamily._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.memberSubfamily","reducibility":null,"statement_dag_size":66,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.memberSubfamily","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":71,"value_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_memberSubfamily","Finset.memberSubfamily","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.nonMemberSubfamily._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.nonMemberSubfamily","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.HarrisKleitman","name":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.nonMemberSubfamily._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.HarrisKleitman.0.IsLowerSet.nonMemberSubfamily","reducibility":null,"statement_dag_size":57,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSetLike","Finset.nonMemberSubfamily","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","DecidableEq","Finset","Finset.instSetLike","Finset.mem_nonMemberSubfamily","Finset.nonMemberSubfamily","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Intersecting","name":"_private.Mathlib.Combinatorics.SetFamily.Intersecting.0.Set.Intersecting.is_max_iff_card_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Intersecting.0.Set.Intersecting.is_max_iff_card_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Intersecting","name":"_private.Mathlib.Combinatorics.SetFamily.Intersecting.0.Set.Intersecting.is_max_iff_card_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Intersecting.0.Set.Intersecting.is_max_iff_card_eq","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Kleitman","name":"_private.Mathlib.Combinatorics.SetFamily.Kleitman.0.Finset.card_biUnion_le_of_intersecting._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Kleitman.0.Finset.card_biUnion_le_of_intersecting","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Finset","Finset.fintype","Fintype","Fintype.card","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","instHPow","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq.symm","Finset","Finset.fintype","Fintype","Fintype.card","Fintype.card_finset","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","instHPow","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.IsInitSeg.shadow._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.IsInitSeg.shadow","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":81,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_shadow_iff_insert_mem","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":100,"type_refs":["And","Colex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finset","Finset.Colex.initSeg","Finset.Colex.instLE","Finset.card","Finset.instSetLike","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","toColex"],"value_dag_size":106,"value_refs":["And","Colex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finset","Finset.Colex.initSeg","Finset.Colex.instLE","Finset.Colex.mem_initSeg","Finset.card","Finset.instSetLike","Fintype","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Nat","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","propext","toColex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","le_iff_eq_or_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":140,"type_refs":["And","Colex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Finset","Finset.Colex.instPartialOrder","Finset.filter","Finset.instSDiff","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toDecidableLT","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","toColex"],"value_dag_size":144,"value_refs":["And","Colex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Finset","Finset.Colex.instPartialOrder","Finset.Colex.lt_iff_exists_filter_lt","Finset.filter","Finset.instSDiff","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toDecidableLT","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","propext","toColex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":56,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":62,"value_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.filter_inj","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":45,"type_refs":["Colex","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","toColex"],"value_dag_size":48,"value_refs":["Colex","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","propext","toColex","toColex_inj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.Colex.shadow_initSeg","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":11,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV","reducibility":"regular","statement_dag_size":14,"type_refs":["Finset","LinearOrder"],"value_dag_size":83,"value_refs":["And","Disjoint","DistribLattice.toLattice","Eq","Exists","Finset","Finset.Nonempty","Finset.card","Finset.instOrderBot","Finset.instPartialOrder","Finset.max'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Nat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","reducibility":"regular","statement_dag_size":16,"type_refs":["DecidableRel","Finset","LinearOrder","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression"],"value_dag_size":19,"value_refs":["Finset","LinearOrder","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel._aux_1"]}
+{"definition_height":12,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel._aux_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel","reducibility":"regular","statement_dag_size":21,"type_refs":["Decidable","Finset","LinearOrder","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression"],"value_dag_size":126,"value_refs":["And","Disjoint","DistribLattice.toLattice","Eq","Exists","Finset","Finset.Nonempty","Finset.card","Finset.decidableDisjoint","Finset.decidableNonempty","Finset.instOrderBot","Finset.instPartialOrder","Finset.max'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toDecidableLT","Nat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","exists_prop_decidable","instDecidableAnd","instDecidableEqNat","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.compression_improved","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV","reducibility":null,"statement_dag_size":159,"type_refs":["Finset","Finset.card","Finset.decidableDisjoint","Finset.decidableEq","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.shadow","LE.le","LT.lt","LinearOrder","LinearOrder.toDecidableEq","Nat","UV.IsCompressed","UV.compression","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","instLENat","instLTNat"],"value_dag_size":1631,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Disjoint","Disjoint.mono","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.Nonempty.card_pos","Finset.Nonempty.mono","Finset.card","Finset.card_eq_zero","Finset.card_erase_lt_of_mem","Finset.card_erase_of_mem","Finset.card_pos","Finset.decidableDisjoint","Finset.decidableEq","Finset.erase","Finset.erase_subset","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.le_max'","Finset.max'","Finset.max'_mem","Finset.max'_subset","Finset.mem_erase","Finset.min'","Finset.min'_lt_max'_of_card","Finset.min'_lt_max'_of_card._proof_2","Finset.min'_mem","Finset.shadow","HSub.hSub","Iff.mp","Iff.mpr","LE.le","LE.le.trans_lt","LT.lt","LT.lt.ne'","LT.lt.trans_le","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","Membership.mem","Nat","Nat.instAddCommMonoid","Nat.instCanonicallyOrderedAdd","Nat.instLinearOrder","Nat.instOrderedSub","Nat.instPartialOrder","Nat.succ","Nat.succ_le_iff","Ne","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","UV.IsCompressed","UV.card_shadow_compression_le","UV.compression","UV.isCompressed_self","Zero.toOfNat0","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","congrArg","eq_or_lt_of_le","id","instDistribLatticeOfLinearOrder","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","propext","tsub_pos_iff_lt"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV","reducibility":"regular","statement_dag_size":9,"type_refs":["Fin","Finset","Nat"],"value_dag_size":57,"value_refs":["Fin","Fin.val","Finset","Finset.sum","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instAddCommMonoid","Nat.instMonoid","OfNat.ofNat","instHPow","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure.eq_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","Fin","Fin.val","Finset","Finset.sum","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instAddCommMonoid","Nat.instMonoid","OfNat.ofNat","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","instHPow","instOfNatNat"],"value_dag_size":16,"value_refs":["Eq.refl","Fin","Finset","Nat","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV","reducibility":null,"statement_dag_size":139,"type_refs":["Fin","Fin.instLinearOrder","Finset","Finset.Nonempty","Finset.decidableDisjoint","Finset.decidableEq","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.max'","LT.lt","Nat","Ne","UV.compression","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","instDecidableEqFin","instLTFin","instLTNat"],"value_dag_size":1732,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Colex","DFunLike.coe","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.instLinearOrder","Fin.val","Fin.val_injective","Fin.val_strictMono","Finset","Finset.Colex.instPartialOrder","Finset.Colex.toColex_image_lt_toColex_image","Finset.Nonempty","Finset.UV.toColex_compress_lt_toColex","Finset.decidableDisjoint","Finset.decidableEq","Finset.decidableMem","Finset.disjoint_filter_filter_not","Finset.filter","Finset.filter_image","Finset.filter_union_filter_not_eq","Finset.geomSum_lt_geomSum_iff_toColex_lt_toColex","Finset.image","Finset.image_empty","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Finset.instUnion","Finset.max'","Finset.not_nonempty_iff_eq_empty._simp_1","Finset.sum","Finset.sum_image","Finset.sum_lt_sum_of_nonempty","Finset.sum_union","Finset.union_empty","Function.Injective.injOn","HAdd.hAdd","HPow.hPow","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableEq","Mathlib.Tactic.Contrapose.contrapose₂","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAddCommMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instMonoid","Nat.instPartialOrder","Nat.instPreorder","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.coe","SetLike.instMembership","UV.compress","UV.compress_disjoint","UV.compress_injOn","UV.compression","UV.compression.eq_1","Union.union","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure.eq_1","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure._proof_1_1","add_lt_add_iff_left","congr","congrArg","contravariant_lt_of_covariant_le","id","implies_congr","instDecidableEqFin","instDecidableEqNat","instDecidableNot","instDistribLatticeOfLinearOrder","instHAdd","instHPow","instIsLeftCancelAddOfAddLeftReflectLE","instLTFin","instLTNat","instOfNatNat","le_rfl","propext","toColex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","Fin","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.decidableMem","Finset.filter","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Membership.mem","Nat","Not","SetLike.instMembership","UV.compress","instDecidableEqFin","instDecidableNot"],"value_dag_size":311,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Fin","Finset","Finset.decidableDisjoint","Finset.decidableEq","Finset.decidableMem","Finset.filter","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Nat","Not","SetLike.instMembership","True","True.intro","UV.compress","congrArg","eq_true","id","instDecidableEqFin","instDecidableNot"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.kruskal_katona_helper","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV","reducibility":null,"statement_dag_size":135,"type_refs":["And","Eq","Exists","Fin","Fin.instLinearOrder","Finset","Finset.card","Finset.decidableDisjoint","Finset.decidableEq","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Finset.shadow","LE.le","Nat","Set.Sized","SetLike.coe","UV.IsCompressed","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","instDecidableEqFin","instLENat"],"value_dag_size":53,"value_refs":["Fin","Finset","Finset.instSetLike","Nat","PSigma.mk","Set.Sized","SetLike.coe","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.kruskal_katona_helper._unary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.kruskal_katona_helper._unary","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.kruskal_katona_helper","reducibility":null,"statement_dag_size":135,"type_refs":["And","Eq","Exists","Fin","Fin.instLinearOrder","Finset","Finset.card","Finset.decidableDisjoint","Finset.decidableEq","Finset.instDecidableLE","Finset.instGeneralizedBooleanAlgebra","Finset.instSetLike","Finset.shadow","LE.le","Nat","PSigma","Set.Sized","SetLike.coe","UV.IsCompressed","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","instDecidableEqFin","instLENat"],"value_dag_size":3450,"value_refs":["And","And.casesOn","And.intro","And.left","And.right","Classical.propDecidable","Decidable.byContradiction","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Fin.instLinearOrder","Finset","Finset.Nonempty","Finset.card","Finset.decidableDisjoint","Finset.decidableEq","Finset.eq_empty_iff_forall_notMem","Finset.eq_empty_or_nonempty","Finset.exists_min_image","Finset.filter","Finset.fintype","Finset.instDecidableLE","Finset.instEmptyCollection","Finset.instGeneralizedBooleanAlgebra","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.max'","Finset.mem_filter","Finset.mem_univ","Finset.shadow","Finset.univ","Iff.mpr","InvImage","LE.le","LE.le.trans","LT.lt","LT.lt.not_ge","Lattice.toSemilatticeInf","Membership.mem","Nat","Nat.instLinearOrder","Nat.instPreorder","Not","Or","Or.casesOn","PSigma","PSigma.casesOn","PSigma.mk","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SemilatticeInf.toPartialOrder","Set.Sized","Set.Sized.uvCompression","SetLike.coe","SetLike.instMembership","UV.IsCompressed","UV.card_compression","UV.compression","WellFounded.Nat.fix","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.UsefulCompression.instDecidableRel","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.compression_improved","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure","_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.familyMeasure_compression_lt_familyMeasure","congrArg","id","instDecidableAnd","instDecidableEqFin","instDecidableNot","instDistribLatticeOfLinearOrder","instFintypeProd","instLENat","instLTNat","le_rfl","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.toColex_compress_lt_toColex._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.toColex_compress_lt_toColex","reducibility":null,"statement_dag_size":56,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":62,"value_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.filter_inj","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.toColex_compress_lt_toColex._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.UV.toColex_compress_lt_toColex","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado","reducibility":null,"statement_dag_size":68,"type_refs":["GT.gt","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1326,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.instDiv","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","GT.gt","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1792,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.cast","Nat.instDiv","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","HMul.hMul","HSub.hSub","Nat","OfNat.ofNat","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":212,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.shadow","LE.le","Membership.mem","Nat","Nat.iterate","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":99,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_shadow_iterate_iff_exists_sdiff","Finset.shadow","LE.le","Membership.mem","Nat","Nat.iterate","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.erdos_ko_rado","reducibility":null,"statement_dag_size":44,"type_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Eq","Finset","Finset.compls","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":48,"value_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Finset","Finset.compls","Finset.instSetLike","Finset.mem_compls","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.kruskal_katona_lovasz_form._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.kruskal_katona_lovasz_form","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","Finset.powersetCard","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":63,"value_refs":["And","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powersetCard","Finset.powersetCard","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.KruskalKatona","name":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.kruskal_katona_lovasz_form._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.KruskalKatona.0.Finset.kruskal_katona_lovasz_form","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.IsAntichain.disjoint_slice_shadow_falling._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.IsAntichain.disjoint_slice_shadow_falling","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.shadow","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_shadow_iff","Finset.shadow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.IsAntichain.disjoint_slice_shadow_falling._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.IsAntichain.disjoint_slice_shadow_falling","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.falling","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.falling","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_falling","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.le_card_falling_div_choose._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.le_card_falling_div_choose","reducibility":null,"statement_dag_size":95,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","LE.le","Nat","Nat.cast","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat"],"value_dag_size":103,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","LE.le","Nat","Nat.cast","Nat.cast_le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_div._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_div","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HMul.hMul","IsLeftCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul"],"value_dag_size":70,"value_refs":["Eq","HMul.hMul","IsLeftCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul","mul_eq_mul_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_mul._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_mul","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_mul._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.local_lubell_yamamoto_meshalkin_inequality_mul","reducibility":null,"statement_dag_size":57,"type_refs":["And","Decidable","Eq","Finset","Finset.bipartiteBelow","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":65,"value_refs":["And","Decidable","Finset","Finset.bipartiteBelow","Finset.instSetLike","Finset.mem_bipartiteBelow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Finset","Finset.card","Fintype","Fintype.card","LE.le","Nat","True","instLENat"],"value_dag_size":31,"value_refs":["Finset","Finset.card","Finset.card_le_univ","Fintype","Fintype.card","LE.le","Nat","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.mem_falling._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.mem_falling","reducibility":null,"statement_dag_size":81,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.falling","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1208,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.decidableEq","Finset.falling","Finset.falling.eq_1","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powersetCard","Finset.mem_sup","Finset.powersetCard","Finset.sup","Iff","LE.le","Lattice.toSemilatticeSup","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Nat","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Finset.slice","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":53,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Finset.mem_slice","Finset.slice","Membership.mem","Nat","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.shadow","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_shadow_iff","Finset.shadow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.LYM","name":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.LYM.0.Finset.slice_union_shadow_falling_succ","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.falling","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.falling","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_falling","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.exists_subset_of_mem_shadow.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.exists_subset_of_mem_shadow","reducibility":"abbrev","statement_dag_size":226,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":321,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.exists_subset_of_mem_upShadow.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.exists_subset_of_mem_upShadow","reducibility":"abbrev","statement_dag_size":230,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":405,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_sup","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.shadow","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_shadow_iff","Finset.shadow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":66,"type_refs":["And","CovBy","DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat"],"value_dag_size":77,"value_refs":["And","CovBy","DecidableEq","Eq","Eq.symm","Finset","Finset.card","Finset.covBy_iff_card_sdiff_eq_one","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":63,"type_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":67,"value_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.covBy_iff_exists_erase","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem","reducibility":null,"statement_dag_size":94,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.shadow","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instOfNatNat"],"value_dag_size":99,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_shadow_iff_exists_sdiff","Finset.shadow","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem","reducibility":null,"statement_dag_size":66,"type_refs":["And","CovBy","DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat"],"value_dag_size":77,"value_refs":["And","CovBy","DecidableEq","Eq","Eq.symm","Finset","Finset.card","Finset.covBy_iff_card_sdiff_eq_one","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iff_insert_mem","reducibility":null,"statement_dag_size":69,"type_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":73,"value_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.covBy_iff_exists_insert","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iterate_iff_exists_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":81,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_shadow_iff_insert_mem","Finset.shadow","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iterate_iff_exists_card._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":90,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":95,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.card_eq_succ","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_sup","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff","reducibility":null,"statement_dag_size":50,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Fintype","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":55,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.mem_compl","Fintype","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.upShadow","Fintype","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instOfNatNat"],"value_dag_size":105,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_upShadow_iff_exists_sdiff","Finset.upShadow","Fintype","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem","reducibility":null,"statement_dag_size":66,"type_refs":["And","CovBy","DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat"],"value_dag_size":77,"value_refs":["And","CovBy","DecidableEq","Eq","Eq.symm","Finset","Finset.card","Finset.covBy_iff_card_sdiff_eq_one","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_erase_mem","reducibility":null,"statement_dag_size":63,"type_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":67,"value_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.covBy_iff_exists_erase","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_mem_card_add._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_mem_card_add","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Finset","Finset.card","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":375,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":98,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_upShadow_iff","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":66,"type_refs":["And","CovBy","DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat"],"value_dag_size":77,"value_refs":["And","CovBy","DecidableEq","Eq","Eq.symm","Finset","Finset.card","Finset.covBy_iff_card_sdiff_eq_one","Finset.instPartialOrder","Finset.instSDiff","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iff_exists_sdiff","reducibility":null,"statement_dag_size":69,"type_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":73,"value_refs":["And","CovBy","DecidableEq","Eq","Exists","Finset","Finset.covBy_iff_exists_insert","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":76,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.upShadow","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":81,"value_refs":["And","DecidableEq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_upShadow_iff_erase_mem","Finset.upShadow","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":90,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":95,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.card_eq_succ","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":58,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":63,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_erase","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_upShadow_iterate_iff_exists_card","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSDiff","Insert.insert","SDiff.sdiff"],"value_dag_size":51,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.erase","Finset.instInsert","Finset.instSDiff","Finset.sdiff_insert","Insert.insert","SDiff.sdiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.shadow","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_shadow_iff","Finset.shadow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":98,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_upShadow_iff","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.shadow_compls","reducibility":null,"statement_dag_size":44,"type_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Eq","Finset","Finset.compls","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":48,"value_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Finset","Finset.compls","Finset.instSetLike","Finset.mem_compls","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls","reducibility":null,"statement_dag_size":82,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.shadow","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instSetLike","Finset.mem_shadow_iff","Finset.shadow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":98,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_upShadow_iff","Finset.upShadow","Fintype","Insert.insert","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls","reducibility":null,"statement_dag_size":44,"type_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Eq","Finset","Finset.compls","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":48,"value_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","Finset","Finset.compls","Finset.instSetLike","Finset.mem_compls","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Set.Sized.shadow_iterate._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Set.Sized.shadow_iterate","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shadow","name":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Set.Sized.shadow_iterate._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Set.Sized.shadow_iterate","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.shadow","LE.le","Membership.mem","Nat","Nat.iterate","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":99,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_shadow_iterate_iff_exists_sdiff","Finset.shadow","LE.le","Membership.mem","Nat","Nat.iterate","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.exists_superset.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.exists_superset","reducibility":"abbrev","statement_dag_size":164,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":241,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.mono_left.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.mono_left","reducibility":"abbrev","statement_dag_size":167,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":244,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.nonempty.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.Shatters.nonempty","reducibility":"abbrev","statement_dag_size":164,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":241,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.aux","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Finset","Finset.Shatters","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":175,"value_refs":["And","And.casesOn","DecidableEq","Exists","Exists.casesOn","Finset","Finset.Shatters","Finset.Shatters.exists_superset","Finset.instPartialOrder","Finset.instSetLike","Finset.notMem_mono","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_le_card_shatterer","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_shatterer_le_sum_vcDim._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_shatterer_le_sum_vcDim","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Finset.card","Finset.univ","Fintype","Fintype.card","Nat"],"value_dag_size":25,"value_refs":["Eq.symm","Finset.card","Finset.card_univ","Finset.univ","Fintype","Fintype.card","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_shatterer_le_sum_vcDim._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.card_shatterer_le_sum_vcDim","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Finset","Finset.card","Finset.powersetCard","Nat","Nat.choose"],"value_dag_size":32,"value_refs":["Eq.symm","Finset","Finset.card","Finset.card_powersetCard","Finset.powersetCard","Nat","Nat.choose"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powerset","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatterer_compress_subset_shatterer._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatterer_compress_subset_shatterer","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatters_empty.match_1_1","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatters_empty","reducibility":"abbrev","statement_dag_size":62,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":86,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SetFamily.Shatter","name":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatters_shatterer._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.shatters_shatterer","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.Shatters","Finset.instSetLike","Finset.shatterer","Membership.mem","SetLike.instMembership"],"value_dag_size":53,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.Shatters","Finset.instSetLike","Finset.mem_shatterer","Finset.shatterer","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_connected_induce_compl_singleton_of_finite_nontrivial.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_connected_induce_compl_singleton_of_finite_nontrivial","reducibility":"abbrev","statement_dag_size":36,"type_refs":["SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.mk"],"value_dag_size":53,"value_refs":["SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.casesOn","SimpleGraph.IsTree.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_isTree_le._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_isTree_le","reducibility":null,"statement_dag_size":89,"type_refs":["And","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Eq","Exists","HeytingAlgebra.toOrderBot","LE.le","Order.Frame.toHeytingAlgebra","OrderBot.toBot","SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.instLE"],"value_dag_size":475,"value_refs":["And","BooleanAlgebra.toBot","BooleanAlgebra.toTop","Bot.bot","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","HeytingAlgebra.toOrderBot","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Nonempty","Not","Or","Order.Frame.toHeytingAlgebra","OrderBot.toBot","Pi.instTopForall","Prop.instBooleanAlgebra","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Connected.casesOn","SimpleGraph.Connected.mk","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.mk","SimpleGraph.Preconnected","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.instLE","SimpleGraph.preconnected_iff_reachable_eq_top","Top.top","True","True.intro","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_isTree_le_of_le_of_isAcyclic._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.exists_isTree_le_of_le_of_isAcyclic","reducibility":null,"statement_dag_size":72,"type_refs":["And","Eq","Exists","LE.le","SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.Reachable","SimpleGraph.instLE"],"value_dag_size":534,"value_refs":["And","BooleanAlgebra.toTop","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Nonempty","Not","Or","Pi.instTopForall","Prop.instBooleanAlgebra","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Connected.casesOn","SimpleGraph.Connected.mk","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.mk","SimpleGraph.Preconnected","SimpleGraph.Reachable","SimpleGraph.instLE","SimpleGraph.preconnected_iff_reachable_eq_top","Top.top","True","True.intro","congrArg","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_one._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_one","reducibility":null,"statement_dag_size":266,"type_refs":["Classical.propDecidable","Compl.compl","Eq","HAdd.hAdd","LE.le","List.count","List.tail","Membership.mem","Nat","OfNat.ofNat","Set","Set.Elem","Set.instCompl","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","Singleton.singleton","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instOfNatNat"],"value_dag_size":642,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Classical.propDecidable","Compl.compl","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.count","List.tail","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set","Set.Elem","Set.instCompl","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","Singleton.singleton","Subtype.val","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.coloringTwoOfVerts._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.coloringTwoOfVerts","reducibility":null,"statement_dag_size":50,"type_refs":["HMod.hMod","LT.lt","Nat","Nat.instMod","OfNat.ofNat","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.connectedComponentMk","SimpleGraph.dist","instHMod","instLTNat","instOfNatNat"],"value_dag_size":38,"value_refs":["Nat","Nat.mod_lt","Nat.zero_lt_two","OfNat.ofNat","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.connectedComponentMk","SimpleGraph.dist","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.coloringTwoOfVerts._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.coloringTwoOfVerts","reducibility":null,"statement_dag_size":141,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Fin","Fin.mk","HAdd.hAdd","HMod.hMod","Nat","Nat.instMod","Nat.mod_lt","Nat.zero_lt_two","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.connectedComponentMk","SimpleGraph.dist","Top.top","instAddNat","instHAdd","instHMod","instOfNatNat"],"value_dag_size":1171,"value_refs":["Bool","Bool.true","BooleanAlgebra.toTop","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.mk","Fin.mk.inj","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_unsat_coeff","Int.instAdd","Int.instDiv","Int.instMod","Int.instMul","Int.instNegInt","LT.lt","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.instMod","Nat.mod_lt","Nat.zero_lt_two","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.connectedComponentMk","SimpleGraph.dist","SimpleGraph.top_adj","Top.top","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.coloringTwoOfVerts._proof_1","congrArg","eagerReduce","eq_false","eq_of_heq","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.dist_eq_dist_add_one_of_adj_of_reachable._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.dist_eq_dist_add_one_of_adj_of_reachable","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.dist","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":2120,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Ne.symm","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.diff_dist_adj","SimpleGraph.IsAcyclic","SimpleGraph.IsAcyclic.dist_ne_of_adj","SimpleGraph.Reachable","SimpleGraph.dist","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.eq_snd_of_adj_start._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.eq_snd_of_adj_start","reducibility":null,"statement_dag_size":70,"type_refs":["Classical.propDecidable","Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil"],"value_dag_size":66,"value_refs":["Classical.propDecidable","Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.takeUntil","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.eq_snd_of_adj_start._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.eq_snd_of_adj_start","reducibility":null,"statement_dag_size":131,"type_refs":["Classical.propDecidable","Eq","List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Path","SimpleGraph.Path.singleton","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.takeUntil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","Subtype.mk","instOfNatNat"],"value_dag_size":1173,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.nestedProof","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.succ","Nat.succ_eq_add_one","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Path","SimpleGraph.Path.singleton","SimpleGraph.Path.singleton_coe","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.takeUntil","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_length_takeUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.length.eq_1","SimpleGraph.Walk.length.eq_2","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.eq_snd_of_adj_start._proof_1_5","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.tail","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support","instHAppendOfAppend"],"value_dag_size":75,"value_refs":["Eq.symm","HAppend.hAppend","List","List.instAppend","List.tail","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support","SimpleGraph.Walk.support_append","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.isPath_iff_isChain","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instLTNat","instOfNatNat"],"value_dag_size":56,"value_refs":["LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.not_nil_iff_lt_length","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.of_card_le_two._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.of_card_le_two","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.of_card_le_two._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.of_card_le_two","reducibility":null,"statement_dag_size":74,"type_refs":["False","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":256,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_sub_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.sup_edge_of_not_reachable._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsAcyclic.sup_edge_of_not_reachable","reducibility":null,"statement_dag_size":39,"type_refs":["Max.max","Not","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":970,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_forall_eq_false","Max.max","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","SDiff.sdiff","Set","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.instUnion","Set.mem_sdiff","Set.mem_singleton_iff","Set.mem_union","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.IsBridge","SimpleGraph.IsBridge.of_not_reachable","SimpleGraph.IsBridge.sup_edge_of_not_reachable_of_isBridge","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edgeSet_edge","SimpleGraph.edgeSet_sup","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.isAcyclic_iff_forall_isBridge","SimpleGraph.isBridge_sup_edge","Singleton.singleton","Sym2","Sym2.Rel","Sym2.diagSet","Sym2.mk","True","True.intro","Union.union","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":84,"type_refs":["BooleanAlgebra.toCompl","Classical.propDecidable","Compl.compl","Eq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.instSingleton","Fintype","Inhabited","Inhabited.default","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","Singleton.singleton"],"value_dag_size":154,"value_refs":["BooleanAlgebra.toCompl","Classical.propDecidable","Compl.compl","Eq","Eq.mp","Eq.trans","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.instSingleton","Finset.mem_compl._simp_1","Finset.mem_singleton._simp_1","Fintype","Inhabited","Inhabited.default","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.not_nil_of_ne","Singleton.singleton","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","HAdd.hAdd","Inhabited","Inhabited.default","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":268,"value_refs":["Bool","Bool.true","Eq","Eq.refl","False.elim","HAdd.hAdd","Inhabited","Inhabited.default","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.copy"],"value_dag_size":66,"value_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.copy","SimpleGraph.Walk.isPath_copy","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"],"value_dag_size":60,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","SimpleGraph.mem_edgeFinset","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":50,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Fintype","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":55,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.mem_compl","Fintype","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coe_subgraphOfAdj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coe_subgraphOfAdj","reducibility":null,"statement_dag_size":165,"type_refs":["And","Eq","False","Insert.insert","Membership.mem","Or","Set","Set.Elem","Set.instInsert","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.penultimate","SimpleGraph.Walk.snd","SimpleGraph.subgraphOfAdj","Singleton.singleton","Subtype.val"],"value_dag_size":1019,"value_refs":["And","And.casesOn","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","HEq.trans","HSub.hSub","Insert.insert","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.Elem","Set.instInsert","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.snd_ne_penultimate","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.penultimate","SimpleGraph.Walk.snd","SimpleGraph.subgraphOfAdj","Singleton.singleton","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.property","Subtype.val","True","True.intro","eq_of_heq","eq_true","heq_of_eq","id","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert","reducibility":null,"statement_dag_size":41,"type_refs":["HMod.hMod","LT.lt","Nat","Nat.instMod","OfNat.ofNat","SimpleGraph","SimpleGraph.dist","instHMod","instLTNat","instOfNatNat"],"value_dag_size":29,"value_refs":["Nat","Nat.mod_lt","Nat.zero_lt_two","OfNat.ofNat","SimpleGraph","SimpleGraph.dist","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Fin","Fin.mk","HMod.hMod","Nat","Nat.instMod","Nat.mod_lt","Nat.zero_lt_two","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsTree","SimpleGraph.dist","instHMod","instOfNatNat"],"value_dag_size":818,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.mk","Fin.mk.noConfusion","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_unsat_coeff","Int.instAdd","Int.instDiv","Int.instMod","Int.instMul","Int.instNegInt","LT.lt","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.instMod","Nat.mod_lt","Nat.zero_lt_two","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsTree","SimpleGraph.IsTree.dist_eq_dist_add_one_of_adj","SimpleGraph.dist","True","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert._proof_1","eagerReduce","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.dist_eq_dist_add_one_of_adj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.dist_eq_dist_add_one_of_adj","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsTree","SimpleGraph.dist","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1996,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Ne.symm","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.diff_dist_adj","SimpleGraph.IsTree","SimpleGraph.IsTree.dist_ne_of_adj","SimpleGraph.dist","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":null,"statement_dag_size":75,"type_refs":["LE.le","Nat","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.concat","SimpleGraph.Walk.length","instLENat"],"value_dag_size":387,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.concat","SimpleGraph.Walk.length","SimpleGraph.Walk.length_concat","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":null,"statement_dag_size":71,"type_refs":["List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.concat","SimpleGraph.Walk.support"],"value_dag_size":192,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.concat","SimpleGraph.Walk.concat","SimpleGraph.Walk.support","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":null,"statement_dag_size":81,"type_refs":["LE.le","Nat","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instLENat"],"value_dag_size":441,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","True","eagerReduce","eq_false","eq_true","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":null,"statement_dag_size":81,"type_refs":["LE.le","Nat","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","instLENat"],"value_dag_size":413,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.length_cons","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":null,"statement_dag_size":77,"type_refs":["List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":209,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.cons","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":"abbrev","statement_dag_size":316,"type_refs":["Exists","Exists.intro","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","instLENat"],"value_dag_size":629,"value_refs":["Exists","Exists.casesOn","Exists.intro","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":"abbrev","statement_dag_size":61,"type_refs":["Exists","Exists.intro","Ne"],"value_dag_size":108,"value_refs":["Exists","Exists.casesOn","Exists.intro","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_ne_and_degree_eq_one","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath"],"value_dag_size":99,"value_refs":["Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_vert_degree_one_of_nontrivial._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.exists_vert_degree_one_of_nontrivial","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableRel","Eq","Exists","Fintype","Membership.mem","Nat","Nontrivial","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsTree","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","instOfNatNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fintype","Int","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_exists","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","NatCast.natCast","Nontrivial","Nontrivial.to_nonempty","Not","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsTree","SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial","SimpleGraph.degree","SimpleGraph.exists_minimal_degree_vertex","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","eagerReduce","eq_true","id","instNatCastNat","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial","reducibility":null,"statement_dag_size":189,"type_refs":["DecidableRel","Eq","Finset.card","Finset.sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HMul.hMul","LE.le","Membership.mem","Nat","Nat.instAddCommMonoid","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","Sym2","Sym2.instFintype","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":579,"value_refs":["Bool","Bool.false","Bool.true","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","False.elim","Finset.card","Finset.sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.mulR","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instAddCommMonoid","NatCast.natCast","Neg.neg","OfNat.ofNat","Prod","Quot","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","Sym2","Sym2.Rel","Sym2.instFintype","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.minDegree_eq_one_of_nontrivial","reducibility":null,"statement_dag_size":72,"type_refs":["DecidableRel","Eq","Fintype","LE.le","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.minDegree","instLENat","instLTNat","instOfNatNat"],"value_dag_size":290,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fintype","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.minDegree","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Iso.isTree_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Iso.isTree_iff","reducibility":"abbrev","statement_dag_size":36,"type_refs":["SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.mk"],"value_dag_size":53,"value_refs":["SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.IsTree.casesOn","SimpleGraph.IsTree.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.exists_mem_contains_edges_of_directed","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk","reducibility":null,"statement_dag_size":108,"type_refs":["And","DirectedOn","Exists","LE.le","List","List.instMembership","Membership.mem","Set","Set.Nonempty","Set.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.edgeSet","SimpleGraph.instLE","SimpleGraph.supSet","SupSet.sSup","Sym2"],"value_dag_size":1327,"value_refs":["And","And.casesOn","And.intro","DirectedOn","Eq","Eq.mpr","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Iff.mp","IsEmpty.forall_iff._simp_1","LE.le","List","List.cons","List.instMembership","List.mem_cons._simp_1","List.nil","List.not_mem_nil._simp_1","Membership.mem","Or","Set","Set.Nonempty","Set.Nonempty.some","Set.Nonempty.some_mem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.rec","SimpleGraph.edgeSet","SimpleGraph.edgeSet_mono","SimpleGraph.instLE","SimpleGraph.le_iff_adj","SimpleGraph.mem_edgeSet._simp_1","SimpleGraph.supSet","SupSet.sSup","Sym2","Sym2.mk","True","congrArg","congrFun'","forall_congr","forall_eq_or_imp._simp_1","funext","id","implies_congr","implies_true","instIsEmptyFalse","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.Walk.length.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.length.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_isAcyclic_reachable_eq_le._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_isAcyclic_reachable_eq_le","reducibility":null,"statement_dag_size":94,"type_refs":["And","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Eq","Exists","HeytingAlgebra.toOrderBot","LE.le","Order.Frame.toHeytingAlgebra","OrderBot.toBot","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.instLE"],"value_dag_size":407,"value_refs":["And","BooleanAlgebra.toBot","Bot.bot","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","HeytingAlgebra.toOrderBot","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Not","Or","Order.Frame.toHeytingAlgebra","OrderBot.toBot","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.instLE","True","True.intro","congrArg","eq_true","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_isAcyclic_reachable_eq_le_of_le_of_isAcyclic._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_isAcyclic_reachable_eq_le_of_le_of_isAcyclic","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","Exists","LE.le","Maximal","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.instLE"],"value_dag_size":634,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","LE.le","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Maximal","Maximal.eq_1","Not","Or","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.instLE","SimpleGraph.maximal_isAcyclic_iff_reachable_eq","True","True.intro","congrArg","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic","reducibility":null,"statement_dag_size":48,"type_refs":["And","LE.le","Set","Set.instLE","Set.ofPred","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE","SimpleGraph.supSet","SupSet.sSup"],"value_dag_size":389,"value_refs":["And","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toPartialOrder","CompleteSemilatticeSup.toSupSet","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.instLE","SimpleGraph.supSet","SupSet.sSup","True","True.intro","eq_false","eq_true","id","of_eq_true","sSup_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic","reducibility":null,"statement_dag_size":56,"type_refs":["And","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE"],"value_dag_size":257,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","LE.le","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Not","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_forall_adj_isBridge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_forall_adj_isBridge","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.IsBridge","SimpleGraph.edgeSet","Sym2"],"value_dag_size":41,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.IsBridge","SimpleGraph.edgeSet","SimpleGraph.isAcyclic_iff_forall_isBridge","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_forall_adj_isBridge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_forall_adj_isBridge","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_free_cycleGraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_free_cycleGraph","reducibility":"abbrev","statement_dag_size":161,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.length"],"value_dag_size":295,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.length"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path","reducibility":null,"statement_dag_size":146,"type_refs":["And","Eq","Exists","Ne","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Path","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.reverse","Subtype","Subtype.val"],"value_dag_size":930,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_congr'","Lean.Grind.exists_and_left","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Ne","Not","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.IsAcyclic.eq_1","SimpleGraph.Path","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.reverse","Subtype","Subtype.coe_inj","Subtype.val","True","True.intro","congrArg","eq_false","eq_true","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path","reducibility":null,"statement_dag_size":43,"type_refs":["Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.getVert","instOfNatNat"],"value_dag_size":57,"value_refs":["Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.adj_snd","SimpleGraph.Walk.getVert","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path","reducibility":null,"statement_dag_size":56,"type_refs":["Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj.toWalk","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.getVert","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_3","instOfNatNat"],"value_dag_size":63,"value_refs":["Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj.symm","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.IsPath.of_adj","SimpleGraph.Walk.adj_snd","SimpleGraph.Walk.getVert","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path","reducibility":null,"statement_dag_size":107,"type_refs":["Eq","False","SimpleGraph","SimpleGraph.Adj.symm","SimpleGraph.Adj.toWalk","SimpleGraph.Path","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.isPath_tail","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.of_adj","SimpleGraph.Walk.adj_snd","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","Subtype.mk"],"value_dag_size":606,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Adj.toWalk","SimpleGraph.Path","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit.three_le_length","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.isCircuit","SimpleGraph.Walk.IsCycle.isPath_tail","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.of_adj","SimpleGraph.Walk.adj_snd","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_cons","SimpleGraph.Walk.length_nil","SimpleGraph.Walk.length_tail_add_one","SimpleGraph.Walk.nil","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","Subtype","Subtype.mk","Subtype.mk.inj","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_iff_subsingleton_path._proof_1_4","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Iff","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":1762,"value_refs":["And","And.casesOn","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","LE.le","Lattice.toSemilatticeSup","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Max.max","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","SDiff.sdiff","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Set","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","Set.subset_def","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edge_le","SimpleGraph.instLE","SimpleGraph.instMax","Singleton.singleton","Sym2","Sym2.IsDiag","Sym2.Rel","Sym2.diagSet","Sym2.mem_diagSet","Sym2.mk","Sym2.mk_isDiag_iff","True","True.intro","congr","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true","sup_eq_left"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff","reducibility":null,"statement_dag_size":65,"type_refs":["And","Eq","Iff","Max.max","Not","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":1772,"value_refs":["And","And.casesOn","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","LE.le","Lattice.toSemilatticeSup","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Max.max","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","SDiff.sdiff","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Set","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","Set.subset_def","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edge_le","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.mem_edgeSet","Singleton.singleton","Sym2","Sym2.Rel","Sym2.diagSet","Sym2.mk","True","True.intro","congr","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true","sup_eq_left"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Not","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable"],"value_dag_size":150,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Not","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isAcyclic_sup_fromEdgeSet_iff","reducibility":"abbrev","statement_dag_size":104,"type_refs":["And","And.intro","Eq","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable"],"value_dag_size":119,"value_refs":["And","And.casesOn","And.intro","Eq","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.Reachable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_connected_and_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_connected_and_card","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.IsBridge","Sym2.mk"],"value_dag_size":36,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAcyclic","SimpleGraph.IsBridge","SimpleGraph.isAcyclic_iff_forall_adj_isBridge","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_connected_and_card.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_connected_and_card","reducibility":"abbrev","statement_dag_size":106,"type_refs":["And","And.intro","Eq","HAdd.hAdd","Nat","Nat.card","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Connected","SimpleGraph.edgeSet","Sym2","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":121,"value_refs":["And","And.casesOn","And.intro","Eq","HAdd.hAdd","Nat","Nat.card","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Connected","SimpleGraph.edgeSet","Sym2","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq","SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree"],"value_dag_size":26,"value_refs":["And","SimpleGraph","SimpleGraph.Connected","SimpleGraph.IsAcyclic","SimpleGraph.IsTree","SimpleGraph.isTree_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Path","Subsingleton"],"value_dag_size":28,"value_refs":["SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.Path","SimpleGraph.isAcyclic_iff_subsingleton_path","Subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Subsingleton"],"value_dag_size":19,"value_refs":["Eq","Subsingleton","propext","subsingleton_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_existsUnique_path","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","SimpleGraph","SimpleGraph.Path","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","Subtype.val","True"],"value_dag_size":49,"value_refs":["SimpleGraph","SimpleGraph.Path","SimpleGraph.Path.isPath","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","Subtype.val","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_maximal_isAcyclic.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_maximal_isAcyclic","reducibility":"abbrev","statement_dag_size":66,"type_refs":["And","And.intro","Maximal","Nonempty","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE"],"value_dag_size":80,"value_refs":["And","And.casesOn","And.intro","Maximal","Nonempty","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_minimal_connected.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_iff_minimal_connected","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath"],"value_dag_size":99,"value_refs":["Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_of_minimal_connected._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.isTree_of_minimal_connected","reducibility":null,"statement_dag_size":65,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Eq","GeneralizedCoheytingAlgebra.toLattice","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":74,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSet_ssubset_edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq","reducibility":null,"statement_dag_size":112,"type_refs":["DFunLike.coe","LE.le","Membership.mem","Prod","Quot","RelEmbedding","SDiff.sdiff","Set","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Singleton.singleton","Sym2","Sym2.Rel","Sym2.diagSet","instFunLikeOrderEmbedding"],"value_dag_size":465,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Prod","Quot","RelEmbedding","SDiff.sdiff","Set","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","Set.subset_def","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Singleton.singleton","Sym2","Sym2.Rel","Sym2.diagSet","True","True.intro","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq","reducibility":"abbrev","statement_dag_size":159,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","LT.lt","PartialOrder.toPreorder","Preorder.toLT","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE","SimpleGraph.instPartialOrder"],"value_dag_size":294,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","PartialOrder.toPreorder","Preorder.toLT","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.instLE","SimpleGraph.instPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.maximal_isAcyclic_iff_reachable_eq","reducibility":"abbrev","statement_dag_size":135,"type_refs":["And","And.intro","Exists","Exists.intro","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Sym2"],"value_dag_size":196,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic","reducibility":null,"statement_dag_size":140,"type_refs":["False","LE.le","Max.max","Membership.mem","Not","Prod.fst","Prod.mk","Prod.snd","Quot.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.instLE","SimpleGraph.instMax"],"value_dag_size":520,"value_refs":["And","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Max.max","Membership.mem","Ne","Not","Or","Prod.fst","Prod.mk","Prod.snd","Quot.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.reachable","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.edge_adj","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.le_iff_adj","SimpleGraph.sup_adj","True","True.intro","and_true","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","id","of_eq_true","true_and","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic","reducibility":null,"statement_dag_size":153,"type_refs":["And","LE.le","Max.max","Maximal","Membership.mem","Not","Prod.fst","Prod.mk","Prod.snd","Quot.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.edge","SimpleGraph.instLE","SimpleGraph.instMax"],"value_dag_size":2403,"value_refs":["And","And.casesOn","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","LE.le","Lattice.toSemilatticeSup","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.Order.le_eq_true","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Max.max","Maximal","Maximal.eq_1","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Prod.fst","Prod.mk","Prod.snd","Quot.mk","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.IsAcyclic","SimpleGraph.Reachable","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.edge_adj","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.instPartialOrder","SimpleGraph.le_iff_adj","SimpleGraph.sup_adj","True","True.intro","and_true","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","id","instIsPartialOrder_mathlib","instIsPreorder_mathlib","of_eq_true","sup_le","true_and","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Acyclic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.reachable_eq_of_maximal_isAcyclic","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"],"value_dag_size":55,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.IsAdjMatrix.compl_compl._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.IsAdjMatrix.compl_compl","reducibility":null,"statement_dag_size":124,"type_refs":["DecidableEq","Eq","Matrix","Matrix.IsAdjMatrix","Not","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","forall_prop_decidable","instDecidableNot","ite"],"value_dag_size":697,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_right","Matrix","Matrix.IsAdjMatrix","Matrix.IsAdjMatrix.casesOn","Matrix.IsSymm","Not","OfNat.ofNat","One","One.toOfNat1","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","forall_prop_decidable","id","instDecidableNot","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.IsAdjMatrix.compl_inj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.IsAdjMatrix.compl_inj","reducibility":null,"statement_dag_size":121,"type_refs":["DecidableEq","Eq","Matrix","Matrix.IsAdjMatrix","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","ite"],"value_dag_size":960,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Matrix","Matrix.IsAdjMatrix","Matrix.IsAdjMatrix.casesOn","Matrix.IsSymm","Not","OfNat.ofNat","One","One.toOfNat1","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_apply._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_apply","reducibility":null,"statement_dag_size":103,"type_refs":["DecidableEq","Eq","Matrix","Not","OfNat.ofNat","One","One.toOfNat1","Or","Zero","Zero.toOfNat0","ite"],"value_dag_size":344,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Matrix","Not","OfNat.ofNat","One","One.toOfNat1","Or","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_of_one_sub_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_of_one_sub_one","reducibility":null,"statement_dag_size":136,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","DFunLike.coe","DecidableEq","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","HSub.hSub","Matrix","Matrix.of","Matrix.one","Matrix.sub","NegZeroClass.toZero","OfNat.ofNat","One","One.toOfNat1","Pi.instOne","SimpleGraph.Top.adjDecidable","SimpleGraph.adjMatrix","SimpleGraph.completeGraph","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","instHSub"],"value_dag_size":143,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","DFunLike.coe","DecidableEq","Eq.symm","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","HSub.hSub","Matrix","Matrix.of","Matrix.one","Matrix.sub","NegZeroClass.toZero","OfNat.ofNat","One","One.toOfNat1","Pi.instOne","SimpleGraph.Top.adjDecidable","SimpleGraph.adjMatrix","SimpleGraph.adjMatrix_completeGraph_eq_of_one_sub_one","SimpleGraph.completeGraph","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_zero","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Matrix","Matrix.IsAdjMatrix","Matrix.compl","One","Zero"],"value_dag_size":87,"value_refs":["DecidableEq","Eq","Eq.symm","Matrix","Matrix.IsAdjMatrix","Matrix.IsAdjMatrix.compl_inj","Matrix.compl","One","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard","reducibility":null,"statement_dag_size":109,"type_refs":["And","Eq","Iff","Matrix","Matrix.IsAdjMatrix","Matrix.IsSymm","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","One.toOfNat1","Or","Zero.toOfNat0"],"value_dag_size":1412,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Matrix","Matrix.IsAdjMatrix","Matrix.IsAdjMatrix.apply_diag._autoParam","Matrix.IsAdjMatrix.casesOn","Matrix.IsAdjMatrix.mk","Matrix.IsAdjMatrix.symm._autoParam","Matrix.IsAdjMatrix.zero_or_one._autoParam","Matrix.IsSymm","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","True","True.intro","Zero.toOfNat0","autoParam","congr","congrArg","eq_false","eq_true","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","IsIdempotentElem","Matrix","Matrix.hadamard","Mul"],"value_dag_size":52,"value_refs":["Eq","IsIdempotentElem","Matrix","Matrix.hadamard","Matrix.hadamard_self_eq_self_iff","Mul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","IsIdempotentElem","IsLeftCancelMulZero","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","One.toOfNat1","Or","Zero.toOfNat0"],"value_dag_size":79,"value_refs":["Eq","IsIdempotentElem","IsIdempotentElem.iff_eq_zero_or_one","IsLeftCancelMulZero","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","One.toOfNat1","Or","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard","reducibility":null,"statement_dag_size":108,"type_refs":["DecidableEq","Eq","Matrix","Matrix.diag","Matrix.hadamard","Matrix.one","Matrix.zero","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","One.toOfNat1","Pi.instZero","Zero.toOfNat0"],"value_dag_size":113,"value_refs":["DecidableEq","Eq","Matrix","Matrix.diag","Matrix.hadamard","Matrix.one","Matrix.one_hadamard_eq_zero_iff","Matrix.zero","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","One.toOfNat1","Pi.instZero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isAdjMatrix_iff_hadamard","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isSymm_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.isSymm_compl","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_pow_apply_eq_card_walk._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_pow_apply_eq_card_walk","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_pow_apply_eq_card_walk._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_pow_apply_eq_card_walk","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_vecMul_apply._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.adjMatrix_vecMul_apply","reducibility":null,"statement_dag_size":117,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","DecidableRel","Distrib.toMul","Eq","Finset.sum","Fintype","Membership.mem","MulZeroClass.toZero","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adjMatrix","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","dotProduct"],"value_dag_size":127,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","DecidableRel","Distrib.toMul","Eq.symm","Finset.sum","Fintype","Membership.mem","MulZeroClass.toZero","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adjMatrix","SimpleGraph.dotProduct_adjMatrix","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","dotProduct"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.isAdjMatrix_adjMatrix._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.isAdjMatrix_adjMatrix","reducibility":null,"statement_dag_size":62,"type_refs":["DecidableRel","Eq","OfNat.ofNat","One","One.toOfNat1","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adjMatrix","Zero","Zero.toOfNat0"],"value_dag_size":289,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Not","OfNat.ofNat","One","One.toOfNat1","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adjMatrix","SimpleGraph.adjMatrix_apply","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.mul_adjMatrix_apply._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.mul_adjMatrix_apply","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.toGraph_adjMatrix_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.toGraph_adjMatrix_eq","reducibility":null,"statement_dag_size":35,"type_refs":["Decidable","Eq","Not","ite"],"value_dag_size":41,"value_refs":["Decidable","Eq","Not","ite","ite_eq_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.toGraph_adjMatrix_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.toGraph_adjMatrix_eq","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["Eq","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","eq_false","zero_ne_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.AdjMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.transpose_adjMatrix._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.SimpleGraph.transpose_adjMatrix","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_congr_of_sym2._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_congr_of_sym2","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_congr_of_sym2._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_congr_of_sym2","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Exists","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.mk"],"value_dag_size":62,"value_refs":["Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SetCoe.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_iff_exists_edge_coe","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Membership.mem","Set","Set.instMembership","Set.ofPred"],"value_dag_size":52,"value_refs":["And","Membership.mem","Set","Set.instMembership","Set.mem_sep_iff","Set.ofPred","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.commonNeighbors_top_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.commonNeighbors_top_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.commonNeighbors_top_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.commonNeighbors_top_eq","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.completeAtomicBooleanAlgebra._simp_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.completeAtomicBooleanAlgebra","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Exists"],"value_dag_size":37,"value_refs":["Classical.skolem","Exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors","reducibility":null,"statement_dag_size":52,"type_refs":["And","Iff","Not","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":699,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":88,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors"],"value_dag_size":48,"value_refs":["And","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.mem_commonNeighbors","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_commonNeighbors","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_fromEdgeSet._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_fromEdgeSet","reducibility":null,"statement_dag_size":137,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","DFunLike.coe","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Iff","Inter.inter","LE.le","Lattice.toSemilatticeInf","Prod","Quot","RelEmbedding","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instInter","Set.instLE","Set.instSDiff","Set.instUnion","SimpleGraph","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2","Sym2.Rel","Sym2.diagSet","Union.union","instFunLikeOrderEmbedding"],"value_dag_size":2527,"value_refs":["And","And.casesOn","BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","BoundedOrder.toOrderBot","Classical.byContradiction","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","DFunLike.coe","Disjoint","Disjoint.mono_left","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Iff","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","Prod","Quot","RelEmbedding","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBooleanAlgebra","Set.instBoundedOrder","Set.instCompl","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instInter","Set.instLE","Set.instMembership","Set.instSDiff","Set.instUnion","Set.mem_compl_iff","Set.mem_inter_iff","Set.mem_sdiff","Set.mem_union","Set.subset_def","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edgeSet_subset_compl_diagSet","SimpleGraph.instLE","Sym2","Sym2.Rel","Sym2.diagSet","True","True.intro","Union.union","congrArg","disjoint_comm","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":112,"type_refs":["Iff","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.incidenceSet","Sym2.Rel"],"value_dag_size":1008,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":88,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Set","Set.iUnion","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.incidenceSet","Sym2"],"value_dag_size":32,"value_refs":["Eq.symm","Set","Set.iUnion","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.iUnion_incidenceSet","SimpleGraph.incidenceSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":82,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","Eq","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra"],"value_dag_size":86,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.disjoint_iUnion_left","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":82,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","Eq","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra"],"value_dag_size":86,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.disjoint_iUnion_right","Set.iUnion","Set.instCompleteAtomicBooleanAlgebra","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_incidenceSet","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":88,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_left","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":88,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_neighborSet","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support","reducibility":null,"statement_dag_size":164,"type_refs":["DFunLike.coe","Exists","LE.le","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2.Rel","instFunLikeOrderEmbedding"],"value_dag_size":494,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_not","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.mem_edgeSet","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","eq_false","eq_true","forall_congr","forall_not_of_not_exists","id","implies_congr","instFunLikeOrderEmbedding","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.disjoint_of_disjoint_support","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support"],"value_dag_size":40,"value_refs":["Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_support","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_eq_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_eq_iff","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_right","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_iInf.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_iInf","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_sInf.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_sInf","reducibility":"abbrev","statement_dag_size":56,"type_refs":["Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SimpleGraph"],"value_dag_size":77,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SimpleGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_sdiff_sdiff_isDiag._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_sdiff_sdiff_isDiag","reducibility":null,"statement_dag_size":94,"type_refs":["DFunLike.coe","Eq","LE.le","Prod","Quot","RelEmbedding","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","SimpleGraph","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2","Sym2.Rel","Sym2.diagSet","instFunLikeOrderEmbedding"],"value_dag_size":788,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","LE.le","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Quot","RelEmbedding","SDiff.sdiff","Set","Set.ext","Set.instLE","Set.instMembership","Set.instSDiff","Set.mem_sdiff","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.not_isDiag_of_mem_edgeSet","Sym2","Sym2.IsDiag","Sym2.Rel","Sym2.diagSet","Sym2.mem_diagSet","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instFunLikeOrderEmbedding","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_subset_compl_diagSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_subset_compl_diagSet","reducibility":null,"statement_dag_size":61,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instCompl","Set.instLE"],"value_dag_size":64,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instCompl","Set.instLE","Set.subset_compl_iff_disjoint_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_subset_sym2_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edgeSet_subset_sym2_iff","reducibility":"abbrev","statement_dag_size":120,"type_refs":["Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support","SimpleGraph.support.match_1"],"value_dag_size":167,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support","SimpleGraph.support.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edge_other_incident_set._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.edge_other_incident_set","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Membership.mem","SetLike.instMembership","Sym2","Sym2.Mem.other'","Sym2.instSetLike","True"],"value_dag_size":53,"value_refs":["DecidableEq","Membership.mem","SetLike.instMembership","Sym2","Sym2.Mem.other'","Sym2.instSetLike","Sym2.other_mem'","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_forall_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_forall_not_adj","reducibility":null,"statement_dag_size":45,"type_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":55,"value_refs":["Bot.bot","Eq","Eq.symm","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_bot_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_forall_not_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_forall_not_adj","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE"],"value_dag_size":41,"value_refs":["LE.le","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE","SimpleGraph.le_iff_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated","reducibility":null,"statement_dag_size":42,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":44,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.eq_bot_iff_forall_not_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated","reducibility":null,"statement_dag_size":33,"type_refs":["EmptyCollection.emptyCollection","Eq","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.neighborSet"],"value_dag_size":42,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.neighborSet","SimpleGraph.neighborSet_eq_empty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_bot_iff_isIsolated","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_isUniversal._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_isUniversal","reducibility":null,"statement_dag_size":46,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":48,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.eq_top_iff_forall_ne_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_ne_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_ne_adj","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top"],"value_dag_size":55,"value_refs":["Eq","Eq.symm","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top","propext","top_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_ne_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.eq_top_iff_forall_ne_adj","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE"],"value_dag_size":41,"value_refs":["LE.le","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE","SimpleGraph.le_iff_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ext.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ext","reducibility":"abbrev","statement_dag_size":34,"type_refs":["SimpleGraph","SimpleGraph.mk","Std.Irrefl","Std.Symm"],"value_dag_size":53,"value_refs":["SimpleGraph","SimpleGraph.casesOn","SimpleGraph.mk","Std.Irrefl","Std.Symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_empty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_empty","reducibility":null,"statement_dag_size":26,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":28,"value_refs":["EmptyCollection.emptyCollection","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_inter._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_inter","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_le","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.instLE","Sym2"],"value_dag_size":46,"value_refs":["Eq.symm","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSet_subset_edgeSet","SimpleGraph.instLE","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_sUnion._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_sUnion","reducibility":null,"statement_dag_size":81,"type_refs":["And","Eq","Exists","Iff","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Sym2","Sym2.Rel"],"value_dag_size":1006,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind._simp_1","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Sym2","Sym2.Rel","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_union._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_union","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_union._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_union","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_univ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.fromEdgeSet_univ","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.univ","True"],"value_dag_size":23,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_univ","Set.univ","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.iUnion_incidenceSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.iUnion_incidenceSet","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.incidenceSet_inter_incidenceSet_of_not_adj","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Iff","Membership.mem","Not","Or","Set","Set.instMembership","Set.univ","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":631,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.instMembership","Set.mem_univ","Set.univ","SimpleGraph","SimpleGraph.Adj","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.insert_neighborSet_eq_univ","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":39,"value_refs":["Eq","Eq.symm","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Iff"],"value_dag_size":19,"value_refs":["Eq","Iff","eq_iff_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.instNontrivial","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.le_fromEdgeSet_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.le_fromEdgeSet_iff","reducibility":null,"statement_dag_size":113,"type_refs":["And","DFunLike.coe","Iff","LE.le","Membership.mem","Not","Prod","Quot","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2","Sym2.IsDiag","Sym2.Rel","instFunLikeOrderEmbedding"],"value_dag_size":682,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","LE.le","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.forall_and","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Quot","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.not_isDiag_of_mem_edgeSet","Sym2","Sym2.IsDiag","Sym2.Rel","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","id","instFunLikeOrderEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.le_fromEdgeSet_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.le_fromEdgeSet_iff","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.instLE","Sym2"],"value_dag_size":46,"value_refs":["Eq.symm","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSet_subset_edgeSet","SimpleGraph.instLE","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.mem_support_iff_not_isIsolated._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.mem_support_iff_not_isIsolated","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support"],"value_dag_size":40,"value_refs":["Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_support","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.mk'._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.mk'","reducibility":null,"statement_dag_size":20,"type_refs":["Bool","Bool.true","Eq","Iff"],"value_dag_size":23,"value_refs":["Bool","Bool.coe_iff_coe","Bool.true","Eq","Iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ne_bot_iff_exists_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ne_bot_iff_exists_adj","reducibility":null,"statement_dag_size":42,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":44,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.eq_bot_iff_forall_not_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ne_top_iff_exists_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.ne_top_iff_exists_not_adj","reducibility":null,"statement_dag_size":46,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":48,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.eq_top_iff_forall_ne_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_bot._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_bot","reducibility":null,"statement_dag_size":36,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","EmptyCollection.emptyCollection","Eq","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.neighborSet"],"value_dag_size":331,"value_refs":["BooleanAlgebra.toBot","Bot.bot","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_eq","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","SimpleGraph","SimpleGraph.Adj","SimpleGraph.bot_adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","True","True.intro","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_compl","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_compl","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_eq_compl_singleton._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_eq_compl_singleton","reducibility":null,"statement_dag_size":39,"type_refs":["Compl.compl","Eq","Iff","Set","Set.instCompl","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsUniversal","SimpleGraph.neighborSet","Singleton.singleton"],"value_dag_size":1004,"value_refs":["And","And.casesOn","Classical.byContradiction","Compl.compl","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Insert.insert","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.ext","Set.instCompl","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_compl_iff","Set.mem_insert_iff","Set.mem_singleton_iff","Set.mem_univ","Set.univ","SimpleGraph","SimpleGraph.IsUniversal","SimpleGraph.insert_neighborSet_eq_univ","SimpleGraph.neighborSet","SimpleGraph.notMem_neighborSet_self","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_eq_empty._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_eq_empty","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_iInf._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_iInf","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Membership.mem","Set","Set.iInter","Set.instMembership"],"value_dag_size":45,"value_refs":["Membership.mem","Set","Set.iInter","Set.instMembership","Set.mem_iInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_iInf._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_iInf","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Nonempty","SimpleGraph","SimpleGraph.Adj","SimpleGraph.infSet","iInf"],"value_dag_size":49,"value_refs":["Nonempty","SimpleGraph","SimpleGraph.Adj","SimpleGraph.iInf_adj_of_nonempty","SimpleGraph.infSet","iInf","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_nonempty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_nonempty","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Ne","Set","Set.Nonempty","Set.instEmptyCollection"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Ne","Set","Set.Nonempty","Set.instEmptyCollection","Set.nonempty_iff_ne_empty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_top._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_top","reducibility":null,"statement_dag_size":44,"type_refs":["BooleanAlgebra.toTop","Compl.compl","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Set","Set.instCompl","Set.instSingletonSet","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.neighborSet","Singleton.singleton","Top.top"],"value_dag_size":384,"value_refs":["BooleanAlgebra.toTop","Classical.byContradiction","Compl.compl","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_congr'","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Ne","Not","Or","Set","Set.ext","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.mem_compl_iff","Set.mem_singleton_iff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","SimpleGraph.top_adj","Singleton.singleton","Top.top","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.neighborSet_union_compl_neighborSet_eq","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.notMem_support_iff_isIsolated._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.notMem_support_iff_isIsolated","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.support"],"value_dag_size":36,"value_refs":["Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.mem_support_iff_not_isIsolated","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.instFintypeSimpleGraphOfDecidableEq","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith","reducibility":null,"statement_dag_size":28,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":10,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":639,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","Fin","Fin.instOfNat","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper","Lean.Grind.ToInt.ofNat_eq","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.instOfNatFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_or","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","eagerReduce","id","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.four_mul_encard_edgeSet_le._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.four_mul_encard_edgeSet_le","reducibility":null,"statement_dag_size":85,"type_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.card","Nat.instMonoid","OfNat.ofNat","Set","Set.ncard","instAddNat","instHAdd","instHMul","instHPow","instLENat","instMulNat","instOfNatNat"],"value_dag_size":833,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","CanonicallyOrderedAdd.toExistsAddOfLE","Classical.byContradiction","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'_norm","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","IsStrictOrderedRing.toMulPosStrictMono","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.card","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instCanonicallyOrderedAdd","Nat.instCommSemiring","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instIsStrictOrderedRing","Nat.instLinearOrder","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.not_le_eq","Nat.pow_le_pow_left","NatCast.natCast","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","Set","Set.ncard","contravariant_lt_of_covariant_le","eagerReduce","four_mul_le_sq_add","id","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instIsLeftCancelAddOfAddLeftReflectLE","instLENat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.four_mul_encard_edgeSet_le.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.four_mul_encard_edgeSet_le","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Exists","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"],"value_dag_size":128,"value_refs":["Exists","Exists.casesOn","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.subgraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.subgraph","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Exists","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"],"value_dag_size":129,"value_refs":["Exists","Exists.casesOn","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.left","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.right","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":121,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_11"],"value_dag_size":134,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Or.inl","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.right","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.left","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":121,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_14"],"value_dag_size":134,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Or.inl","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":57,"type_refs":["And","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":57,"type_refs":["And","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_14","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":147,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Not","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_16","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_17"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_15","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":57,"type_refs":["And","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_6"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":57,"type_refs":["And","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_7"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":147,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Not","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_19","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_20"],"value_dag_size":92,"value_refs":["And","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.resolve_left","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_8"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_22","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":50,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":267,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.IsBipartiteWith.mem_of_adj","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_3","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_23","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":50,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":267,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.IsBipartiteWith.mem_of_adj","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_4","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_24","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":141,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_22","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_23"],"value_dag_size":267,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.IsBipartiteWith.mem_of_adj","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_5","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_25","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":50,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":235,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_true","Membership.mem","Not","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_19","eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_26","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":50,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":235,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_true","Membership.mem","Not","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_20","eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_27","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":141,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_25","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_26"],"value_dag_size":235,"value_refs":["And","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_true","Membership.mem","Not","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_21","eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_28","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":574,"type_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","DFunLike.coe","DecidableRel","Eq","LE.le","Membership.mem","Or.by_cases","Or.inl","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","RelEmbedding","Set","Set.Elem","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.symm","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","Sym2","Sym2.Rel","completeBipartiteGraph","instDecidableAnd","instFunLikeOrderEmbedding","rfl","symm"],"value_dag_size":2056,"value_refs":["And","And.casesOn","And.intro","And.left","And.right","Bool","Bool.true","BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","DFunLike.coe","DecidableRel","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HeytingAlgebra.toOrderBot","Iff","LE.le","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.by_cases","Or.by_cases.eq_1","Or.casesOn","Or.inl","Or.resolve_left","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","RelEmbedding","SemilatticeInf.toPartialOrder","Set","Set.Elem","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.symm","Subtype","Subtype.casesOn","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","Sym2","Sym2.Rel","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_11","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_12","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_14","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_15","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_16","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_17","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_18","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_19","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_20","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_21","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_22","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_23","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_24","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_25","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_26","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_27","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_8","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_9","completeBipartiteGraph","dite","eq_false","eq_true","id","instDecidableAnd","instFunLikeOrderEmbedding","of_eq_true","rfl","symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.left","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_30","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":49,"type_refs":["And","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"],"value_dag_size":58,"value_refs":["And","And.left","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_31","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":49,"type_refs":["And","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"],"value_dag_size":58,"value_refs":["And","And.right","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_32","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":132,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_30","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_31"],"value_dag_size":147,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Or.inl","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_33","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":84,"type_refs":["And","Membership.mem","Not","Prod","Prod.fst","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.edgeSet","Sym2","Sym2.Rel"],"value_dag_size":113,"value_refs":["And","And.right","Membership.mem","Not","Or.resolve_left","Prod","Prod.fst","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.edgeSet","Sym2","Sym2.Rel"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_34","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":84,"type_refs":["And","Membership.mem","Not","Prod","Prod.fst","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.edgeSet","Sym2","Sym2.Rel"],"value_dag_size":113,"value_refs":["And","And.left","Membership.mem","Not","Or.resolve_left","Prod","Prod.fst","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.edgeSet","Sym2","Sym2.Rel"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_35","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":173,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Not","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.edgeSet","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","Sym2","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_33","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_34"],"value_dag_size":202,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Not","Or.inl","Or.resolve_left","Prod","Prod.fst","Prod.mk","Prod.snd","Quot.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.edgeSet","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","Sym2","Sym2.Rel","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_36","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":53,"type_refs":["Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"],"value_dag_size":88,"value_refs":["And","Eq.trans","Lean.Grind.and_eq_of_eq_true_left","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_30","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_37","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":53,"type_refs":["Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership"],"value_dag_size":88,"value_refs":["And","Eq.trans","Lean.Grind.and_eq_of_eq_true_left","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_31","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_38","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":139,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_36","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_37"],"value_dag_size":88,"value_refs":["And","Eq.trans","Lean.Grind.and_eq_of_eq_true_left","Membership.mem","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","True","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_32","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_39","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":492,"type_refs":["And","DFunLike.coe","DecidableRel","Eq","LE.le","Lean.Grind.nestedDecidable","Membership.mem","Not","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sym2","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_30","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_31","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_32","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_33","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_34","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_35","completeBipartiteGraph","dite","instDecidableAnd","instFunLikeOrderEmbedding"],"value_dag_size":5774,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","HEq.trans","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.fst_swap","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.snd_swap","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.mk.noConfusion","Subtype.property","Subtype.val","Sum","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","Sum.isLeft","Sum.isRight","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_30","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_31","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_32","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_33","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_34","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_35","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_36","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_37","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_38","completeBipartiteGraph","congr","congrArg","dite","eq_false","eq_of_heq","eq_true","heq_eq_eq","heq_of_eq","id","instDecidableAnd","instFunLikeOrderEmbedding","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.right","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":121,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_4"],"value_dag_size":134,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Or.inl","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.right","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":37,"type_refs":["And","Membership.mem","Set","Set.instMembership"],"value_dag_size":43,"value_refs":["And","And.left","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":121,"type_refs":["And","Bool","Bool.true","Eq","Membership.mem","Or","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_7"],"value_dag_size":134,"value_refs":["And","And.intro","And.left","And.right","Bool","Bool.true","Eq","Membership.mem","Or.inl","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isRight","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.edgeSetEmbeddingCompleteBipartiteGraph","reducibility":null,"statement_dag_size":53,"type_refs":["And","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith"],"value_dag_size":53,"value_refs":["Set","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.mem_of_adj","SimpleGraph.symm","symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.subgraph._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartiteWith.subgraph","reducibility":null,"statement_dag_size":103,"type_refs":["ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","HeytingAlgebra.toOrderBot","Membership.mem","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts","Subtype","Subtype.val"],"value_dag_size":928,"value_refs":["BoundedOrder.toOrderBot","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HeytingAlgebra.toOrderBot","Iff","Lattice.toSemilatticeInf","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SimpleGraph","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts","Subtype","Subtype.casesOn","Subtype.mk","Subtype.val","True","True.intro","disjoint_comm","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.between_comm._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.between_comm","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover","reducibility":null,"statement_dag_size":60,"type_refs":["False","SimpleGraph","SimpleGraph.Adj","SimpleGraph.bipartiteDoubleCover.match_1","Sum"],"value_dag_size":643,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","Lean.Grind.MatchCond","Lean.Grind.PreMatchCond","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_true","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_symm","SimpleGraph.bipartiteDoubleCover.match_1","SimpleGraph.bipartiteDoubleCover.match_1.congr_eq_1","SimpleGraph.bipartiteDoubleCover.match_1.congr_eq_2","SimpleGraph.bipartiteDoubleCover.match_1.congr_eq_3","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inr","True","True.intro","eq_false","eq_true","heq_eq_eq","id","implies_congr","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":68,"value_refs":["Eq.refl","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":68,"value_refs":["Eq.refl","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1","reducibility":null,"statement_dag_size":113,"type_refs":["Eq","False","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":797,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","False.elim","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","SimpleGraph.bipartiteDoubleCover._sparseCasesOn_1","SimpleGraph.bipartiteDoubleCover._sparseCasesOn_1.else_eq","SimpleGraph.bipartiteDoubleCover._sparseCasesOn_2","SimpleGraph.bipartiteDoubleCover._sparseCasesOn_2.else_eq","SimpleGraph.bipartiteDoubleCover.match_1","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_5","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1","reducibility":"abbrev","statement_dag_size":100,"type_refs":["Eq","False","Sum","Sum.inl","Sum.inr"],"value_dag_size":343,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_5","absurd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inr"],"value_dag_size":103,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter._sparseCasesOn_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inl"],"value_dag_size":101,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover_le.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.bipartiteDoubleCover_le","reducibility":"abbrev","statement_dag_size":145,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.bipartiteDoubleCover","Sum","Sum.inl","Sum.inr"],"value_dag_size":240,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.bipartiteDoubleCover","Sum","Sum.casesOn","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover","reducibility":null,"statement_dag_size":302,"type_refs":["DecidableRel","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.two_mul_card_edgeFinset.match_1","Sum","Sum.inl","Sum.inr","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover.match_1_1","instFintypeProd"],"value_dag_size":1377,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.filter","Finset.filter_congr","Finset.instSetLike","Finset.univ","Fintype","HEq","Iff","Iff.of_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.intro_with_eq'","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.two_mul_card_edgeFinset.match_1","Sum","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover.match_1_1","congr","congrArg","congrFun'","eq_false","eq_true","heq_eq_eq","id","instFintypeProd","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover","reducibility":"abbrev","statement_dag_size":202,"type_refs":["DecidableRel","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Prod","Prod.fst","Prod.mk","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.two_mul_card_edgeFinset.match_1","instFintypeProd"],"value_dag_size":305,"value_refs":["DecidableRel","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.two_mul_card_edgeFinset.match_1","instFintypeProd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover.match_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.card_edgeFinset_bipartiteDoubleCover","reducibility":"abbrev","statement_dag_size":145,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.bipartiteDoubleCover","Sum","Sum.inl","Sum.inr"],"value_dag_size":240,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.bipartiteDoubleCover","Sum","Sum.casesOn","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.chromaticNumber_eq_two_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.chromaticNumber_eq_two_iff","reducibility":"abbrev","statement_dag_size":97,"type_refs":["And","And.intro","BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.IsBipartite","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":112,"value_refs":["And","And.casesOn","And.intro","BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.IsBipartite","SimpleGraph.completeAtomicBooleanAlgebra"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover","reducibility":null,"statement_dag_size":84,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween","SimpleGraph.IsContained","Sum","completeBipartiteGraph"],"value_dag_size":91,"value_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween","SimpleGraph.IsContained","SimpleGraph.completeBipartiteGraph_isContained_iff","Sum","completeBipartiteGraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover.match_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover","reducibility":"abbrev","statement_dag_size":274,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween","SimpleGraph.bipartiteDoubleCover","Sum"],"value_dag_size":553,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween","SimpleGraph.bipartiteDoubleCover","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover.match_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_bipartiteDoubleCover","reducibility":"abbrev","statement_dag_size":240,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween"],"value_dag_size":505,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":240,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween"],"value_dag_size":505,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsCompleteBetween"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":63,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","Sum","completeBipartiteGraph"],"value_dag_size":75,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","Sum","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":553,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Function.Embedding","Function.Embedding.mk","Function.Injective.comp","Function.comp","Function.instFunLikeEmbedding","Membership.mem","RelHom.instFunLike","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.injective","SimpleGraph.Copy.instFunLike","SimpleGraph.Copy.toHom","SimpleGraph.Hom","Sum","Sum.inl","Sum.inl_injective","completeBipartiteGraph"],"value_dag_size":703,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Function.Embedding","Function.Embedding.mk","Function.Injective.comp","Function.comp","Function.instFunLikeEmbedding","Membership.mem","RelHom.instFunLike","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.injective","SimpleGraph.Copy.instFunLike","SimpleGraph.Copy.toHom","SimpleGraph.Hom","Sum","Sum.inl","Sum.inl_injective","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff.match_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":553,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Function.Embedding","Function.Embedding.mk","Function.Injective.comp","Function.comp","Function.instFunLikeEmbedding","Membership.mem","RelHom.instFunLike","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.injective","SimpleGraph.Copy.instFunLike","SimpleGraph.Copy.toHom","SimpleGraph.Hom","Sum","Sum.inr","Sum.inr_injective","completeBipartiteGraph"],"value_dag_size":703,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Function.Embedding","Function.Embedding.mk","Function.Injective.comp","Function.comp","Function.instFunLikeEmbedding","Membership.mem","RelHom.instFunLike","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.injective","SimpleGraph.Copy.instFunLike","SimpleGraph.Copy.toHom","SimpleGraph.Hom","Sum","Sum.inr","Sum.inr_injective","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.degree_le_between_add._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.degree_le_between_add","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.degree_le_between_add_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.degree_le_between_add_compl","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.edgeSet_completeBipartiteGraph._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.edgeSet_completeBipartiteGraph","reducibility":null,"statement_dag_size":155,"type_refs":["DFunLike.coe","Eq","LE.le","Membership.mem","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sum","Sum.inl","Sum.inr","Sym2","Sym2.Rel","Sym2.mk","completeBipartiteGraph","instFunLikeOrderEmbedding"],"value_dag_size":558,"value_refs":["And","Bool","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","LE.le","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.mem_edgeSet","Sum","Sum.inl","Sum.inr","Sum.isLeft","Sum.isLeft_eq_false","Sum.isLeft_inl","Sum.isLeft_inr","Sum.isRight","Sym2","Sym2.Rel","Sym2.mk","True","completeBipartiteGraph","completeBipartiteGraph_adj","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.edgeSet_completeBipartiteGraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.edgeSet_completeBipartiteGraph","reducibility":"abbrev","statement_dag_size":190,"type_refs":["Eq","Exists.intro","Membership.mem","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Set.range","Sum","Sum.inl","Sum.inr","Sym2","Sym2.mk"],"value_dag_size":317,"value_refs":["Eq","Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Set.range","Sum","Sum.inl","Sum.inr","Sym2","Sym2.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.encard_edgeSet_completeBipartiteGraph._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.encard_edgeSet_completeBipartiteGraph","reducibility":null,"statement_dag_size":56,"type_refs":["Function.Injective","Prod","Prod.fst","Prod.mk","Prod.snd","Quot","Quot.mk","Sum","Sum.inl","Sum.inr","Sym2.Rel"],"value_dag_size":940,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Function.Injective","Function.Injective.eq_1","HEq","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.of_forall_eq_false","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","Sum","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_true","heq_eq_eq","id","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_bipartiteDoubleCover._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_bipartiteDoubleCover","reducibility":null,"statement_dag_size":73,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":76,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_iff_forall_ne","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_sum_degrees_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_sum_degrees_eq","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_support_subset.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartiteWith_support_subset","reducibility":"abbrev","statement_dag_size":120,"type_refs":["Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support","SimpleGraph.support.match_1"],"value_dag_size":167,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support","SimpleGraph.support.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Bipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartite_iff_exists_isBipartiteWith.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.isBipartite_iff_exists_isBipartiteWith","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Exists","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"],"value_dag_size":129,"value_refs":["Exists","Exists.casesOn","Exists.intro","Set","SimpleGraph","SimpleGraph.IsBipartiteWith"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":38,"value_refs":["Eq.symm","Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":30,"value_refs":["And","Eq.symm","Or","and_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj'","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":78,"value_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj'","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":25,"value_refs":["And","Or","and_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj_mul_iff_right._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_adj_mul_iff_right","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":78,"value_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj'","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_erase_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_erase_one","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":78,"value_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj'","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_gc._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_gc","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HMul.hMul","LE.le","Membership.mem","Mul","Ne","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE","SimpleGraph.mulCayley","instHMul"],"value_dag_size":80,"value_refs":["HMul.hMul","LE.le","Membership.mem","Mul","Ne","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instLE","SimpleGraph.mulCayley","SimpleGraph.mulCayley_le_iff","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_insert_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_insert_one","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Insert.insert","Set","Set.instInsert","Set.instSingletonSet","Set.instUnion","Singleton.singleton","Union.union"],"value_dag_size":41,"value_refs":["Eq.symm","Insert.insert","Set","Set.instInsert","Set.instSingletonSet","Set.instUnion","Set.union_singleton","Singleton.singleton","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_insert_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_insert_one","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","MulOne.toMul","MulOne.toOne","MulOneClass","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","SDiff.sdiff","Set","Set.instSDiff","Set.instSingletonSet","SimpleGraph","SimpleGraph.mulCayley","Singleton.singleton"],"value_dag_size":60,"value_refs":["Eq.symm","MulOne.toMul","MulOne.toOne","MulOneClass","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","SDiff.sdiff","Set","Set.instSDiff","Set.instSingletonSet","SimpleGraph","SimpleGraph.mulCayley","SimpleGraph.mulCayley_erase_one","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_inv._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_inv","reducibility":null,"statement_dag_size":93,"type_refs":["And","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":98,"value_refs":["And","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_inv._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_inv","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":78,"value_refs":["And","Eq","Exists","HMul.hMul","Membership.mem","Mul","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj'","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_le_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Cayley","name":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_univ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_univ","reducibility":null,"statement_dag_size":93,"type_refs":["And","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","instHMul"],"value_dag_size":98,"value_refs":["And","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Ne","Or","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.mulCayley","SimpleGraph.mulCayley_adj","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Circulant","name":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_erase_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_erase_zero","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.fromRel"],"value_dag_size":43,"value_refs":["And","Ne","Or","SimpleGraph.Adj","SimpleGraph.fromRel","SimpleGraph.fromRel_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Circulant","name":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_erase_zero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_erase_zero","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Circulant","name":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm","reducibility":null,"statement_dag_size":79,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","And","Eq","HSub.hSub","Iff","Membership.mem","Not","Or","Set","Set.instMembership","SubNegMonoid.toSub","SubtractionMonoid.toSubNegMonoid","instHSub"],"value_dag_size":837,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","HSub.hSub","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_assoc","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.instMembership","SubNegMonoid.toSub","SubtractionMonoid.toSubNegMonoid","True","True.intro","congr","congrArg","eq_false","eq_true","id","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Circulant","name":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Circulant","name":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.circulantGraph_eq_symm","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Membership.mem","Neg","Neg.neg","Set","Set.instMembership","Set.neg"],"value_dag_size":43,"value_refs":["Membership.mem","Neg","Neg.neg","Set","Set.instMembership","Set.mem_neg","Set.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Ne","Not","ne_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":32,"type_refs":["DecidableEq","Eq","False","SimpleGraph","SimpleGraph.Adj","SimpleGraph.replaceVertex"],"value_dag_size":35,"value_refs":["DecidableEq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.not_adj_replaceVertex_same","SimpleGraph.replaceVertex","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":37,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":40,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":25,"value_refs":["Eq","Ne","Not","not_ne_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","False","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":21,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.irrefl","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.CliqueFree.replaceVertex","reducibility":"abbrev","statement_dag_size":118,"type_refs":["DFunLike.coe","DecidableEq","Fin","Function.Embedding","Function.instFunLikeEmbedding","Iff","Nat","RelEmbedding.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Embedding","SimpleGraph.completeGraph","SimpleGraph.replaceVertex"],"value_dag_size":179,"value_refs":["DFunLike.coe","DecidableEq","Fin","Function.Embedding","Function.instFunLikeEmbedding","Iff","Nat","RelEmbedding.casesOn","RelEmbedding.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Embedding","SimpleGraph.completeGraph","SimpleGraph.replaceVertex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce","reducibility":"abbrev","statement_dag_size":191,"type_refs":["Eq.refl","Exists","Exists.intro","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype","Subtype.mk"],"value_dag_size":228,"value_refs":["Eq.refl","Exists","Exists.casesOn","Exists.intro","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.sdiff_of_sup_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.sdiff_of_sup_edge","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax"],"value_dag_size":46,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax","SimpleGraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.sdiff_of_sup_edge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.sdiff_of_sup_edge","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsIndepSet.card_le_indepNum._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsIndepSet.card_le_indepNum","reducibility":null,"statement_dag_size":36,"type_refs":["Compl.compl","Eq","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl"],"value_dag_size":46,"value_refs":["Compl.compl","Eq.symm","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl","SimpleGraph.isNClique_compl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsNClique.mono._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsNClique.mono","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.card_cliqueFinset_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.card_cliqueFinset_le","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Finset.powersetCard","Finset.univ","Fintype","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":51,"value_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Finset.mem_powersetCard_univ","Finset.powersetCard","Finset.univ","Fintype","Membership.mem","Nat","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFinset_eq_empty_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFinset_eq_empty_iff","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_empty._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_empty","reducibility":null,"statement_dag_size":29,"type_refs":["EmptyCollection.emptyCollection","Eq","LE.le","Set","Set.instEmptyCollection","Set.instLE"],"value_dag_size":31,"value_refs":["EmptyCollection.emptyCollection","Eq","LE.le","Set","Set.instEmptyCollection","Set.instLE","Set.subset_empty_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_singleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_singleton","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_singleton._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_singleton","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton"],"value_dag_size":65,"value_refs":["Eq","Eq.symm","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.subset_singleton_iff'","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":67,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":71,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.card_eq_two","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","Insert.insert","LE.le","Membership.mem","Set","Set.instInsert","Set.instLE","Set.instMembership"],"value_dag_size":50,"value_refs":["And","Insert.insert","LE.le","Membership.mem","Set","Set.insert_subset_iff","Set.instInsert","Set.instLE","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFreeOn_two","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":40,"value_refs":["LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.singleton_subset_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_induce_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_induce_iff","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Finset","Finset.map","Function.Embedding.subtype","Membership.mem","Nat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.induce","Subtype"],"value_dag_size":68,"value_refs":["Finset","Finset.map","Function.Embedding.subtype","Membership.mem","Nat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.induce","SimpleGraph.isNClique_induce_iff","Subtype","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_one","reducibility":null,"statement_dag_size":12,"type_refs":["Eq","False","IsEmpty"],"value_dag_size":13,"value_refs":["False","IsEmpty","isEmpty_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two","reducibility":null,"statement_dag_size":46,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","EmptyCollection.emptyCollection","Eq","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","Sym2"],"value_dag_size":54,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","EmptyCollection.emptyCollection","Eq","Eq.symm","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.edgeSet_eq_empty","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueNum_induce_le.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueNum_induce_le","reducibility":"abbrev","statement_dag_size":95,"type_refs":["Exists","Exists.intro","Finset","Set","Set.Elem","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueNum","SimpleGraph.induce"],"value_dag_size":119,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Set","Set.Elem","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueNum","SimpleGraph.induce"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueSet_eq_empty_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueSet_eq_empty_iff","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueSet_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueSet_one","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.exists_isNIndepSet_indepNum._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.exists_isNIndepSet_indepNum","reducibility":null,"statement_dag_size":36,"type_refs":["Compl.compl","Eq","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl"],"value_dag_size":46,"value_refs":["Compl.compl","Eq.symm","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl","SimpleGraph.isNClique_compl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.finite_cliqueNum_bddAbove","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph","reducibility":null,"statement_dag_size":33,"type_refs":["BddAbove","Exists","Finite","Finset","Nat","Set.ofPred","SimpleGraph","SimpleGraph.IsNClique","instLENat"],"value_dag_size":194,"value_refs":["And","And.right","Eq","Eq.mp","Eq.mpr","Eq.symm","Exists","Exists.casesOn","Exists.intro","Finite","Finset","Finset.card","Finset.card_le_card","Finset.instSetLike","Finset.subset_univ","Finset.univ","Fintype","Fintype.card","Fintype.ofFinite","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","congrArg","id","instLENat","propext","upperBounds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three","reducibility":null,"statement_dag_size":84,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three","reducibility":"abbrev","statement_dag_size":420,"type_refs":["And","And.intro","Classical.propDecidable","Eq","Exists","Exists.intro","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","SimpleGraph","SimpleGraph.Adj","Singleton.singleton"],"value_dag_size":1227,"value_refs":["And","And.casesOn","And.intro","Classical.propDecidable","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","SimpleGraph","SimpleGraph.Adj","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_iff_exists_cycle_length_three","reducibility":"abbrev","statement_dag_size":398,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List.Nodup","List.tail","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","instOfNatNat"],"value_dag_size":5644,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","False","False.elim","HAdd.hAdd","HEq","HEq.refl","List.Nodup","List.tail","Nat","Nat.Internal.elimOffset","Nat.ctorIdx","Nat.succ","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.IsTrail.casesOn","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","Sym2","eq_of_heq","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_triple_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_triple_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_triple_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.is3Clique_triple_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_rotate","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_compl","reducibility":null,"statement_dag_size":40,"type_refs":["And","Compl.compl","Eq","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instCompl"],"value_dag_size":44,"value_refs":["And","Compl.compl","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.compl_adj","SimpleGraph.instCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_map_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_map_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Set","Set.Pairwise","Set.Subsingleton","SimpleGraph","SimpleGraph.Adj","True"],"value_dag_size":28,"value_refs":["Set","Set.Subsingleton","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsClique.of_subsingleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_map_image_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_map_image_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Set","Set.Pairwise","Set.Subsingleton","SimpleGraph","SimpleGraph.Adj","True"],"value_dag_size":28,"value_refs":["Set","Set.Subsingleton","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsClique.of_subsingleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_range_copy_top.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isClique_range_copy_top","reducibility":"abbrev","statement_dag_size":187,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Exists.intro","Membership.mem","Set","Set.instMembership","Set.range","SimpleGraph","SimpleGraph.Copy","SimpleGraph.Copy.instFunLike","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":237,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.instMembership","Set.range","SimpleGraph","SimpleGraph.Copy","SimpleGraph.Copy.instFunLike","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isIndepSet_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isIndepSet_compl","reducibility":null,"statement_dag_size":40,"type_refs":["And","Compl.compl","Eq","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instCompl"],"value_dag_size":44,"value_refs":["And","Compl.compl","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.compl_adj","SimpleGraph.instCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isIndepSet_neighborSet_of_triangleFree._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isIndepSet_neighborSet_of_triangleFree","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalClique_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalClique_compl","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsIndepSet"],"value_dag_size":56,"value_refs":["And","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.isMaximalIndepSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalClique_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalClique_compl","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsClique"],"value_dag_size":56,"value_refs":["And","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.isMaximalClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalIndepSet_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalIndepSet_compl","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsIndepSet"],"value_dag_size":56,"value_refs":["And","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.isMaximalIndepSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalIndepSet_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximalIndepSet_compl","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsClique"],"value_dag_size":56,"value_refs":["And","LE.le","Maximal","Set","Set.instLE","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.isMaximalClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumClique_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumClique_compl","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsMaximumIndepSet","instLENat"],"value_dag_size":68,"value_refs":["And","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsMaximumIndepSet","SimpleGraph.isMaximumIndepSet_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumClique_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumClique_compl","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsMaximumClique","instLENat"],"value_dag_size":68,"value_refs":["And","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsMaximumClique","SimpleGraph.isMaximumClique_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumIndepSet_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumIndepSet_compl","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsMaximumIndepSet","instLENat"],"value_dag_size":68,"value_refs":["And","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsMaximumIndepSet","SimpleGraph.isMaximumIndepSet_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumIndepSet_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isMaximumIndepSet_compl","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsMaximumClique","instLENat"],"value_dag_size":68,"value_refs":["And","Finite","Finset","Finset.card","Finset.instSetLike","LE.le","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsMaximumClique","SimpleGraph.isMaximumClique_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_compl","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_empty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_empty","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_empty._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_empty","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_induce_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_induce_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_induce_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_induce_iff","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.induce","Subtype","Subtype.val"],"value_dag_size":61,"value_refs":["Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.induce","SimpleGraph.isClique_induce_iff","Subtype","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_map_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_map_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Finset","Finset.card","Finset.card_eq_one","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_one","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_singleton._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_singleton","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_singleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_singleton","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNClique_zero","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNIndepSet_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNIndepSet_compl","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsNIndepSet"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsNIndepSet","SimpleGraph.isNIndepSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNIndepSet_induce._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.isNIndepSet_induce","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsNIndepSet"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsNIndepSet","SimpleGraph.isNIndepSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_card_eq_indepNum._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_card_eq_indepNum","reducibility":null,"statement_dag_size":36,"type_refs":["Compl.compl","Eq","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl"],"value_dag_size":46,"value_refs":["Compl.compl","Eq.symm","Finset","Nat","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.IsNIndepSet","SimpleGraph.instCompl","SimpleGraph.isNClique_compl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_exists._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_exists","reducibility":null,"statement_dag_size":37,"type_refs":["Compl.compl","Eq","Finite","Finset","SimpleGraph","SimpleGraph.IsMaximumClique","SimpleGraph.IsMaximumIndepSet","SimpleGraph.instCompl"],"value_dag_size":47,"value_refs":["Compl.compl","Eq.symm","Finite","Finset","SimpleGraph","SimpleGraph.IsMaximumClique","SimpleGraph.IsMaximumIndepSet","SimpleGraph.instCompl","SimpleGraph.isMaximumClique_compl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_exists._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_exists","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Finite","Finset","SimpleGraph","SimpleGraph.IsMaximumClique","True"],"value_dag_size":30,"value_refs":["Exists","Finite","Finset","SimpleGraph","SimpleGraph.IsMaximumClique","SimpleGraph.maximumClique_exists","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Clique","name":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.not_isClique_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.not_isClique_iff","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Set","Set.Pairwise","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsClique"],"value_dag_size":30,"value_refs":["Set","Set.Pairwise","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsClique","SimpleGraph.isClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.Coloring.even_length_iff_congr._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.Coloring.even_length_iff_congr","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Even","HAdd.hAdd","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":34,"value_refs":["Even","HAdd.hAdd","Nat","Nat.even_add_one","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.chromaticNumber_cycleGraph_of_even._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.chromaticNumber_cycleGraph_of_even","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin","Fin.instSub","Fin.val","HSub.hSub","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","instHSub","instOfNatNat"],"value_dag_size":60,"value_refs":["Eq","Fin","Fin.instSub","Fin.val","HSub.hSub","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph_adj'","instHSub","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.chromaticNumber_pathGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.chromaticNumber_pathGraph","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.pathGraph","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.pathGraph","SimpleGraph.pathGraph_adj","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Decidable","Decidable.decide","Eq","Iff"],"value_dag_size":33,"value_refs":["Bool","Decidable","Decidable.decide","Eq","Iff","decide_eq_decide","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph_adj","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even","reducibility":"abbrev","statement_dag_size":134,"type_refs":["Even","Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":240,"value_refs":["Even","Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":38,"type_refs":["Fin","Fin.val","HMod.hMod","LT.lt","Nat","Nat.instMod","OfNat.ofNat","instHMod","instLTNat","instOfNatNat"],"value_dag_size":516,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.finVal","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.instMod","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HMod.hMod","Iff","Nat","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":1445,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.eq_congr","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_false","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":103,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","instSubNat"],"value_dag_size":1667,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","instSubNat"],"value_dag_size":983,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Even","HMod.hMod","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq","Even","HMod.hMod","Nat","Nat.even_iff","Nat.instMod","OfNat.ofNat","instAddNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Even","False","Nat","OfNat.ofNat","instAddNat","instOfNatNat"],"value_dag_size":17,"value_refs":["Even","Nat","Nat.not_even_one","OfNat.ofNat","eq_false","instAddNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":13,"type_refs":["Eq","False","Iff","Not"],"value_dag_size":13,"value_refs":["Iff","Not","eq_false","not_iff_self"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":13,"type_refs":["Eq","False","Iff","Not"],"value_dag_size":13,"value_refs":["Iff","Not","eq_false","iff_not_self"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLTInt","Int.ofNat_lt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._simp_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring.match_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring","reducibility":"abbrev","statement_dag_size":136,"type_refs":["Fin","HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":242,"value_refs":["Fin","HAdd.hAdd","LE.le","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.pathGraph.bicoloring._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.pathGraph.bicoloring","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Iff","Not"],"value_dag_size":20,"value_refs":["Iff","Not","not_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.pathGraph.bicoloring._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.pathGraph.bicoloring","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HAdd.hAdd","HMod.hMod","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instOfNatNat"],"value_dag_size":54,"value_refs":["Eq","HAdd.hAdd","HMod.hMod","Nat","Nat.instMod","Nat.succ_mod_two_eq_zero_iff","OfNat.ofNat","instAddNat","instHAdd","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":28,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":10,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":80,"type_refs":["Membership.mem","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Reachable","Subtype","Subtype.mk"],"value_dag_size":85,"value_refs":["Membership.mem","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Connected.preconnected","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.connected_toSimpleGraph","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":222,"type_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","Classical.choice","Eq","HAdd.hAdd","HMod.hMod","Membership.mem","Nat","Nat.instAddCommSemigroup","Nat.instMod","Nonempty.some","OfNat.ofNat","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Connected.preconnected","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.connected_toSimpleGraph","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","Subtype","Subtype.mk","instHAdd","instHMod","instOfNatNat"],"value_dag_size":1069,"value_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","Bool","Bool.true","Classical.byContradiction","Classical.choice","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instAddCommSemigroup","Nat.instMod","NatCast.natCast","Neg.neg","Nonempty.some","Not","OfNat.ofNat","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Connected.preconnected","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.connected_toSimpleGraph","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.Walk.length","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._proof_1_5","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Even","Nat","Nat.instSemiring","Not","Odd","instAddNat"],"value_dag_size":27,"value_refs":["Eq.symm","Even","Nat","Nat.instSemiring","Nat.not_odd_iff_even","Not","Odd","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Fin","Fin.NatCast.instNatCast","Fin.val","HMod.hMod","Nat","Nat.cast","Nat.instMod","NeZero","Zero.ofOfNat0","instHMod","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq.symm","Fin","Fin.NatCast.instNatCast","Fin.val","Fin.val_natCast","HMod.hMod","Nat","Nat.cast","Nat.instMod","NeZero","Zero.ofOfNat0","instHMod","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.two_colorable_iff_forall_loop_even","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Fin","Fin.NatCast.instNatCast","Fin.ofNat","Nat","Nat.cast","NeZero","Zero.ofOfNat0","instOfNatNat"],"value_dag_size":39,"value_refs":["Eq.symm","Fin","Fin.NatCast.instNatCast","Fin.ofNat","Fin.ofNat_eq_cast","Nat","Nat.cast","NeZero","Zero.ofOfNat0","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.ext_get.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.ext_get","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Subtype.mk","Sym2"],"value_dag_size":88,"value_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Subtype.casesOn","Subtype.mk","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph","reducibility":null,"statement_dag_size":142,"type_refs":["DFunLike.coe","Eq","Exists","Iff","LE.le","Membership.mem","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype.mk","Sym2.Rel","instFunLikeOrderEmbedding"],"value_dag_size":630,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","LE.le","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype.mk","Sym2.Rel","True","True.intro","congr","congrArg","eq_false","eq_true","forall_congr","id","instFunLikeOrderEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Exists","SimpleGraph","SimpleGraph.Adj","SimpleGraph.supSet","iSup"],"value_dag_size":47,"value_refs":["Exists","SimpleGraph","SimpleGraph.Adj","SimpleGraph.iSup_adj","SimpleGraph.supSet","iSup","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.iSup_labelGraph","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.edgeSet","Subtype.mk","Sym2","Sym2.mk"],"value_dag_size":85,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.EdgeLabeling.labelGraph_adj","SimpleGraph.edgeSet","Subtype.mk","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":101,"type_refs":["DFunLike.coe","LE.le","Membership.mem","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2.Rel","instFunLikeOrderEmbedding"],"value_dag_size":119,"value_refs":["DFunLike.coe","Iff.mpr","Iff.of_eq","LE.le","Membership.mem","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._simp_1_2","instFunLikeOrderEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":22,"type_refs":["SimpleGraph","SimpleGraph.Adj"],"value_dag_size":35,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":208,"type_refs":["And","DFunLike.coe","Eq","Exists","Iff","Iff.mpr","Iff.of_eq","LE.le","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype.mk","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._simp_1_2","instFunLikeOrderEmbedding"],"value_dag_size":1367,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","Iff.mpr","Iff.of_eq","LE.le","Lean.Grind._simp_1","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.Elem","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.EdgeLabeling","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype","Subtype.mk","Sym2","Sym2.Rel","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._simp_1_2","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","exists_prop_congr","id","instFunLikeOrderEmbedding","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Membership.mem","Ne","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.fromEdgeSet","Sym2","Sym2.mk"],"value_dag_size":51,"value_refs":["And","Membership.mem","Ne","Set","Set.instMembership","SimpleGraph.Adj","SimpleGraph.fromEdgeSet","SimpleGraph.fromEdgeSet_adj","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_le._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_le","reducibility":null,"statement_dag_size":22,"type_refs":["SimpleGraph","SimpleGraph.Adj"],"value_dag_size":35,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_le._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_le","reducibility":null,"statement_dag_size":39,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph"],"value_dag_size":365,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Iff.mpr","Iff.of_eq","LE.le","Lean.Grind.iff_eq","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.EdgeLabeling.labelGraph_adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype.mk","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.labelGraph_le._proof_1_1","congrArg","eq_false","eq_true","exists_prop_congr","id","instFunLikeOrderEmbedding","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.mk._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.mk","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph","reducibility":null,"statement_dag_size":22,"type_refs":["SimpleGraph","SimpleGraph.Adj"],"value_dag_size":35,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph","reducibility":null,"statement_dag_size":54,"type_refs":["Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph"],"value_dag_size":765,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Iff.mpr","Iff.of_eq","LE.le","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_not","Membership.mem","Ne","Not","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.Elem","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.EdgeLabeling.labelGraph_adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Subtype","Subtype.mk","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph._proof_1_1","congrArg","eq_false","eq_of_heq","eq_true","exists_prop_congr","id","instFunLikeOrderEmbedding","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_adj","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.edgeSet","Subtype.mk","Sym2","Sym2.mk"],"value_dag_size":85,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.EdgeLabeling.labelGraph_adj","SimpleGraph.edgeSet","Subtype.mk","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling","reducibility":null,"statement_dag_size":36,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":107,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.completeAtomicBooleanAlgebra","Top.top","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling","reducibility":null,"statement_dag_size":133,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DecidableEq","Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.EdgeLabeling.get","SimpleGraph.EdgeLabeling.instDecidableRelAdjLabelGraphOfDecidableEq","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.Top.adjDecidable","SimpleGraph.TopEdgeLabeling","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.toTopEdgeLabeling","Top.top","instDecidableEqFin","instOfNatNat"],"value_dag_size":1278,"value_refs":["Bool","Bool.true","BooleanAlgebra.toTop","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.instOfNat","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper","Lean.Grind.ToInt.ofNat_eq","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instOfNatFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.EdgeLabeling.get","SimpleGraph.EdgeLabeling.instDecidableRelAdjLabelGraphOfDecidableEq","SimpleGraph.EdgeLabeling.labelGraph","SimpleGraph.Top.adjDecidable","SimpleGraph.TopEdgeLabeling","SimpleGraph.TopEdgeLabeling.labelGraph_adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.toTopEdgeLabeling","SimpleGraph.toTopEdgeLabeling_get","Top.top","True","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling._proof_1_3","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","forall_not_of_not_exists","id","instDecidableEqFin","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.toTopEdgeLabeling_labelGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.toTopEdgeLabeling_labelGraph","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.toTopEdgeLabeling_labelGraph_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling.0.SimpleGraph.toTopEdgeLabeling_labelGraph_compl","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.chromaticNumber_pos._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.chromaticNumber_pos","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.cliqueFree","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.map.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Colorable.map","reducibility":"abbrev","statement_dag_size":237,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Ne","Relation.Map","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map"],"value_dag_size":614,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Ne","Relation.Map","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Coloring.surjOn_of_card_le_isClique._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.Coloring.surjOn_of_card_le_isClique","reducibility":null,"statement_dag_size":46,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Set","Set.Elem","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.induce","Top.top"],"value_dag_size":55,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.symm","Set","Set.Elem","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.induce","SimpleGraph.induce_eq_top","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.card_le_chromaticNumber_iff_forall_surjective._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.card_le_chromaticNumber_iff_forall_surjective","reducibility":null,"statement_dag_size":63,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf"],"value_dag_size":68,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf","le_iInf_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.card_le_chromaticNumber_iff_forall_surjective._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.card_le_chromaticNumber_iff_forall_surjective","reducibility":null,"statement_dag_size":95,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","LE.le","Nat","Nat.cast","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat"],"value_dag_size":103,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","LE.le","Nat","Nat.cast","Nat.cast_le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.chromaticNumber_le_of_forall_imp._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.chromaticNumber_le_of_forall_imp","reducibility":null,"statement_dag_size":63,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf"],"value_dag_size":68,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf","le_iInf_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.cliqueNum_le_chromaticNumber.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.cliqueNum_le_chromaticNumber","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Exists","Exists.intro","Finset","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueNum"],"value_dag_size":86,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_iff_exists_bdd_nat_coloring._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_iff_exists_bdd_nat_coloring","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":43,"value_refs":["Eq","Fin","Fin.mk","Fin.mk_eq_mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_iff_forall_connectedComponent.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_iff_forall_connectedComponent","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Fin","Nat","Nonempty.intro","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring"],"value_dag_size":52,"value_refs":["Fin","Nat","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_one_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_one_iff","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Fin","Nat","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instOfNatNat"],"value_dag_size":56,"value_refs":["Fin","Nat","Nonempty.casesOn","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_zero_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.colorable_zero_iff","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Fin","Nat","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instOfNatNat"],"value_dag_size":56,"value_refs":["Fin","Nat","Nonempty.casesOn","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card","reducibility":null,"statement_dag_size":50,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":123,"value_refs":["And","Classical.propDecidable","Eq","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase._simp_1","Finset.mem_univ._simp_1","Finset.univ","Fintype","Membership.mem","Not","SetLike.instMembership","True","and_self","congr","congrArg","eq_false","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card","reducibility":null,"statement_dag_size":49,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":123,"value_refs":["And","Classical.propDecidable","Eq","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase._simp_1","Finset.mem_univ._simp_1","Finset.univ","Fintype","Membership.mem","Ne","Not","SetLike.instMembership","True","and_self","congr","congrArg","eq_false","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card","reducibility":null,"statement_dag_size":64,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":149,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne'","True","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_1","eq_false","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card","reducibility":null,"statement_dag_size":306,"type_refs":["And","Classical.propDecidable","Eq","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase._simp_1","Finset.mem_univ._simp_1","Finset.univ","Fintype","Membership.mem","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","Subtype.mk","True","and_self","congr","congrArg","dite","eq_false","instDecidableNot","not_false_eq_true","of_eq_true"],"value_dag_size":1102,"value_refs":["And","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase._simp_1","Finset.mem_univ._simp_1","Finset.univ","Fintype","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_not","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne'","SimpleGraph.adj_symm","Subtype","Subtype.mk","Subtype.mk.inj","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_3","and_self","congr","congrArg","dite","eq_false","eq_of_heq","eq_true","id","instDecidableNot","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.eq_top_of_chromaticNumber_eq_card","reducibility":null,"statement_dag_size":47,"type_refs":["False","Fintype","Fintype.card","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":620,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","Fintype.card","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instInfiniteColoringOfNonempty._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instInfiniteColoringOfNonempty","reducibility":null,"statement_dag_size":118,"type_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Hom","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.completeGraph","Top.top"],"value_dag_size":350,"value_refs":["BooleanAlgebra.toTop","Classical.byContradiction","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.Perm","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_def","EquivLike.toFunLike","False","Not","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Hom","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.completeGraph","Top.top","True","True.intro","congrArg","eq_false","eq_self","eq_true","id","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":null,"statement_dag_size":179,"type_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","Ne","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Hom","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.completeGraph","Top.top"],"value_dag_size":359,"value_refs":["BooleanAlgebra.toTop","Classical.byContradiction","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.Perm","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_def","EquivLike.toFunLike","False","Ne","Not","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Hom","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.completeGraph","Top.top","True","True.intro","congrArg","eq_false","eq_self","eq_true","id","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":null,"statement_dag_size":105,"type_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","Function.Injective","RelHom","RelHom.instFunLike","RelIso.toEquiv","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":87,"value_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv.injective","Equiv.swap","RelHom","RelHom.instFunLike","RelIso.toEquiv","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":null,"statement_dag_size":114,"type_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","Iff","RelHom","RelHom.instFunLike","RelIso.toEquiv","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":89,"value_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv.swap","RelHom","RelHom.instFunLike","RelIso.map_rel_iff'","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":null,"statement_dag_size":168,"type_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","Function.Embedding","Function.Embedding.mk","Function.instFunLikeEmbedding","RelEmbedding.mk","RelEmbedding.toEmbedding","RelHom","RelHom.instFunLike","RelIso.toEquiv","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_8"],"value_dag_size":177,"value_refs":["BooleanAlgebra.toTop","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Equiv","Equiv.injective","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","Function.Embedding.mk","RelEmbedding.mk","RelEmbedding.toRelHom._proof_1","RelHom","RelHom.instFunLike","RelIso.map_rel_iff'","RelIso.toEquiv","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.Iso.completeGraph","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Nonempty","Nonempty.intro","SimpleGraph","SimpleGraph.Coloring"],"value_dag_size":49,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Coloring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty.match_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty.match_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.instNontrivialColoringOfNonempty","reducibility":"abbrev","statement_dag_size":139,"type_refs":["DFunLike.coe","Exists","Exists.intro","Ne","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.completeGraph"],"value_dag_size":175,"value_refs":["DFunLike.coe","Exists","Exists.casesOn","Exists.intro","Ne","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.completeGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.le_chromaticNumber_iff_coloring._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.le_chromaticNumber_iff_coloring","reducibility":null,"statement_dag_size":42,"type_refs":["ENat","ENat.instNatCast","Eq","LE.le","Nat","Nat.cast","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.chromaticNumber","instLEENat","instLENat"],"value_dag_size":45,"value_refs":["ENat","ENat.instNatCast","LE.le","Nat","Nat.cast","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.chromaticNumber","SimpleGraph.le_chromaticNumber_iff_colorable","instLEENat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex","name":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.le_chromaticNumber_iff_forall_surjective._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex.0.SimpleGraph.le_chromaticNumber_iff_forall_surjective","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","ENat","ENat.instNatCast","Eq","Fintype","Fintype.card","Function.Surjective","LE.le","Nat.cast","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.chromaticNumber","SimpleGraph.completeGraph","instLEENat"],"value_dag_size":80,"value_refs":["DFunLike.coe","ENat","ENat.instNatCast","Eq.symm","Fintype","Fintype.card","Function.Surjective","LE.le","Nat.cast","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Coloring","SimpleGraph.card_le_chromaticNumber_iff_forall_surjective","SimpleGraph.chromaticNumber","SimpleGraph.completeGraph","instLEENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.CompleteEquipartiteSubgraph.card_verts._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.CompleteEquipartiteSubgraph.card_verts","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HMul.hMul","IsRightCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul"],"value_dag_size":71,"value_refs":["Eq","HMul.hMul","IsRightCancelMulZero","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Or","Zero.toOfNat0","instHMul","mul_eq_mul_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.CompleteEquipartiteSubgraph.ext.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.CompleteEquipartiteSubgraph.ext","reducibility":"abbrev","statement_dag_size":116,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Membership.mem","Nat","OfNat.ofNat","Or","Set.Pairwise","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.mk","SimpleGraph.IsCompleteBetween","instOfNatNat"],"value_dag_size":183,"value_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Membership.mem","Nat","OfNat.ofNat","Or","Set.Pairwise","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.casesOn","SimpleGraph.CompleteEquipartiteSubgraph.mk","SimpleGraph.IsCompleteBetween","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso._simp_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap"],"value_dag_size":45,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.comap_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso._simp_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso","reducibility":null,"statement_dag_size":37,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":40,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso._simp_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsCompleteMultipartite.iso","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Quotient","Quotient.mk","Setoid","Setoid.r"],"value_dag_size":37,"value_refs":["Eq","Quotient","Quotient.eq","Quotient.mk","Setoid","Setoid.r","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding._simp_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding","reducibility":null,"statement_dag_size":40,"type_refs":["And","Compl.compl","Eq","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instCompl"],"value_dag_size":44,"value_refs":["And","Compl.compl","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.compl_adj","SimpleGraph.instCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding._simp_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.pathGraph","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.pathGraph","SimpleGraph.pathGraph_adj","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding._simp_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq.refl","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq.refl","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":57,"value_refs":["Eq.refl","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding","reducibility":"abbrev","statement_dag_size":72,"type_refs":["And","And.intro","Not","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":88,"value_refs":["And","And.casesOn","And.intro","Not","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph.isCompleteMultipartite._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph.isCompleteMultipartite","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_eq_bot_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_eq_bot_iff","reducibility":"abbrev","statement_dag_size":93,"type_refs":["Exists.intro","Fin","Membership.mem","Nat","Prod","Set","Set.Nonempty","Set.instMembership","SimpleGraph.completeEquipartiteGraph","SimpleGraph.edgeSet","Sym2"],"value_dag_size":118,"value_refs":["Exists.casesOn","Exists.intro","Fin","Membership.mem","Nat","Prod","Set","Set.Nonempty","Set.instMembership","SimpleGraph.completeEquipartiteGraph","SimpleGraph.edgeSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_eq_bot_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_eq_bot_iff","reducibility":"abbrev","statement_dag_size":83,"type_refs":["And","And.intro","Exists","Exists.intro","Fin","Nat","Ne","Nonempty","Nonempty.intro","Nontrivial","Nontrivial.mk"],"value_dag_size":218,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Fin","Nat","Ne","Nonempty","Nonempty.casesOn","Nonempty.intro","Nontrivial","Nontrivial.casesOn","Nontrivial.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_isContained_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Fin","Nat","Nonempty.intro","Prod","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeEquipartiteGraph"],"value_dag_size":80,"value_refs":["Fin","Nat","Nonempty.casesOn","Nonempty.intro","Prod","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeEquipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_isContained_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nat","Nonempty","Nonempty.intro","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph"],"value_dag_size":55,"value_refs":["Nat","Nonempty","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":62,"value_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Finset.mem_cons","Membership.mem","Not","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","Std.Symm"],"value_dag_size":27,"value_refs":["Std.Symm","propext","symm_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Set","SimpleGraph","SimpleGraph.IsCompleteBetween"],"value_dag_size":30,"value_refs":["Set","SimpleGraph","SimpleGraph.IsCompleteBetween","SimpleGraph.isCompleteBetween_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","IsEmpty","True"],"value_dag_size":22,"value_refs":["IsEmpty","IsEmpty.forall_iff","True","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Exists","Nonempty","True"],"value_dag_size":16,"value_refs":["Exists","Nonempty","True","exists_true_iff_nonempty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff.match_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":"abbrev","statement_dag_size":297,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instSetLike","Membership.mem","Nat","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.IsCompleteBetween"],"value_dag_size":475,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instSetLike","Membership.mem","Nat","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.IsCompleteBetween"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff.match_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff","reducibility":"abbrev","statement_dag_size":70,"type_refs":["HAdd.hAdd","Nat","Nonempty","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":79,"value_refs":["HAdd.hAdd","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.isContained_completeEquipartiteGraph_of_colorable._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.isContained_completeEquipartiteGraph_of_colorable","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.neighborFinset_completeEquipartiteGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.neighborFinset_completeEquipartiteGraph","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.neighborSet_completeEquipartiteGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.neighborSet_completeEquipartiteGraph","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.not_isCompleteMultipartite_iff_exists_isPathGraph3Compl.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.not_isCompleteMultipartite_iff_exists_isPathGraph3Compl","reducibility":"abbrev","statement_dag_size":124,"type_refs":["Exists","Exists.intro","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.mk"],"value_dag_size":279,"value_refs":["Exists","Exists.casesOn","Exists.intro","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.casesOn","SimpleGraph.IsPathGraph3Compl.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge","reducibility":null,"statement_dag_size":106,"type_refs":["List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":243,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge","reducibility":null,"statement_dag_size":168,"type_refs":["Classical.propDecidable","Eq","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":335,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk"],"value_dag_size":50,"value_refs":["Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isBridge_iff","Singleton.singleton","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Connected.connected_delete_edge_of_not_isBridge","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","reducibility":null,"statement_dag_size":83,"type_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map"],"value_dag_size":89,"value_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map","SimpleGraph.map_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap"],"value_dag_size":45,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.comap_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp.match_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp","reducibility":"abbrev","statement_dag_size":175,"type_refs":["Exists","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp"],"value_dag_size":257,"value_refs":["Exists","Exists.casesOn","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.connected_toSimpleGraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.connected_toSimpleGraph","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","Subtype","Subtype.mk"],"value_dag_size":116,"value_refs":["Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp","reducibility":null,"statement_dag_size":64,"type_refs":["DFunLike.coe","Eq","RelIso.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Iso","SimpleGraph.Reachable"],"value_dag_size":71,"value_refs":["DFunLike.coe","RelIso.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Iso","SimpleGraph.Iso.reachable_iff","SimpleGraph.Reachable","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map","reducibility":null,"statement_dag_size":88,"type_refs":["DFunLike.coe","Eq","RelIso.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Iso","SimpleGraph.Iso.symm","SimpleGraph.Reachable"],"value_dag_size":95,"value_refs":["DFunLike.coe","RelIso.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Iso","SimpleGraph.Iso.symm","SimpleGraph.Iso.symm_apply_reachable","SimpleGraph.Reachable","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff","reducibility":"abbrev","statement_dag_size":109,"type_refs":["And.intro","LE.le","Maximal","Set","Set.Elem","Set.instLE","SimpleGraph","SimpleGraph.Connected","SimpleGraph.induce"],"value_dag_size":152,"value_refs":["And.casesOn","And.intro","LE.le","Maximal","Set","Set.Elem","Set.instLE","SimpleGraph","SimpleGraph.Connected","SimpleGraph.induce"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Eq","Exists","Exists.intro","Set","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp"],"value_dag_size":100,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Set","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.maximal_connected_induce_iff","reducibility":"abbrev","statement_dag_size":56,"type_refs":["Membership.mem","Nonempty","Nonempty.intro","Set","Set.Elem","Set.instMembership","Subtype.mk"],"value_dag_size":82,"value_refs":["Membership.mem","Nonempty","Nonempty.casesOn","Nonempty.intro","Set","Set.Elem","Set.instMembership","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.supp_injective._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.supp_injective","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent","reducibility":"regular","statement_dag_size":86,"type_refs":["Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","Subtype","Subtype.mk"],"value_dag_size":111,"value_refs":["Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","reducibility":null,"statement_dag_size":27,"type_refs":["HEq","SimpleGraph","SimpleGraph.Walk"],"value_dag_size":25,"value_refs":["HEq.refl","SimpleGraph","SimpleGraph.Walk"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","reducibility":"regular","statement_dag_size":93,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","Subtype","Subtype.mk"],"value_dag_size":1274,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","InvImage","LT.lt","Membership.mem","Nat","PSigma","PSigma.casesOn","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk._sizeOf_inst","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SizeOf.sizeOf","Subtype","Subtype.mk","WellFounded.Nat.fix","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_8","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_9","instLTNat","instSizeOfDefault"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":27,"type_refs":["HEq","SimpleGraph","SimpleGraph.Walk"],"value_dag_size":25,"value_refs":["HEq.refl","SimpleGraph","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":82,"type_refs":["Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":71,"value_refs":["Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":27,"type_refs":["HEq","SimpleGraph","SimpleGraph.Walk"],"value_dag_size":25,"value_refs":["HEq.refl","SimpleGraph","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":82,"type_refs":["Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":71,"value_refs":["Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":47,"type_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"],"value_dag_size":47,"value_refs":["Membership.mem","PSigma","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":297,"type_refs":["Eq","HEq","InvImage","LT.lt","Membership.mem","Nat","PSigma","PSigma.casesOn","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk._sizeOf_inst","SimpleGraph.Walk.cons","SizeOf.sizeOf","Subtype","Subtype.mk","instLTNat","instSizeOfDefault"],"value_dag_size":1024,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.ndrec","Eq.symm","Eq.trans","HAdd.hAdd","HEq","InvImage","LT.lt","Membership.mem","Nat","Nat.instAddMonoid","Nat.instNeZeroSucc","Nat.instOne","Nat.instPartialOrder","Nat.instZeroLEOneClass","Nat.lt_add_left_iff_pos._simp_1","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk._sizeOf_inst","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons.sizeOf_spec","SimpleGraph.connectedComponentMk","SizeOf.sizeOf","Subtype","Subtype.mk","True","add_zero","congrArg","congrFun'","eq_of_heq","id","instAddNat","instHAdd","instLTNat","instOfNatNat","instSizeOfDefault","of_eq_true","zero_lt_one._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary.eq_def","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","reducibility":null,"statement_dag_size":725,"type_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","Membership.mem","PSigma","PSigma.casesOn","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_11","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_12","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_13"],"value_dag_size":5935,"value_refs":["Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HEq","HEq.refl","InvImage","LT.lt","Membership.mem","Nat","PSigma","PSigma.casesOn","PSigma.mk","PSigma.rec","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk._sizeOf_inst","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.rec","SizeOf.sizeOf","Subtype","Subtype.mk","WellFounded.Nat.fix","WellFounded.Nat.fix_eq","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.PSigma.casesOn._arg_pusher","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_11","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_12","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_8","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_9","congrArg","congrFun","congrFun'","funext","have_body_congr'","id","instLTNat","instSizeOfDefault","wfParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unsafe_rec","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","reducibility":"opaque","statement_dag_size":86,"type_refs":["Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","Subtype","Subtype.mk"],"value_dag_size":537,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unsafe_rec"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph.eq_def","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","reducibility":null,"statement_dag_size":575,"type_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._proof_1"],"value_dag_size":618,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","Membership.mem","PSigma","PSigma.mk","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary.eq_def","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Reachable"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Reachable","SimpleGraph.reachable_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge.reachable_iff_adj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge.reachable_iff_adj","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2.Rel","Sym2.mk"],"value_dag_size":217,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Not","Prod","Prod.mk","Quot","Quot.mk","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isBridge_iff","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge.reachable_iff_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.IsBridge.reachable_iff_adj","reducibility":null,"statement_dag_size":129,"type_refs":["DFunLike.coe","LE.le","LT.lt","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.deleteEdges","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.instPartialOrder","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk","instFunLikeOrderEmbedding"],"value_dag_size":668,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","Classical.byContradiction","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GeneralizedCoheytingAlgebra.toLattice","Iff","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instLE","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","Set.ssubset_def","Set.subset_def","SimpleGraph","SimpleGraph.deleteEdges","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edgeSet_deleteEdges","SimpleGraph.edgeSet_strict_mono","SimpleGraph.instLE","SimpleGraph.instPartialOrder","Singleton.singleton","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","eq_false","eq_true","id","instFunLikeOrderEmbedding","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.degree_pos_of_nontrivial._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.degree_pos_of_nontrivial","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Fintype","LT.lt","Membership.mem","Nat","OfNat.ofNat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.support","instLTNat","instOfNatNat"],"value_dag_size":61,"value_refs":["Fintype","LT.lt","Membership.mem","Nat","OfNat.ofNat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.degree","SimpleGraph.degree_pos_iff_mem_support","SimpleGraph.neighborSet","SimpleGraph.support","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.exists_adj_of_nontrivial.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.exists_adj_of_nontrivial","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Exists","Exists.intro","Ne"],"value_dag_size":62,"value_refs":["Exists","Exists.casesOn","Exists.intro","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.exists_adj_of_nontrivial.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.exists_adj_of_nontrivial","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"],"value_dag_size":55,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.induce_of_degree_eq_one._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.induce_of_degree_eq_one","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Membership.mem","Not","Set","Set.instMembership"],"value_dag_size":106,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Not","Set","Set.instMembership","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.not_isIsolated._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.not_isIsolated","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.support"],"value_dag_size":42,"value_refs":["Eq.symm","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsIsolated","SimpleGraph.mem_support_iff_not_isIsolated","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.support_eq_univ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Preconnected.support_eq_univ","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.univ"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Set","Set.eq_univ_iff_forall","Set.instMembership","Set.univ","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Reachable.mem_subgraphVerts.aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Reachable.mem_subgraphVerts","reducibility":null,"statement_dag_size":76,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.verts","SimpleGraph.Walk"],"value_dag_size":119,"value_refs":["Membership.mem","PSigma","PSigma.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Reachable.mem_subgraphVerts.aux._unary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Reachable.mem_subgraphVerts.aux._unary","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.Reachable.mem_subgraphVerts.aux","reducibility":null,"statement_dag_size":73,"type_refs":["Membership.mem","PSigma","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.verts","SimpleGraph.Walk"],"value_dag_size":945,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","InvImage","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.edge_vert","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.adj_snd","SimpleGraph.Walk.getVert","SimpleGraph.Walk.instDecidableNil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_tail_add_one","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","True","WellFounded.Nat.fix","congrArg","dite","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.adj_of_mem_walk_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.adj_of_mem_walk_support","reducibility":null,"statement_dag_size":57,"type_refs":["And","Exists","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk.Nil","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":188,"value_refs":["And","Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Lean.Grind.forall_forall_or","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","List","List.instMembership","Membership.mem","Not","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk.Nil","SimpleGraph.Walk.nil","SimpleGraph.Walk.nil_nil","SimpleGraph.Walk.support","True","True.intro","eq_false","eq_true","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.adj_of_mem_walk_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.adj_of_mem_walk_support","reducibility":null,"statement_dag_size":112,"type_refs":["And","Exists","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":2086,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.cons.inj","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","List.tail","Membership.mem","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons_tail_support","SimpleGraph.Walk.nil_iff_support_eq","SimpleGraph.Walk.support","SimpleGraph.Walk.support_cons","SimpleGraph.adj_comm","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_bot_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_bot_iff","reducibility":null,"statement_dag_size":29,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.completeAtomicBooleanAlgebra","Subsingleton"],"value_dag_size":30,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.preconnected_bot_iff_subsingleton","Subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_bot_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_bot_iff","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected"],"value_dag_size":25,"value_refs":["And","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected","SimpleGraph.connected_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_or_preconnected_compl.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_or_preconnected_compl","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Exists","Exists.intro","Not","SimpleGraph","SimpleGraph.Reachable"],"value_dag_size":77,"value_refs":["Exists","Exists.casesOn","Exists.intro","Not","SimpleGraph","SimpleGraph.Reachable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_top_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.connected_top_iff","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected"],"value_dag_size":25,"value_refs":["And","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected","SimpleGraph.connected_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.iUnion_connectedComponentSupp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.iUnion_connectedComponentSupp","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.iUnion_connectedComponentSupp._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.iUnion_connectedComponentSupp","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SetLike","SetLike.coe","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","SetLike","SetLike.coe","SetLike.instMembership","SetLike.mem_coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_deleteEdges_singleton._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_deleteEdges_singleton","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk"],"value_dag_size":50,"value_refs":["Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isBridge_iff","Singleton.singleton","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_iff_forall_cycle_notMem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_iff_forall_cycle_notMem","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk"],"value_dag_size":50,"value_refs":["Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isBridge_iff","Singleton.singleton","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_iff_forall_cycle_notMem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_iff_forall_cycle_notMem","reducibility":null,"statement_dag_size":89,"type_refs":["And","Eq","Exists","List","List.instMembership","Membership.mem","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.edges","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk"],"value_dag_size":99,"value_refs":["And","Eq.symm","Exists","List","List.instMembership","Membership.mem","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.edges","SimpleGraph.adj_and_reachable_delete_edges_iff_exists_cycle","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_sup_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.isBridge_sup_edge","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","Sym2.mk"],"value_dag_size":50,"value_refs":["Not","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsBridge","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isBridge_iff","Singleton.singleton","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.not_connected_bot._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.not_connected_bot","reducibility":null,"statement_dag_size":32,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","False","Nontrivial","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":32,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Nontrivial","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.not_preconnected_bot","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.not_connected_bot._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.not_connected_bot","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected"],"value_dag_size":25,"value_refs":["And","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected","SimpleGraph.connected_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.pairwise_disjoint_supp_connectedComponent._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.pairwise_disjoint_supp_connectedComponent","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_bot.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_bot","reducibility":"abbrev","statement_dag_size":109,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":515,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.casesOn","False.elim","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.completeAtomicBooleanAlgebra","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_deleteEdges_iff_exists_walk._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_deleteEdges_iff_exists_walk","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_fromEdgeSet_eq_reflTransGen_toRel._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.reachable_fromEdgeSet_eq_reflTransGen_toRel","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Or","Relation.ReflGen"],"value_dag_size":35,"value_refs":["Eq","Or","Relation.ReflGen","Relation.reflGen_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.Walk.IsTrail.isEdgeReachable_two_of_isEdgeReachable_two_aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.Walk.IsTrail","reducibility":null,"statement_dag_size":67,"type_refs":["List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.support","instOfNatNat"],"value_dag_size":374,"value_refs":["Classical.not_forall._simp_1","Classical.propDecidable","Eq","Eq.mp","Eq.trans","Exists","Exists.casesOn","Iff.mp","List","List.instMembership","List.mem_reverse._simp_1","List.reverse","Mathlib.Tactic.Contrapose.contrapose₁","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.Reachable","SimpleGraph.Reachable.trans","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.IsTrail.disjoint_edges_takeUntil_dropUntil","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.edges","SimpleGraph.Walk.edges_reverse","SimpleGraph.Walk.mem_edges_of_not_reachable_deleteEdges","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","SimpleGraph.deleteEdges","SimpleGraph.isEdgeReachable_two","Singleton.singleton","Sym2","_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.Walk.IsTrail.isEdgeReachable_two_of_isEdgeReachable_two_aux._simp_1_1","congrArg","congrFun'","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.Walk.IsTrail.isEdgeReachable_two_of_isEdgeReachable_two_aux._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.Walk.IsTrail.isEdgeReachable_two_of_isEdgeReachable_two_aux","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Nat","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.Reachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","instOfNatNat"],"value_dag_size":57,"value_refs":["Nat","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.Reachable","SimpleGraph.deleteEdges","SimpleGraph.isEdgeReachable_two","Singleton.singleton","Sym2","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.exists_adj_isEdgeReachable_two._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.exists_adj_isEdgeReachable_two","reducibility":null,"statement_dag_size":32,"type_refs":["Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil"],"value_dag_size":127,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.not_nil_of_ne","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeConnected_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeConnected_two","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","HAdd.hAdd","Nat","Ne","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeConnected","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":72,"value_refs":["HAdd.hAdd","Nat","Ne","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeConnected","SimpleGraph.deleteEdges","SimpleGraph.isEdgeConnected_add_one","Singleton.singleton","Sym2","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeReachable_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeReachable_one","reducibility":null,"statement_dag_size":149,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LT.lt","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder"],"value_dag_size":156,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LT.lt","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Order.lt_one_iff","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeReachable_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isEdgeReachable_two","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAdd.hAdd","Nat","Ne","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.deleteEdges","Singleton.singleton","Sym2","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":82,"value_refs":["HAdd.hAdd","Nat","Ne","OfNat.ofNat","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.IsEdgeReachable","SimpleGraph.deleteEdges","SimpleGraph.isEdgeReachable_add_one","Singleton.singleton","Sym2","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Nat","Nat.card","Set","Set.Elem","Set.ncard"],"value_dag_size":24,"value_refs":["Eq.symm","Nat","Nat.card","Nat.card_coe_set_eq","Set","Set.Elem","Set.ncard"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","SetLike.coe"],"value_dag_size":30,"value_refs":["Eq.symm","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","Set.ncard_coe_finset","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk"],"value_dag_size":47,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.mem_supp_iff","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ncard_oddComponents_mono.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.ncard_oddComponents_mono","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.oddComponents","Subtype.mk"],"value_dag_size":94,"value_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.oddComponents","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Finset.card","Fintype","Nat","Set","Set.Elem","Set.ncard","Set.toFinset"],"value_dag_size":34,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set","Set.Elem","Set.ncard","Set.ncard_eq_toFinset_card'","Set.toFinset"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents","reducibility":null,"statement_dag_size":44,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Set","Set.ofPred","SetLike.coe"],"value_dag_size":50,"value_refs":["DecidablePred","Eq.symm","Finset","Finset.coe_filter_univ","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Set","Set.ofPred","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.reachable_iff_exists_finsetWalkLength_nonempty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.reachable_iff_exists_finsetWalkLength_nonempty","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength"],"value_dag_size":79,"value_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","SimpleGraph.mem_finsetWalkLength_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk"],"value_dag_size":47,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.mem_supp_iff","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk"],"value_dag_size":47,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.mem_supp_iff","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.Represents.existsUnique_rep","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep","reducibility":null,"statement_dag_size":48,"type_refs":["LE.le","Nat","Ne","OfNat.ofNat","Set.ncard","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","instLENat","instOfNatNat"],"value_dag_size":161,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","Ne","Not","OfNat.ofNat","Set.ncard","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Even","Nat","Nat.instSemiring","Not","Odd","instAddNat"],"value_dag_size":27,"value_refs":["Eq.symm","Even","Nat","Nat.instSemiring","Nat.not_odd_iff_even","Not","Odd","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents.0.SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_rep","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Even","HSub.hSub","Iff","LE.le","Nat","instAddNat","instHSub","instLENat","instSubNat"],"value_dag_size":42,"value_refs":["Even","HSub.hSub","Iff","LE.le","Nat","Nat.even_sub","instAddNat","instHSub","instLENat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff","reducibility":"abbrev","statement_dag_size":125,"type_refs":["And.intro","LE.le","Maximal","PartialOrder.toPreorder","Preorder.toLE","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Connected","SimpleGraph.Subgraph.instPartialOrder"],"value_dag_size":149,"value_refs":["And.casesOn","And.intro","LE.le","Maximal","PartialOrder.toPreorder","Preorder.toLE","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Connected","SimpleGraph.Subgraph.instPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff","reducibility":"abbrev","statement_dag_size":82,"type_refs":["Eq","Exists","Exists.intro","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.toSubgraph","SimpleGraph.Subgraph"],"value_dag_size":106,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.toSubgraph","SimpleGraph.Subgraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff","reducibility":"abbrev","statement_dag_size":67,"type_refs":["Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts"],"value_dag_size":91,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk"],"value_dag_size":47,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.mem_supp_iff","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk"],"value_dag_size":37,"value_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.eq","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Preconnected.map.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.Preconnected.map","reducibility":"abbrev","statement_dag_size":268,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists.intro","Membership.mem","RelHom.instFunLike","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.verts","Subtype.mk"],"value_dag_size":454,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists.casesOn","Exists.intro","Membership.mem","RelHom.instFunLike","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.verts","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.connected_iff'.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.connected_iff'","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Set.Elem","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Connected","SimpleGraph.Subgraph.Connected.mk","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":72,"value_refs":["Set.Elem","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Connected","SimpleGraph.Subgraph.Connected.casesOn","SimpleGraph.Subgraph.Connected.mk","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.preconnected_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.preconnected_iff","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Set.Elem","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Preconnected","SimpleGraph.Subgraph.Preconnected.mk","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":72,"value_refs":["Set.Elem","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Preconnected","SimpleGraph.Subgraph.Preconnected.casesOn","SimpleGraph.Subgraph.Preconnected.mk","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraph","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts","True"],"value_dag_size":56,"value_refs":["LE.le","PartialOrder.toPreorder","Preorder.toLE","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.coeSubgraph_le","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_connected._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_connected","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_connected._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_connected","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two","reducibility":null,"statement_dag_size":81,"type_refs":["And","Eq","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instLENat","instLTNat","instOfNatNat"],"value_dag_size":383,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two","reducibility":null,"statement_dag_size":77,"type_refs":["And","Eq","LE.le","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":347,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","Exists","LE.le","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat"],"value_dag_size":79,"value_refs":["And","Eq","Exists","LE.le","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.mem_support_iff_exists_getVert","SimpleGraph.Walk.support","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":146,"type_refs":["And","Eq","Exists","HAdd.hAdd","HSub.hSub","Iff","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":12591,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.ctorIdx","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.getVert_endpoint_iff","SimpleGraph.Walk.Nil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.snd","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_true","false_or","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.neighborSet"],"value_dag_size":47,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.mem_neighborSet","SimpleGraph.Subgraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":98,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_iff","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":783,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":117,"type_refs":["And","Eq","Exists","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1044,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":126,"type_refs":["And","Eq","Exists","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1059,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":67,"type_refs":["And","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":367,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.Simproc.add_le_gt","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congr","congrArg","eagerReduce","false_or","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","LE.le","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instLTNat","instOfNatNat"],"value_dag_size":392,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":68,"type_refs":["HSub.hSub","LT.lt","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":991,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.neighborSet"],"value_dag_size":47,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.mem_neighborSet","SimpleGraph.Subgraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":98,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_iff","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two","reducibility":null,"statement_dag_size":74,"type_refs":["HSub.hSub","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":710,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two","reducibility":null,"statement_dag_size":64,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":298,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_two","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","False","HAdd.hAdd","HSub.hSub","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":769,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":783,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":46,"type_refs":["LE.le","LT.lt","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instLTNat"],"value_dag_size":273,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":46,"type_refs":["LE.le","LT.lt","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instLTNat"],"value_dag_size":273,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":64,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":298,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":70,"type_refs":["HSub.hSub","LT.lt","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":993,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.neighborSet"],"value_dag_size":47,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.mem_neighborSet","SimpleGraph.Subgraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":98,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_iff","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":134,"type_refs":["And","Eq","Exists","HAdd.hAdd","Iff","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":2138,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.getVert_eq_start_iff","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.neighborSet"],"value_dag_size":47,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.mem_neighborSet","SimpleGraph.Subgraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":98,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_iff","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":null,"statement_dag_size":90,"type_refs":["And","Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":385,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","True","and_true","congr","congrArg","congrFun'","eagerReduce","eq_self","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":117,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":null,"statement_dag_size":94,"type_refs":["And","Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":368,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","reducibility":"abbrev","statement_dag_size":172,"type_refs":["And","Eq","Exists","Exists.intro","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":209,"value_refs":["And","Eq","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","Sym2","Sym2.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.end_mem_verts_toSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.end_mem_verts_toSubgraph","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph"],"value_dag_size":65,"value_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_forall_mem_support_imp_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_forall_mem_support_imp_eq","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":50,"type_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"],"value_dag_size":63,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":141,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.erase","HAdd.hAdd","LE.le","LT.lt","List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":625,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.erase","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":43,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph","reducibility":null,"statement_dag_size":147,"type_refs":["And","Iff","List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","Sym2.Rel"],"value_dag_size":1181,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","Sym2.Rel","True","True.intro","congr","congrArg","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph"],"value_dag_size":65,"value_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.isInduced_toSubgraph","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk"],"value_dag_size":68,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.adj_toSubgraph_iff_mem_edges","SimpleGraph.Walk.edges","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.map.match_1","SimpleGraph.Walk.nil","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.map.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.map.match_1","SimpleGraph.Walk.nil","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.map.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.map.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_eq_induce._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_eq_induce","reducibility":null,"statement_dag_size":87,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","Subtype.val"],"value_dag_size":221,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","List","List.instMembership","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","Subtype.property","Subtype.val","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_eq_induce.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_eq_induce","reducibility":"abbrev","statement_dag_size":175,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":605,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_hom.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.map_mapToSubgraph_hom","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.mem_verts_toSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.mem_verts_toSubgraph","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","or_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.start_mem_verts_toSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.start_mem_verts_toSubgraph","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph"],"value_dag_size":65,"value_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.toSubgraph.match_1","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.toSubgraph.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.toSubgraph.match_1","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.toSubgraph.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.toSubgraph.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instMax"],"value_dag_size":56,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instMax","SimpleGraph.Subgraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_getVert","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_iff","reducibility":null,"statement_dag_size":108,"type_refs":["And","Eq","Exists","HAdd.hAdd","Iff","LT.lt","Nat","OfNat.ofNat","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.toSubgraph","Sym2.Rel","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1405,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.forall_forall_or","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.mk","Quot","Quot.mk","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.adj_toSubgraph_iff_mem_edges","SimpleGraph.Walk.edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.mk_mem_edges_iff_exists","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_penultimate._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_penultimate","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":644,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_penultimate._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_adj_penultimate","reducibility":null,"statement_dag_size":62,"type_refs":["HSub.hSub","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":696,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_bypass_le_toSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_bypass_le_toSubgraph","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk"],"value_dag_size":68,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.adj_toSubgraph_iff_mem_edges","SimpleGraph.Walk.edges","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_le_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.toSubgraph_le_iff","reducibility":"abbrev","statement_dag_size":180,"type_refs":["And","And.intro","Exists","Exists.intro","List","List.instMembership","Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.instSetLike"],"value_dag_size":258,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.instSetLike"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","LE.le","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder"],"value_dag_size":52,"value_refs":["And","LE.le","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","propext","sup_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instUnion","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instPartialOrder","True","Union.union"],"value_dag_size":58,"value_refs":["LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instUnion","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.le_induce_union_left","Union.union","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instUnion","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instPartialOrder","True","Union.union"],"value_dag_size":58,"value_refs":["LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instUnion","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.le_induce_union_right","Union.union","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","Insert.insert","LE.le","Membership.mem","Set","Set.instInsert","Set.instLE","Set.instMembership"],"value_dag_size":50,"value_refs":["And","Insert.insert","LE.le","Membership.mem","Set","Set.insert_subset_iff","Set.instInsert","Set.instLE","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.connected_induce_union","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":40,"value_refs":["LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.singleton_subset_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","List","List.instMembership","List.toFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","List","List.instMembership","List.mem_toFinset","List.toFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","True"],"value_dag_size":43,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.start_mem_support","SimpleGraph.Walk.support","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.extend_finset_to_connected","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Exists","True","True.intro"],"value_dag_size":16,"value_refs":["Exists","True","True.intro","exists_true_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.induce_sUnion_connected_of_pairwise_not_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.induce_sUnion_connected_of_pairwise_not_disjoint","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.instMembership","Set.sUnion"],"value_dag_size":52,"value_refs":["And","Exists","Membership.mem","Set","Set.instMembership","Set.mem_sUnion","Set.sUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.Copy.maxDegree_mono._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.Copy.maxDegree_mono","reducibility":null,"statement_dag_size":105,"type_refs":["DecidableRel","Eq","Fintype","LE.le","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.degree","SimpleGraph.maxDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","instLENat"],"value_dag_size":585,"value_refs":["Bool","Bool.true","Classical.byContradiction","DFunLike.coe","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.degree_le","SimpleGraph.Copy.instFunLike","SimpleGraph.degree","SimpleGraph.degree_le_maxDegree","SimpleGraph.maxDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsContained.maxDegree_mono.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsContained.maxDegree_mono","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsContained.trans.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsContained.trans","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsIndContained.isContained.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsIndContained.isContained","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsIndContained.trans.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.IsIndContained.trans","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph","reducibility":null,"statement_dag_size":69,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","Nonempty","Set.Elem","Set.Nonempty","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.verts","SimpleGraph.completeAtomicBooleanAlgebra","Sym2"],"value_dag_size":368,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Eq","Eq.mpr","Eq.symm","Exists.casesOn","Exists.intro","Iff.mpr","Membership.mem","Ne","Nonempty","RelIso.instFunLike","Set","Set.Elem","Set.Nonempty","Set.Nonempty.image","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Iso","SimpleGraph.Iso.map_mem_edgeSet_iff","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.image_coe_edgeSet_coe","SimpleGraph.Subgraph.verts","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.edgeSet_nonempty","Subtype.val","Sym2","Sym2.map","_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux.match_1_1","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux","reducibility":"abbrev","statement_dag_size":88,"type_refs":["Nonempty","Nonempty.intro","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":97,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.bot_isContained_iff_card_le.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.bot_isContained_iff_card_le","reducibility":"abbrev","statement_dag_size":88,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":100,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":61,"value_refs":["And","Eq","Finset","Finset.eq_singleton_iff_unique_mem","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":51,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_bot","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nonempty","Nonempty.intro"],"value_dag_size":25,"value_refs":["Nonempty","Nonempty.forall","Nonempty.intro","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_eq_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_eq_zero","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":54,"value_refs":["Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.isContained_iff_exists_iso_subgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_eq_zero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_eq_zero","reducibility":null,"statement_dag_size":54,"type_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":59,"value_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.filter_eq_empty_iff","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":54,"value_refs":["Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.isContained_iff_exists_iso_subgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.card","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":34,"value_refs":["Finset","Finset.Nonempty","Finset.card","Finset.card_pos","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.copyCount_pos","reducibility":null,"statement_dag_size":50,"type_refs":["And","DecidablePred","Eq","Exists","Finset","Finset.Nonempty","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":55,"value_refs":["And","DecidablePred","Exists","Finset","Finset.Nonempty","Finset.filter","Finset.filter_nonempty_iff","Finset.instSetLike","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_bot.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_bot","reducibility":"abbrev","statement_dag_size":134,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Function.Injective","Nonempty.intro","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.mk","SimpleGraph.Hom","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":206,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DFunLike.coe","Function.Injective","Nonempty.casesOn","Nonempty.intro","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.casesOn","SimpleGraph.Copy.mk","SimpleGraph.Hom","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.free_killCopies","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_iso_subgraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_iso_subgraph","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_iso_subgraph.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_iso_subgraph","reducibility":"abbrev","statement_dag_size":121,"type_refs":["Exists","Exists.intro","Nonempty","Nonempty.intro","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":181,"value_refs":["Exists","Exists.casesOn","Exists.intro","Nonempty","Nonempty.casesOn","Nonempty.intro","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_le_comap.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_le_comap","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_le_comap.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isContained_iff_exists_le_comap","reducibility":"abbrev","statement_dag_size":132,"type_refs":["DFunLike.coe","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","LE.le","SimpleGraph","SimpleGraph.comap","SimpleGraph.instLE"],"value_dag_size":164,"value_refs":["DFunLike.coe","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","LE.le","SimpleGraph","SimpleGraph.comap","SimpleGraph.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_comap_eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_comap_eq","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_comap_eq.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_comap_eq","reducibility":"abbrev","statement_dag_size":123,"type_refs":["DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.comap"],"value_dag_size":153,"value_refs":["DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.comap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_induce.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_induce","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"],"value_dag_size":58,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Embedding","SimpleGraph.IsIndContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_induce.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_induce","reducibility":"abbrev","statement_dag_size":101,"type_refs":["Exists","Exists.intro","Nonempty","Nonempty.intro","Set","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.induce"],"value_dag_size":156,"value_refs":["Exists","Exists.casesOn","Exists.intro","Nonempty","Nonempty.casesOn","Nonempty.intro","Set","Set.Elem","SimpleGraph","SimpleGraph.Iso","SimpleGraph.induce"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_subgraph._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.isIndContained_iff_exists_iso_subgraph","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Function.Injective","Relation.Map"],"value_dag_size":68,"value_refs":["Function.Injective","Relation.Map","Relation.map_apply_apply","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts"],"value_dag_size":54,"value_refs":["Exists","Nonempty","Set.Elem","SimpleGraph","SimpleGraph.IsContained","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.isContained_iff_exists_iso_subgraph","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":64,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","Eq","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","SimpleGraph","SimpleGraph.deleteEdges","SimpleGraph.edgeSet","Sym2"],"value_dag_size":67,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","Eq","HeytingAlgebra.toOrderBot","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","SimpleGraph","SimpleGraph.deleteEdges","SimpleGraph.deleteEdges_eq_self","SimpleGraph.edgeSet","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","IsEmpty","Nonempty","Not"],"value_dag_size":15,"value_refs":["IsEmpty","Nonempty","Not","not_nonempty_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nonempty","Nonempty.intro"],"value_dag_size":25,"value_refs":["Nonempty","Nonempty.forall","Nonempty.intro","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_of_ne_bot","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph","reducibility":null,"statement_dag_size":111,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","Nonempty","Set","Set.Elem","Set.Nonempty.some","Set.iUnion","Set.instSingletonSet","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.verts","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.deleteEdges","SimpleGraph.killCopies","Singleton.singleton","Sym2","_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux"],"value_dag_size":233,"value_refs":["BooleanAlgebra.toBot","Bot.bot","Classical.propDecidable","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Eq.mpr","Ne","Nonempty","Not","Set","Set.Elem","Set.Nonempty.some","Set.iUnion","Set.instSingletonSet","SimpleGraph","SimpleGraph.Iso","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.verts","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.deleteEdges","SimpleGraph.killCopies","SimpleGraph.killCopies_def","Singleton.singleton","Sym2","_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.aux","congrArg","dif_neg","dite","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.labelledCopyCount_eq_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.labelledCopyCount_eq_zero","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Fintype","Fintype.card","IsEmpty","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":31,"value_refs":["Eq","Fintype","Fintype.card","Fintype.card_eq_zero_iff","IsEmpty","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.labelledCopyCount_pos._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.labelledCopyCount_pos","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fintype","Fintype.card","LT.lt","Nat","Nonempty","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":33,"value_refs":["Fintype","Fintype.card","Fintype.card_pos_iff","LT.lt","Nat","Nonempty","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set.Elem","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_edgeSet","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.le_card_edgeFinset_killCopies","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.top_isIndContained_iff_top_isContained.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.top_isIndContained_iff_top_isContained","reducibility":"abbrev","statement_dag_size":88,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":100,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Copy","name":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.wrapped._proof_1._@.Mathlib.Combinatorics.SimpleGraph.Copy.3082331781._hygCtx._hyg.14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.wrapped._proof_1._@.Mathlib.Combinatorics.SimpleGraph.Copy.3082331781._hygCtx._hyg","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","SimpleGraph","SimpleGraph.definition._@.Mathlib.Combinatorics.SimpleGraph.Copy.3082331781._hygCtx._hyg.14"],"value_dag_size":17,"value_refs":["SimpleGraph","SimpleGraph.definition._@.Mathlib.Combinatorics.SimpleGraph.Copy.3082331781._hygCtx._hyg.14","rfl"]}
+{"definition_height":12,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph","reducibility":"regular","statement_dag_size":53,"type_refs":["Fin","Fin.instOfNat","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk","SimpleGraph.cycleGraph","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":259,"value_refs":["Fin","Fin._sizeOf_inst","Fin.instOfNat","Fin.mk","HAdd.hAdd","InvImage","LT.lt","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","SizeOf.sizeOf","WellFounded.Nat.fix","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":66,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_9","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":375,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","Fin","Fin.instOfNat","Fin.instSub","Fin.mk","Fin.mk_le_mk._simp_1","Fin.sub_val_of_le","Fin.val","HAdd.hAdd","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.lt_of_succ_lt","Nat.one_mod","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","add_tsub_cancel_left","congr","congrArg","contravariant_lt_of_covariant_le","eq_self","instAddNat","instHAdd","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLEFin","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","le_add_iff_nonneg_right._simp_1","of_eq_true","true_or","zero_le._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":43,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.lt_of_succ_lt","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":66,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_2","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":375,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","Fin","Fin.instOfNat","Fin.instSub","Fin.mk","Fin.mk_le_mk._simp_1","Fin.sub_val_of_le","Fin.val","HAdd.hAdd","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.lt_of_succ_lt","Nat.one_mod","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","add_tsub_cancel_left","congr","congrArg","contravariant_lt_of_covariant_le","eq_self","instAddNat","instHAdd","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLEFin","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","le_add_iff_nonneg_right._simp_1","of_eq_true","true_or","zero_le._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":75,"type_refs":["Fin","Fin._sizeOf_inst","Fin.mk","HAdd.hAdd","InvImage","LT.lt","Nat","Nat.succ","OfNat.ofNat","SizeOf.sizeOf","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_2","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":262,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","Eq.trans","Fin","Fin._sizeOf_inst","Fin.mk","Fin.sizeOf","HAdd.hAdd","InvImage","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LT.lt","Lattice.toSemilatticeInf","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instAddMonoidWithOne","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSuccAddOrder","Nat.lt_of_succ_lt","Nat.succ","OfNat.ofNat","One.toOfNat1","Order.lt_one_iff._simp_1","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SizeOf.sizeOf","True","Zero.toOfNat0","congr","congrArg","contravariant_lt_of_covariant_le","eq_self","id","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instIsLeftCancelAddOfAddLeftReflectLE","instLTNat","instOfNatNat","lt_add_iff_pos_right._simp_1","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":43,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.lt_of_succ_lt","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":66,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":375,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","Fin","Fin.instOfNat","Fin.instSub","Fin.mk","Fin.mk_le_mk._simp_1","Fin.sub_val_of_le","Fin.val","HAdd.hAdd","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.lt_of_succ_lt","Nat.one_mod","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","add_tsub_cancel_left","congr","congrArg","contravariant_lt_of_covariant_le","eq_self","instAddNat","instHAdd","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLEFin","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","le_add_iff_nonneg_right._simp_1","of_eq_true","true_or","zero_le._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":43,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.lt_of_succ_lt","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph_adj","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._unsafe_rec","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":"opaque","statement_dag_size":53,"type_refs":["Fin","Fin.instOfNat","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk","SimpleGraph.cycleGraph","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":458,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","Fin","Fin.instOfNat","Fin.instSub","Fin.mk","Fin.mk_le_mk._simp_1","Fin.sub_val_of_le","Fin.val","HAdd.hAdd","HSub.hSub","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.lt_of_succ_lt","Nat.one_mod","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._unsafe_rec","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","add_tsub_cancel_left","congr","congrArg","contravariant_lt_of_covariant_le","eq_self","instAddNat","instHAdd","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLEFin","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","le_add_iff_nonneg_right._simp_1","of_eq_true","true_or","zero_le._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq.refl","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":106,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","OfNat.ofNat","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":207,"value_refs":["Eq.refl","Eq.trans","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_def","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_def","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":null,"statement_dag_size":167,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":1033,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.mpr","Eq.refl","Eq.trans","Fin","Fin._sizeOf_inst","Fin.instOfNat","Fin.instSub","Fin.mk","Fin.mk_le_mk._simp_1","Fin.sub_val_of_le","Fin.val","HAdd.hAdd","HSub.hSub","InvImage","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.lt_of_succ_lt","Nat.one_mod","Nat.succ","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","SizeOf.sizeOf","True","WellFounded.Nat.fix","WellFounded.Nat.fix_eq","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_3","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._simp_4","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1._arg_pusher","add_tsub_cancel_left","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","eq_self","id","instAddNat","instHAdd","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLEFin","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","le_add_iff_nonneg_right._simp_1","of_eq_true","true_or","zero_le._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":121,"value_refs":["Fin","Fin.casesOn","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1._arg_pusher","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","reducibility":null,"statement_dag_size":165,"type_refs":["Eq","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":386,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1.splitter","id","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","reducibility":null,"statement_dag_size":91,"type_refs":["Eq","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":89,"value_refs":["Eq.refl","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","reducibility":null,"statement_dag_size":95,"type_refs":["Eq","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":92,"value_refs":["Eq.refl","Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1,"value_refs":["_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":36,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","Or","Std.Symm","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_10","instAddNat","instHAdd","instHSub","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_4","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","Or","Std.Irrefl","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_10","instAddNat","instHAdd","instHSub","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_6","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":107,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","Nat","Nat.instMod","Nat.instNeZeroSucc","Nat.mod_lt","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","SimpleGraph.cycleGraph.getVert_cycle._proof_2","instAddNat","instHAdd","instHMod","instHSub","instLENat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat"],"value_dag_size":550,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.ext","Fin.instOfNat","Fin.last","Fin.mk","Fin.mk.congr_simp","Fin.val","Fin.val_last","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Nat","Nat.Simproc.add_le_add_le","Nat.Simproc.add_sub_add_ge","Nat.decLe","Nat.instMod","Nat.instNeZeroSucc","Nat.mod_lt","Not","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons_succ","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","SimpleGraph.cycleGraph.cycle._proof_1","SimpleGraph.cycleGraph.cycle._proof_2","SimpleGraph.cycleGraph.cycle.eq_1","SimpleGraph.cycleGraph.getVert_cycle._proof_2","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_9","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","congrArg","congrFun'","eq_false","eq_true","id","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycle","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":137,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.Simproc.add_sub_add_ge","Nat.decLe","Nat.instMod","Nat.mod_lt","OfNat.ofNat","SimpleGraph.cycleGraph.getVert_cycle._proof_2","congrArg","congrFun'","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","Nat","Nat.instMod","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instHMod","instHSub","instLENat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat"],"value_dag_size":548,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.casesOn","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.casesAuxOn","Nat.instAddCommMonoid","Nat.instMod","Nat.instNeZeroSucc","Nat.instOrderedSub","Nat.instPartialOrder","Nat.mod_eq_of_lt","Nat.recAux","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_zero","SimpleGraph.cycleGraph","True","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_19","congr","congrArg","congrFun'","eq_self","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","of_eq_true","tsub_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":123,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.instMod","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat"],"value_dag_size":179,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.instMod","Nat.instNeZeroSucc","Nat.le_zero_eq","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","eq_true","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":43,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":75,"value_refs":["Bool","Bool.true","Eq.refl","Eq.substr","HAdd.hAdd","LE.le","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_9","instAddNat","instHAdd","instLENat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":42,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":110,"value_refs":["Bool","Bool.true","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_11","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":36,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","Or","Std.Symm","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_13","instAddNat","instHAdd","instHSub","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_4","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","Or","Std.Irrefl","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_13","instAddNat","instHAdd","instHSub","instOfNatNat"],"value_dag_size":23,"value_refs":["HAdd.hAdd","Nat","OfNat.ofNat","SimpleGraph.cycleGraph._proof_6","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":71,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_9","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":49,"value_refs":["HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","Nat","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":124,"type_refs":["Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","Nat","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_8","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":131,"value_refs":["Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_8","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_9","instAddNat","instHAdd","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":82,"type_refs":["Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","Nat","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_8","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":159,"value_refs":["Bool","Bool.true","Eq.mp","Eq.refl","Eq.trans","Fin","Fin.instOfNat","Fin.isLt","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_17","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":172,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.instMod","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","instSubNat"],"value_dag_size":1200,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","Fin","Fin.instOfNat","Fin.mk","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.toInt","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.Simproc.add_sub_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.cast","Nat.decLe","Nat.instMod","Nat.instNeZeroSucc","Nat.succ","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons_succ","SimpleGraph.cycleGraph","True","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_9","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_2","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_9","congrArg","congrFun'","eagerReduce","eq_true","forall_congr","forall_prop_domain_congr","id","instAddNat","instHAdd","instHMod","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.getVert_cycleCons","reducibility":null,"statement_dag_size":43,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Bool","Bool.true","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":137,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.Simproc.add_sub_add_ge","Nat.decLe","Nat.instMod","Nat.mod_lt","OfNat.ofNat","SimpleGraph.cycleGraph.getVert_cycle._proof_2","congrArg","congrFun'","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle","reducibility":null,"statement_dag_size":43,"type_refs":["HAdd.hAdd","HMod.hMod","LT.lt","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":129,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Nat","Nat.add_sub_assoc","Nat.decLe","Nat.instMod","Nat.mod_lt","OfNat.ofNat","SimpleGraph.cycleGraph.getVert_cycle._proof_2","congrArg","congrFun'","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle","reducibility":null,"statement_dag_size":242,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","List.length","List.tail","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.getVert","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":5137,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.ext","Fin.instOfNat","Fin.mk","Fin.mk.congr_simp","Fin.mk.inj","Fin.val","HAdd.hAdd","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.natCast_mod","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.ofNat_FinZero","Lean.Grind.of_eq_eq_true","Lean.Grind.toInt_fin","Lean.Grind.true_imp_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","List.length_tail","List.tail","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.Simproc.add_sub_add_ge","Nat.Simproc.le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.add_sub_assoc","Nat.cast","Nat.decLe","Nat.instMod","Nat.instNeZeroSucc","Nat.mod_eq_of_lt","Nat.mod_lt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","SimpleGraph.cycleGraph.getVert_cycle","SimpleGraph.cycleGraph.getVert_cycle._proof_2","SimpleGraph.cycleGraph.length_cycle","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle._proof_1_6","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instHMod","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle","reducibility":"abbrev","statement_dag_size":360,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","List.get","List.length","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":422,"value_refs":["Eq","Fin","Fin.casesOn","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","List.get","List.length","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.isPath_tail_cycle","reducibility":"abbrev","statement_dag_size":350,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","List.get","List.length","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":411,"value_refs":["Eq","Fin","Fin.casesOn","Fin.instOfNat","Fin.mk","HAdd.hAdd","LT.lt","List.get","List.length","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph.cycle","instAddNat","instHAdd","instLTNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.length_cycle_cons","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.val","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SimpleGraph.Walk.length","SimpleGraph.cycleGraph","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":610,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","Eq.mpr","Eq.refl","Eq.trans","Fin","Fin._sizeOf_inst","Fin.instOfNat","Fin.mk","Fin.sizeOf","Fin.val","HAdd.hAdd","InvImage","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LT.lt","Lattice.toSemilatticeInf","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instAddMonoidWithOne","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instLinearOrderedCommMonoidWithZero","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSuccAddOrder","Nat.succ","OfNat.ofNat","One.toOfNat1","Order.lt_one_iff._simp_1","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","SimpleGraph.cycleGraph","SizeOf.sizeOf","True","WellFounded.Nat.fix","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_5","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_6","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.cycleCons.eq_def","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.length_cycle_cons.match_1_1","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","eq_self","id","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instIsLeftCancelAddOfAddLeftReflectLE","instLTNat","instNeZeroNatHAdd_1","instOfNatNat","lt_add_iff_pos_right._simp_1","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.length_cycle_cons.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.length_cycle_cons","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":121,"value_refs":["Fin","Fin.casesOn","Fin.mk","HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.cycleGraph.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["SimpleGraph.cycleGraph.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","False","Fin","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","instOfNatNat"],"value_dag_size":27,"value_refs":["Fin","Nat","OfNat.ofNat","SimpleGraph.Adj","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph_one_adj","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","Fin","Fin.instOfNat","Fin.instSub","HAdd.hAdd","HSub.hSub","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","SimpleGraph.Adj","SimpleGraph.cycleGraph","SimpleGraph.cycleGraph_adj","instAddNat","instHAdd","instHSub","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_adj'","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":130,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_degree_three_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_degree_three_le","reducibility":null,"statement_dag_size":62,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":67,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub","propext","sub_eq_iff_eq_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_degree_three_le._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_degree_three_le","reducibility":null,"statement_dag_size":63,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","HAdd.hAdd","IsLeftCancelAdd","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":68,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","HAdd.hAdd","IsLeftCancelAdd","OfNat.ofNat","Zero.toOfNat0","instHAdd","left_eq_add","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_8","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":90,"type_refs":["Fin.mk","Fin.succ","Fin.val","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_10","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.refl","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_9","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":26,"type_refs":["GT.gt","LT.lt","Nat","Ne","Not","instLTNat"],"value_dag_size":336,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","GT.gt","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Fin","Fin.instSub","Fin.mk","Fin.val","GT.gt","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat"],"value_dag_size":1024,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instSub","Fin.mk","Fin.sub_val_of_le","Fin.val","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.ToInt.of_not_le","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLEFinCoOfNatIntCast","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLEFin","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1282,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin.mk","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":922,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin.mk","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":603,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","instLTNat","instOfNatNat"],"value_dag_size":414,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.length_tail_add_one","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","True","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","False","Fin","Fin.val","LT.lt","List.length","Nat","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","instLTNat"],"value_dag_size":613,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":785,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":42,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":116,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Fin","Fin.succ","Fin.val","HAdd.hAdd","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":648,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.succ","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":53,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","Fin.mk","Fin.succ","Fin.val","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_8","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":93,"value_refs":["Eq","Eq.substr","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Fin","Nat","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.cycleGraph"],"value_dag_size":64,"value_refs":["Fin","Nat","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Copy","SimpleGraph.IsContained","SimpleGraph.cycleGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff.match_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_isContained_iff","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":41,"value_refs":["Fin","Fin.casesOn","Fin.mk","LT.lt","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_neighborSet","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_three_eq_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_three_eq_top","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":34,"value_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_three_eq_top._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_three_eq_top","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_two_eq_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_two_eq_top","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":34,"value_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_two_eq_top._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.cycleGraph_two_eq_top","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.CycleGraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.pathGraph_le_cycleGraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.CycleGraph.0.SimpleGraph.pathGraph_le_cycleGraph","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_card_eq_sum_degrees._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_card_eq_sum_degrees","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Finset.card","Finset.univ","Fintype","Fintype.card","Nat"],"value_dag_size":25,"value_refs":["Eq.symm","Finset.card","Finset.card_univ","Finset.univ","Fintype","Fintype.card","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_card_eq_sum_degrees._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_card_eq_sum_degrees","reducibility":null,"statement_dag_size":97,"type_refs":["DecidableEq","DecidableRel","Eq","Finset.card","Finset.filter","Finset.univ","Fintype","Membership.mem","Nat","Prod.fst","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.fintype","SimpleGraph.Dart.toProd","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"],"value_dag_size":105,"value_refs":["DecidableEq","DecidableRel","Eq","Eq.symm","Finset.card","Finset.filter","Finset.univ","Fintype","Membership.mem","Nat","Prod.fst","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.fintype","SimpleGraph.Dart.toProd","SimpleGraph.dart_fst_fiber_card_eq_degree","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Exists","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.mk"],"value_dag_size":62,"value_refs":["Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SetCoe.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.dart_fst_fiber","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.odd_card_odd_degree_vertices_ne._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.odd_card_odd_degree_vertices_ne","reducibility":null,"statement_dag_size":111,"type_refs":["AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Distrib.toAdd","Distrib.toMul","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.instAddCommSemigroup","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Semiring.toNonAssocSemiring","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHSub","instLTNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat"],"value_dag_size":756,"value_refs":["AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Bool","Bool.true","Classical.byContradiction","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instAddCommSemigroup","Nat.instSemiring","NatCast.natCast","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","Not","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Semiring.toNonAssocSemiring","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instDistribOfSemiring","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.sum_degrees_support_eq_twice_card_edges._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.sum_degrees_support_eq_twice_card_edges","reducibility":null,"statement_dag_size":103,"type_refs":["DecidableRel","Eq","Finset.card","Finset.sum","Finset.univ","Fintype","HMul.hMul","Membership.mem","Nat","Nat.instAddCommMonoid","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","Sym2","Sym2.instFintype","instHMul","instMulNat","instOfNatNat"],"value_dag_size":109,"value_refs":["DecidableRel","Eq.symm","Finset.card","Finset.sum","Finset.univ","Fintype","HMul.hMul","Membership.mem","Nat","Nat.instAddCommMonoid","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.sum_degrees_eq_twice_card_edges","Subtype.fintype","Sym2","Sym2.instFintype","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DegreeSum","name":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.sum_degrees_support_eq_twice_card_edges._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DegreeSum.0.SimpleGraph.sum_degrees_support_eq_twice_card_edges","reducibility":null,"statement_dag_size":63,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","HAdd.hAdd","IsLeftCancelAdd","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":68,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","HAdd.hAdd","IsLeftCancelAdd","OfNat.ofNat","Zero.toOfNat0","instHAdd","left_eq_add","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_edgeFinset_deleteIncidenceSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_edgeFinset_deleteIncidenceSet","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.incidenceFinset","SimpleGraph.neighborSet","Sym2"],"value_dag_size":52,"value_refs":["DecidableEq","Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_incidenceFinset_eq_degree","SimpleGraph.degree","SimpleGraph.incidenceFinset","SimpleGraph.neighborSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_edgeFinset_induce_compl_singleton._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_edgeFinset_induce_compl_singleton","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_support_deleteIncidenceSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_support_deleteIncidenceSet","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_support_deleteIncidenceSet._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.card_support_deleteIncidenceSet","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSDiff","Fintype","SDiff.sdiff","Set","Set.Elem","Set.instSDiff","Set.toFinset"],"value_dag_size":75,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.instSDiff","Fintype","SDiff.sdiff","Set","Set.Elem","Set.instSDiff","Set.toFinset","Set.toFinset_sdiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.deleteEdges_eq_inter_edgeSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.deleteEdges_eq_inter_edgeSet","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.deleteFar_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.deleteFar_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","True","instLENat"],"value_dag_size":45,"value_refs":["Finset","Finset.card","Finset.card_le_card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap"],"value_dag_size":45,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.comap_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteIncidenceSet"],"value_dag_size":46,"value_refs":["And","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteIncidenceSet","SimpleGraph.deleteIncidenceSet_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.induce_deleteIncidenceSet_of_notMem","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.support_deleteIncidenceSet_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.support_deleteIncidenceSet_subset","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support"],"value_dag_size":40,"value_refs":["Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_support","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.DeleteEdges","name":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.support_deleteIncidenceSet_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.DeleteEdges.0.SimpleGraph.support_deleteIncidenceSet_subset","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteIncidenceSet"],"value_dag_size":46,"value_refs":["And","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteIncidenceSet","SimpleGraph.deleteIncidenceSet_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidablePred","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","SetLike.instMembership"],"value_dag_size":107,"value_refs":["And","DecidablePred","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","Rel.mem_interedges_iff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","Eq.symm","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidablePred","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","SetLike.instMembership"],"value_dag_size":107,"value_refs":["And","DecidablePred","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","Rel.mem_interedges_iff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right.match_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right","reducibility":"abbrev","statement_dag_size":296,"type_refs":["And","And.intro","Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership"],"value_dag_size":596,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right.match_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_biUnion_right","reducibility":"abbrev","statement_dag_size":312,"type_refs":["And","And.intro","Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership"],"value_dag_size":637,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_eq_biUnion._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_eq_biUnion","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidablePred","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","SetLike.instMembership"],"value_dag_size":107,"value_refs":["And","DecidablePred","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","Rel.mem_interedges_iff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Density","name":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_mono._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Density.0.Rel.interedges_mono","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidablePred","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","SetLike.instMembership"],"value_dag_size":107,"value_refs":["And","DecidablePred","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","Rel.interedges","Rel.mem_interedges_iff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.connected_iff_ediam_ne_top.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.connected_iff_ediam_ne_top","reducibility":"abbrev","statement_dag_size":94,"type_refs":["ENat","Eq","Exists","Exists.intro","SimpleGraph","SimpleGraph.ediam","SimpleGraph.edist"],"value_dag_size":153,"value_refs":["ENat","Eq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.ediam","SimpleGraph.edist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.diam_ne_zero_of_ediam_ne_top.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.diam_ne_zero_of_ediam_ne_top","reducibility":"abbrev","statement_dag_size":62,"type_refs":["Exists","Exists.intro","Ne"],"value_dag_size":109,"value_refs":["Exists","Exists.casesOn","Exists.intro","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_eq_zero_of_subsingleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_eq_zero_of_subsingleton","reducibility":null,"statement_dag_size":47,"type_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":52,"value_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","SimpleGraph.edist_eq_zero_iff","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_ne_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_ne_zero","reducibility":null,"statement_dag_size":61,"type_refs":["CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","iSup","instCommSemiringENat","instCompleteLinearOrderENat","instMulZeroClassOfSemiring"],"value_dag_size":64,"value_refs":["CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","ENat","ENat.iSup_eq_zero","Eq","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","iSup","instCommSemiringENat","instCompleteLinearOrderENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_ne_zero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.eccent_ne_zero","reducibility":null,"statement_dag_size":47,"type_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":52,"value_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","SimpleGraph.edist_eq_zero_iff","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_eq_top._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_eq_top","reducibility":null,"statement_dag_size":133,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder","CompleteLinearOrder.toBiheytingAlgebra","CompleteLinearOrder.toCompleteLattice","CompleteSemilatticeInf.toPartialOrder","CompleteSemilatticeSup.toSupSet","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","LT.lt","Lattice.toSemilatticeSup","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeSup.toPartialOrder","Top.top","iSup"],"value_dag_size":137,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder","CompleteLinearOrder.toBiheytingAlgebra","CompleteLinearOrder.toCompleteLattice","CompleteSemilatticeInf.toPartialOrder","CompleteSemilatticeSup.toSupSet","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","LT.lt","Lattice.toSemilatticeSup","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeSup.toPartialOrder","Top.top","iSup","iSup_eq_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_eq_top._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_eq_top","reducibility":null,"statement_dag_size":71,"type_refs":["CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder","CompleteLinearOrder.toCompleteLattice","CompleteSemilatticeInf.toPartialOrder","CompleteSemilatticeSup.toSupSet","Eq","Exists","LT.lt","PartialOrder.toPreorder","Preorder.toLT","iSup"],"value_dag_size":76,"value_refs":["CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder","CompleteLinearOrder.toCompleteLattice","CompleteSemilatticeInf.toPartialOrder","CompleteSemilatticeSup.toSupSet","Exists","LT.lt","PartialOrder.toPreorder","Preorder.toLT","iSup","lt_iSup_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_ne_zero._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_ne_zero","reducibility":null,"statement_dag_size":61,"type_refs":["CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","iSup","instCommSemiringENat","instCompleteLinearOrderENat","instMulZeroClassOfSemiring"],"value_dag_size":64,"value_refs":["CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","ENat","ENat.iSup_eq_zero","Eq","MulZeroClass.toZero","OfNat.ofNat","Zero.toOfNat0","iSup","instCommSemiringENat","instCompleteLinearOrderENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_ne_zero._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.ediam_ne_zero","reducibility":null,"statement_dag_size":47,"type_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":52,"value_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","SimpleGraph","SimpleGraph.edist","SimpleGraph.edist_eq_zero_iff","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_eq_zero_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_eq_zero_iff","reducibility":null,"statement_dag_size":42,"type_refs":["CommSemiring.toSemiring","ENat","Eq","False","MulZeroClass.toZero","Nontrivial","OfNat.ofNat","SimpleGraph","SimpleGraph.radius","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring"],"value_dag_size":44,"value_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","Nontrivial","OfNat.ofNat","SimpleGraph","SimpleGraph.radius","SimpleGraph.radius_ne_zero_of_nontrivial","Zero.toOfNat0","eq_false","instCommSemiringENat","instMulZeroClassOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_eq_zero_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_eq_zero_iff","reducibility":"abbrev","statement_dag_size":36,"type_refs":["And","And.intro","Nonempty","Subsingleton"],"value_dag_size":50,"value_refs":["And","And.casesOn","And.intro","Nonempty","Subsingleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Diam","name":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_ne_zero_of_nontrivial._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Diam.0.SimpleGraph.radius_ne_zero_of_nontrivial","reducibility":null,"statement_dag_size":120,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","IsBotZeroClass","LE.le","Ne","NeZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SuccAddOrder","Zero.toOfNat0"],"value_dag_size":127,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","IsBotZeroClass","LE.le","Ne","NeZero","OfNat.ofNat","One.toOfNat1","Order.one_le_iff_ne_zero","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SuccAddOrder","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.disjoint_right.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.disjoint_right","reducibility":"abbrev","statement_dag_size":130,"type_refs":["And.intro","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike"],"value_dag_size":150,"value_refs":["And.casesOn","And.intro","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.ind.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.ind","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Compl.compl","Membership.mem","Set","Set.Elem","Set.instCompl","Set.instMembership","Subtype.mk"],"value_dag_size":93,"value_refs":["Compl.compl","Membership.mem","Set","Set.Elem","Set.instCompl","Set.instMembership","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges","reducibility":null,"statement_dag_size":62,"type_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instUnion","Union.union"],"value_dag_size":66,"value_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_union_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instUnion","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges","reducibility":null,"statement_dag_size":64,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE"],"value_dag_size":67,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Inter.inter","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_iff","Set.instBoundedOrder","Set.instDistribLattice","Set.instEmptyCollection","Set.instInter","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.mem_of_adj.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.mem_of_adj","reducibility":"abbrev","statement_dag_size":112,"type_refs":["Eq","Exists.intro","Membership.mem","Not","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike","SimpleGraph.componentComplMk"],"value_dag_size":153,"value_refs":["Eq","Exists.casesOn","Exists.intro","Membership.mem","Not","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike","SimpleGraph.componentComplMk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.pairwise_disjoint.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.pairwise_disjoint","reducibility":"abbrev","statement_dag_size":148,"type_refs":["And.intro","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike"],"value_dag_size":169,"value_refs":["And.casesOn","And.intro","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ComponentCompl","SimpleGraph.ComponentCompl.setLike"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.supp_injective._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.supp_injective","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.supp_injective._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.ComponentCompl.supp_injective","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk"],"value_dag_size":37,"value_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.eq","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_finite._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_finite","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_finite._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_finite","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_nonempty_of_infinite.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.componentCompl_nonempty_of_infinite","reducibility":"abbrev","statement_dag_size":95,"type_refs":["Compl.compl","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Set","Set.Nonempty","Set.instCompl","Set.instMembership","SetLike.coe"],"value_dag_size":126,"value_refs":["Compl.compl","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Set","Set.Nonempty","Set.instCompl","Set.instMembership","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.infinite_iff_in_eventualRange._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.infinite_iff_in_eventualRange","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Membership.mem","Set","Set.iInter","Set.instMembership"],"value_dag_size":45,"value_refs":["Membership.mem","Set","Set.iInter","Set.instMembership","Set.mem_iInter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Defs","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.infinite_iff_in_eventualRange._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Defs.0.SimpleGraph.infinite_iff_in_eventualRange","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Ends.Properties","name":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Properties.0.SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Properties.0.SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.univ","True"],"value_dag_size":23,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_univ","Set.univ","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.exists_isExtremal_iff_exists.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.exists_isExtremal_iff_exists","reducibility":"abbrev","statement_dag_size":115,"type_refs":["DecidableRel","Exists","Exists.intro","Fintype","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsExtremal"],"value_dag_size":181,"value_refs":["DecidableRel","Exists","Exists.casesOn","Exists.intro","Fintype","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsExtremal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.exists_isExtremal_iff_exists.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.exists_isExtremal_iff_exists","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Exists","Exists.intro","SimpleGraph"],"value_dag_size":57,"value_refs":["Exists","Exists.casesOn","Exists.intro","SimpleGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.extremalNumber_le_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.extremalNumber_le_iff","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.extremalNumber_le_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.extremalNumber_le_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":51,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff","reducibility":null,"statement_dag_size":113,"type_refs":["And","DistribLattice.toLattice","Eq","Exists","Finset","Finset.instSetLike","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":120,"value_refs":["And","DistribLattice.toLattice","Exists","Finset","Finset.instSetLike","Finset.lt_sup_iff","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":51,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff","reducibility":"abbrev","statement_dag_size":222,"type_refs":["And","And.intro","Classical.propDecidable","DistribLattice.toLattice","Exists","Exists.intro","Finset.card","Fintype","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2","Sym2.instFintype","instDistribLatticeOfLinearOrder"],"value_dag_size":330,"value_refs":["And","And.casesOn","And.intro","Classical.propDecidable","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset.card","Fintype","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2","Sym2.instFintype","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Basic.0.SimpleGraph.lt_extremalNumber_iff","reducibility":"abbrev","statement_dag_size":230,"type_refs":["And","And.intro","DecidableRel","Exists","Exists.intro","Finset.card","Fintype","LT.lt","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2","Sym2.instFintype","instLTNat"],"value_dag_size":390,"value_refs":["And","And.casesOn","And.intro","DecidableRel","Exists","Exists.casesOn","Exists.intro","Finset.card","Fintype","LT.lt","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2","Sym2.instFintype","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.between_verts_isBipartiteWith","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":70,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.instSetLike","Nat","Set","Set.instCompl","SetLike.coe","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.IsBipartiteWith","SimpleGraph.between","instDecidableEqFin"],"value_dag_size":147,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Eq","Eq.mpr","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.coe_compl","Finset.instSetLike","Nat","Order.Frame.toHeytingAlgebra","Set","Set.instCompl","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.IsBipartiteWith","SimpleGraph.between","SimpleGraph.between_isBipartiteWith","congrArg","disjoint_compl_right","id","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.card_edgeFinset_between_verts_le","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":225,"type_refs":["Compl.compl","DecidableRel","Fin","Fin.fintype","Finset","Finset.card","Finset.decidableMem'","Finset.instSetLike","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","Nat","Nat.cast","OfNat.ofNat","Real","Real.instAdd","Real.instLE","Real.instMul","Real.instNatCast","Real.instSub","Set","Set.decidableCompl","Set.instCompl","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","Sym2","Sym2.instFintype","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instDecidableEqFin","instHAdd","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dag_size":1925,"value_refs":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","And","BooleanAlgebra.toCompl","CommRing.toNonUnitalCommRing","Compl.compl","DecidableRel","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.card","Finset.card_compl","Finset.card_le_card","Finset.card_le_univ","Finset.card_sdiff_of_subset","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.decidableMem'","Finset.filter","Finset.filter_subset","Finset.fintype","Finset.instSDiff","Finset.instSetLike","Finset.powersetCard","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.sum_sdiff","Fintype.card","Fintype.card_fin","Fintype.decidableForallFintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans_eq","LT.lt","LT.lt.le","Membership.mem","NSMul.toSMul","Nat","Nat.cast","Nat.cast_add._simp_1","Nat.cast_inj._simp_1","Nat.cast_le._simp_1","Nat.cast_sub","Nat.cast_sum._simp_1","Nat.decidableForallFin","Nat.instAddCommMonoid","Nat.instPreorder","Nat.le_mul_of_pos_left","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSub","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SDiff.sdiff","Semiring.toNonAssocSemiring","Set","Set.decidableCompl","Set.instCompl","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.card_verts","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.isBipartiteWith_degree_le'","SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges'","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Subtype.fintype","Sym2","Sym2.instFintype","Trans.trans","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.between_verts_isBipartiteWith","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.eq_1","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter_subset_compl_verts","add_le_add","cast","congrArg","congrFun'","covariant_swap_add_of_covariant_add","eq_comm","forall_prop_decidable","id","instAddNat","instDecidableEqFin","instHAdd","instHMul","instHSMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat","instTransEq","instTransEq_1","mul_sub","nsmul_eq_mul","propext","rfl","sub_add","sub_add_cancel","sub_add_eq_add_sub","sub_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":265,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.card","Finset.decidableMem'","Finset.instSDiff","Finset.instSetLike","HAdd.hAdd","HSub.hSub","LT.lt","Membership.mem","Nat","OfNat.ofNat","SDiff.sdiff","Set","Set.decidableCompl","Set.instCompl","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.degree","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instAddNat","instDecidableEqFin","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":3069,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddZero.toAdd","AddZeroClass.toAddZero","And","And.casesOn","And.intro","And.left","BooleanAlgebra.toCompl","Classical.not_not._simp_2","Compl.compl","DecidableRel","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Fin","Fin.fintype","Finset","Finset.Nonempty","Finset.booleanAlgebra","Finset.card","Finset.card_disjiUnion","Finset.card_filter_le","Finset.card_sdiff_of_subset","Finset.card_singleton","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.decidableMem'","Finset.disjiUnion","Finset.filter","Finset.filter_disjiUnion","Finset.filter_subset","Finset.fintype","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter","Finset.mem_powersetCard","Finset.mem_sdiff","Finset.pairwiseDisjoint_filter","Finset.powersetCard","Finset.powersetCard_mono","Finset.powersetCard_nonempty","Finset.singleton_subset_iff","Finset.sum","Finset.sum_congr","Finset.sum_const","Finset.sum_eq_sum_sdiff_singleton_add","Finset.sum_le_sum","Fintype.decidableForallFintype","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mp","Iff.mpr","Iff.of_eq","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","LT.lt.ne'","LinearOrder.toPartialOrder","Mathlib.Tactic.Contrapose.contrapose₁","Mathlib.Tactic.Push.not_and_eq","Mathlib.Tactic.Push.not_exists._simp_1","Mathlib.Tactic.Push.not_forall_eq","Membership.mem","NSMul.toSMul","Nat","Nat.decidableForallFin","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instPartialOrder","Nat.instPreorder","Nat.sub_one_mul","Not","OfNat.ofNat","Or","Or.resolve_right","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","Set","Set.decidableCompl","Set.instCompl","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.card_mem_parts","SimpleGraph.CompleteEquipartiteSubgraph.card_parts","SimpleGraph.CompleteEquipartiteSubgraph.card_verts","SimpleGraph.CompleteEquipartiteSubgraph.disjoint","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.between_adj","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.isBipartiteWith_neighborFinset'","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Singleton.singleton","Subtype.fintype","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.between_verts_isBipartiteWith","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_9","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","add_lt_add_of_le_of_lt","binderNameHint","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","exists_prop_congr","false_or","forall_congr","forall_prop_decidable","funext","id","implies_congr","instAddNat","instDecidableEqFin","instHAdd","instHMul","instHSMul","instHSub","instIsLeftCancelAddOfAddLeftReflectLE","instLENat","instLTNat","instMulNat","instOfNatNat","instSMulOfMul","instSubNat","not_lt._simp_1","not_or._simp_2","propext","rfl","smul_eq_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":25,"value_refs":["And","Or","and_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":13,"type_refs":["And","Eq","False","Not"],"value_dag_size":15,"value_refs":["And","False","Not","and_not_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.degree_between_verts_lt_of_mem_sdiff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":14,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":"regular","statement_dag_size":34,"type_refs":["DecidableRel","Fin","Finset","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph"],"value_dag_size":242,"value_refs":["And","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Exists","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.filter","Finset.fintype","Finset.instSetLike","Finset.powersetCard","Fintype.decidableForallFintype","Membership.mem","Nat","Nat.decidableForallFin","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","forall_prop_decidable","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.congr_simp","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","reducibility":null,"statement_dag_size":85,"type_refs":["DecidableRel","Eq","Fin","Finset","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"],"value_dag_size":209,"value_refs":["Decidable","DecidableRel","Eq","Eq.ndrec","Eq.rec","Eq.refl","Fin","Finset","Nat","Pi.instSubsingleton","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subsingleton.elim","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instSubsingletonDecidable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","reducibility":null,"statement_dag_size":254,"type_refs":["And","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Eq","Exists","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.filter","Finset.fintype","Finset.instSetLike","Finset.powersetCard","Fintype.decidableForallFintype","Membership.mem","Nat","Nat.decidableForallFin","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","forall_prop_decidable","instDecidableEqFin"],"value_dag_size":47,"value_refs":["DecidableRel","Eq.refl","Fin","Finset","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"]}
+{"definition_height":15,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","reducibility":"regular","statement_dag_size":141,"type_refs":["DecidableRel","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instDecidableEqFin"],"value_dag_size":342,"value_refs":["And","DecidableRel","Exists","Exists.choose","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":null,"statement_dag_size":131,"type_refs":["And","DecidableRel","Exists","Fin","Finset","Finset.instSetLike","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"],"value_dag_size":271,"value_refs":["And","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Exists","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.fintype","Finset.instSetLike","Finset.powersetCard","Finset.val","Fintype.decidableForallFintype","Membership.mem","Multiset.of_mem_filter","Nat","Nat.decidableForallFin","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","forall_prop_decidable","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":null,"statement_dag_size":181,"type_refs":["And","DecidableRel","Exists.choose","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_1","instDecidableEqFin"],"value_dag_size":281,"value_refs":["And","And.left","DecidableRel","Exists.choose","Exists.choose_spec","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.mem_pi","Finset.pi","Finset.powersetCard","Iff.mpr","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_1","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":null,"statement_dag_size":246,"type_refs":["And","DecidableRel","Eq","Exists.choose","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi._proof_2","instDecidableEqFin"],"value_dag_size":176,"value_refs":["DecidableRel","Eq.refl","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":null,"statement_dag_size":542,"type_refs":["DecidableRel","DivInvMonoid.toDiv","Eq","Exists","Fin","Fin.fintype","Finset","Finset.Subtype.fintype","Finset.card","Finset.decidableEq","Finset.decidableMem","Finset.filter","Finset.fintype","Finset.instSetLike","Finset.pi","Finset.powersetCard","Finset.univ","Fintype.decidablePiFintype","Function.decidableEqPFun","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","LT.lt","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.choose","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.minDegree","Subtype","Subtype.instDecidableEq","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","instDecidableEqFin","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1876,"value_refs":["AddCommGroupWithOne.toAddGroupWithOne","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddMonoid.toAddSemigroup","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","CommMonoid.toMonoid","CommRing.toNonAssocCommRing","DecidableRel","Distrib.toMul","DivInvMonoid.toDiv","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.fintype","Finset","Finset.Nonempty","Finset.Subtype.fintype","Finset.card","Finset.card_pi","Finset.card_powersetCard","Finset.decidableEq","Finset.decidableMem","Finset.fintype","Finset.instSetLike","Finset.pi","Finset.powersetCard","Finset.prod","Finset.prod_congr","Finset.prod_const","Fintype.card","Fintype.card_coe","Fintype.decidablePiFintype","Fintype.exists_le_card_fiber_of_mul_le_card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.decidableEqPFun","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.cast","Int.cast_add","Int.cast_mul","Int.cast_mul._simp_1","Int.cast_natCast","Int.cast_pow","Int.cast_subNatNat._simp_1","Int.instMonoid","Int.instMul","Int.instRing","Int.instSemiring","Int.subNatNat","IsOrderedAddMonoid.toAddLeftMono","LE.le","LT.lt","LT.lt.le","LT.lt.ne'","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.cast_add","Nat.cast_add._simp_1","Nat.cast_le","Nat.cast_mul","Nat.cast_mul._simp_1","Nat.cast_pow","Nat.cast_pow._simp_1","Nat.cast_sub","Nat.choose","Nat.instCommMonoid","Nat.instMonoid","Nat.instPreorder","Nat.instTransLe","Nat.le_of_mul_le_mul_right","Nat.sub_pos_of_lt","NonAssocCommRing.toNonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Nonempty","OfNat.ofNat","One.toOfNat1","Or.resolve_right","PartialOrder.toPreorder","Preorder.toLE","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instFloorRing","Real.instIntCast","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.card_mem_parts","SimpleGraph.CompleteEquipartiteSubgraph.card_parts","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.minDegree","SubNegMonoid.toSub","Subtype","Subtype.instDecidableEq","Trans.trans","True","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.mul_le_card_filter_mul","cast","congr","congrArg","congrFun'","eq_self","forall_congr","id","implies_congr","instAddNat","instDecidableEqFin","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNatNat","instSubNat","instTransEq","le_refl","of_eq_true","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","Nonempty","SetLike.instMembership","Subtype"],"value_dag_size":37,"value_refs":["Finset","Finset.Nonempty","Finset.instSetLike","Finset.nonempty_coe_sort","Membership.mem","Nonempty","SetLike.instMembership","Subtype","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.pi","Membership.mem","SetLike.instMembership"],"value_dag_size":63,"value_refs":["DecidableEq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.pi","Finset.pi_nonempty","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.exists_le_card_fiber","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.card","Finset.powersetCard","LE.le","Nat","instLENat"],"value_dag_size":35,"value_refs":["Finset","Finset.Nonempty","Finset.card","Finset.powersetCard","Finset.powersetCard_nonempty","LE.le","Nat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":"abbrev","statement_dag_size":139,"type_refs":["DecidableRel","Fin","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"],"value_dag_size":170,"value_refs":["DecidableRel","Fin","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subtype","Subtype.casesOn","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1","reducibility":null,"statement_dag_size":178,"type_refs":["DecidableRel","Eq","Fin","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1"],"value_dag_size":175,"value_refs":["DecidableRel","Eq.refl","Fin","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1","reducibility":"abbrev","statement_dag_size":139,"type_refs":["DecidableRel","Fin","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","Subtype","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter"],"value_dag_size":1,"value_refs":["_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi.mem_val","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","reducibility":null,"statement_dag_size":215,"type_refs":["DecidableRel","Fin","Finset","Finset.decidableEq","Finset.instSetLike","Finset.pi","Finset.powersetCard","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","instDecidableEqFin"],"value_dag_size":475,"value_refs":["And","And.right","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Exists","Exists.choose","Exists.choose_spec","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.fintype","Finset.instSetLike","Finset.powersetCard","Finset.val","Fintype.decidableForallFintype","Membership.mem","Multiset.of_mem_filter","Nat","Nat.decidableForallFin","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","Subtype","Subtype.prop","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","forall_prop_decidable","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter_subset_compl_verts","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":78,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instDecidableEqFin"],"value_dag_size":242,"value_refs":["And","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Exists","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.decidableEq","Finset.decidableExistsAndFinsetCoe","Finset.decidableMem","Finset.filter_subset","Finset.fintype","Finset.instSetLike","Finset.powersetCard","Fintype.decidableForallFintype","Membership.mem","Nat","Nat.decidableForallFin","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","SimpleGraph.CompleteEquipartiteSubgraph.verts","forall_prop_decidable","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.le_card_edgeFinset_between_verts","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":181,"type_refs":["Compl.compl","DecidableRel","Fin","Fin.fintype","Finset","Finset.card","Finset.decidableMem'","Finset.instSetLike","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.cast","Real","Real.instLE","Real.instMul","Real.instNatCast","Real.instSub","Set","Set.decidableCompl","Set.instCompl","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.minDegree","Sym2","Sym2.instFintype","instDecidableEqFin","instHMul","instHSub"],"value_dag_size":820,"value_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","BooleanAlgebra.toCompl","Compl.compl","DecidableRel","Distrib.toMul","Eq","Eq.mpr","Eq.symm","Eq.trans","Fin","Fin.fintype","Finset","Finset.booleanAlgebra","Finset.card","Finset.decidableMem'","Finset.instSetLike","Finset.sum","Finset.sum_const","Finset.sum_le_sum","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","HAdd.hAdd","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","LE.le","LE.le.trans","Membership.mem","NSMul.toSMul","Nat","Nat.cast","Nat.cast_add._simp_1","Nat.cast_le._simp_1","Nat.cast_sum","Nat.instAddCommMonoid","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Preorder.toLE","Real","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRing","Real.instSub","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toNonAssocSemiring","Set","Set.decidableCompl","Set.instCompl","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.degree","SimpleGraph.degree_le_between_add","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges","SimpleGraph.minDegree","SimpleGraph.minDegree_le_degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Subtype.fintype","Sym2","Sym2.instFintype","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.between_verts_isBipartiteWith","cast","congrArg","covariant_swap_add_of_covariant_add","id","instAddNat","instDecidableEqFin","instHAdd","instHMul","instHSMul","instHSub","instLENat","nsmul_eq_mul","sub_le_iff_le_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.mul_le_card_filter_mul","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone","reducibility":null,"statement_dag_size":180,"type_refs":["DecidableRel","DivInvMonoid.toDiv","Fin","Fin.fintype","Finset.card","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","LT.lt","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.minDegree","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instOfNatNat"],"value_dag_size":1815,"value_refs":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CommMagma.toMul","CommMonoidWithZero.toMonoidWithZero","CommRing.toNonUnitalCommRing","CommSemigroup.toCommMagma","Compl.compl","DecidableRel","Distrib.leftDistribClass","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Fin","Fin.fintype","Finset","Finset.card","Finset.decidableMem'","Finset.instSetLike","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GE.ge","GroupWithZero.toMulDivCancelClass","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LE.le.trans","LT.lt","LT.lt.ne'","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast","Nat.cast_inj._simp_1","Nat.cast_mul","Nat.cast_nonneg","Nat.cast_zero","Nat.instPreorder","Ne","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toHasDistribNeg","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instCommMonoidWithZero","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instSemigroup","Real.instSub","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semigroup.toMul","Semiring.toNonAssocSemiring","Set","Set.decidableCompl","Set.instCompl","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.card_verts","SimpleGraph.CompleteEquipartiteSubgraph.verts","SimpleGraph.between","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjBetweenOfDecidablePredMemSet","SimpleGraph.minDegree","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","Sym2","Sym2.instFintype","Trans.trans","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.card_edgeFinset_between_verts_le","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.le_card_edgeFinset_between_verts","add_sub_assoc","add_sub_cancel_right","add_sub_sub_cancel","cast","congrArg","covariant_swap_add_of_covariant_add","id","instDecidableEqFin","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatNat","instTransEq","instTransEq_1","instTransLE","mul_add","mul_assoc","mul_div_cancel_left₀","mul_le_mul_of_nonneg_left","mul_one","mul_one_div","mul_rotate","mul_sub","neg_mul","neg_sub","rfl","sub_add_cancel","sub_add_eq_add_sub","sub_add_sub_cancel","sub_eq_add_neg","sub_le_sub_right","sub_left_le_of_le_add","sub_mul","sub_right_comm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Finset","Finset.attach","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","True"],"value_dag_size":60,"value_refs":["Finset","Finset.attach","Finset.instSetLike","Finset.mem_attach","Membership.mem","SetLike.instMembership","Subtype","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":"abbrev","statement_dag_size":263,"type_refs":["DecidableRel","DivInvMonoid.toDiv","Exists","Exists.intro","Fin","Fin.fintype","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.cast","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Prod","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsContained","SimpleGraph.completeEquipartiteGraph","SimpleGraph.minDegree","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instOfNatNat","instSubNat"],"value_dag_size":301,"value_refs":["DecidableRel","DivInvMonoid.toDiv","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.cast","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Prod","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsContained","SimpleGraph.completeEquipartiteGraph","SimpleGraph.minDegree","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":"abbrev","statement_dag_size":1127,"type_refs":["And","And.intro","DecidableRel","Eq","Exists","Exists.intro","Fin","Fin.fintype","Finset","Finset.Subtype.fintype","Finset.card","Finset.decidableEq","Finset.decidableMem","Finset.filter","Finset.fintype","Finset.instPartialOrder","Finset.instSetLike","Finset.pi","Finset.powersetCard","Finset.univ","Fintype.decidablePiFintype","Function.decidableEqPFun","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.instDecidableEq","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","instDecidableEqFin"],"value_dag_size":1402,"value_refs":["And","And.casesOn","And.intro","DecidableRel","Eq","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Finset","Finset.Subtype.fintype","Finset.card","Finset.decidableEq","Finset.decidableMem","Finset.filter","Finset.fintype","Finset.instPartialOrder","Finset.instSetLike","Finset.pi","Finset.powersetCard","Finset.univ","Fintype.decidablePiFintype","Function.decidableEqPFun","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype","Subtype.instDecidableEq","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.ErdosStone.filter.pi","instDecidableEqFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree.match_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits.0.SimpleGraph.eventually_completeEquipartiteGraph_isContained_of_minDegree","reducibility":"abbrev","statement_dag_size":354,"type_refs":["Eq","Eq.refl","Exists","Exists.intro","Fin","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype.mk","Subtype.prop"],"value_dag_size":471,"value_refs":["Eq","Eq.refl","Exists","Exists.casesOn","Exists.intro","Fin","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.CompleteEquipartiteSubgraph","SimpleGraph.CompleteEquipartiteSubgraph.parts","Subtype.mk","Subtype.prop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Set","Set.Pairwise","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsClique"],"value_dag_size":30,"value_refs":["Set","Set.Pairwise","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsClique","SimpleGraph.isClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","DecidableRel","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Fintype","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.cliqueFinset"],"value_dag_size":67,"value_refs":["DecidableEq","DecidableRel","EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.instEmptyCollection","Fintype","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.cliqueFinset","SimpleGraph.cliqueFinset_eq_empty_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":54,"type_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":59,"value_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.filter_eq_empty_iff","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","True","True.intro"],"value_dag_size":16,"value_refs":["True","True.intro","forall_true_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.card_parts","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.degree_eq_card_sub_part_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.degree_eq_card_sub_part_card","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.degree_eq_of_not_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.degree_eq_of_not_adj","reducibility":null,"statement_dag_size":300,"type_refs":["Classical.propDecidable","DecidableRel","Eq","Finset.card","Fintype","HAdd.hAdd","HSub.hSub","LT.lt","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.instLinearOrder","Ne","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjReplaceVertex","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.replaceVertex","Subtype.fintype","Sym2","Sym2.Rel","Sym2.instFintype","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":1393,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Classical.propDecidable","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset.card","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjReplaceVertex","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.replaceVertex","Subtype.fintype","Sym2","Sym2.Rel","Sym2.instFintype","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.equivalence_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.equivalence_not_adj","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.isEquipartition._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.isEquipartition","reducibility":null,"statement_dag_size":37,"type_refs":["False","Finset","Finset.card","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":127,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.isEquipartition._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.isEquipartition","reducibility":null,"statement_dag_size":130,"type_refs":["DecidableRel","Finset","Finset.card","Fintype","Fintype.card","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2.Rel","Sym2.instFintype","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2070,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Fintype","Fintype.card","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.instLinearOrder","Nat.not_le_eq","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","Sym2.Rel","Sym2.instFintype","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Fin","Fin.val","HMod.hMod","Nat","Nat.instMod","Ne","SimpleGraph.Adj","SimpleGraph.turanGraph","instHMod"],"value_dag_size":51,"value_refs":["Fin","Fin.val","HMod.hMod","Nat","Nat.instMod","Ne","SimpleGraph.Adj","SimpleGraph.turanGraph","SimpleGraph.turanGraph_adj","instHMod","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":393,"type_refs":["Classical.propDecidable","DecidableRel","Eq","Finset.card","Fintype","HAdd.hAdd","HSub.hSub","LT.lt","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjReplaceVertex","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.replaceVertex","Subtype.fintype","Sym2.Rel","Sym2.instFintype","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2252,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Classical.propDecidable","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset.card","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Prod","Quot","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instDecidableRelAdjReplaceVertex","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.replaceVertex","Subtype.fintype","Sym2.Rel","Sym2.instFintype","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":32,"type_refs":["DecidableEq","Eq","False","SimpleGraph","SimpleGraph.Adj","SimpleGraph.replaceVertex"],"value_dag_size":35,"value_refs":["DecidableEq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.not_adj_replaceVertex_same","SimpleGraph.replaceVertex","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.IsTuranMaximal.not_adj_trans","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph","reducibility":null,"statement_dag_size":112,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NPow.toPow","Nat","Nat.instDiv","Nat.instMod","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":304,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HPow.hPow","HSub.hSub","Int","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.instDiv","Nat.instMod","Nat.instMonoid","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHPow","instHSub","instMulNat","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":667,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph","reducibility":null,"statement_dag_size":115,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HPow.hPow","HSub.hSub","Monoid.toNPow","NPow.toPow","Nat","Nat.choose","Nat.instDiv","Nat.instMod","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":360,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HPow.hPow","HSub.hSub","Int","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.choose","Nat.instDiv","Nat.instMod","Nat.instMonoid","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHPow","instHSub","instMulNat","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add","reducibility":null,"statement_dag_size":103,"type_refs":["DecidableRel","Eq","Finset.card","Finset.sum","Finset.univ","Fintype","HMul.hMul","Membership.mem","Nat","Nat.instAddCommMonoid","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","Sym2","Sym2.instFintype","instHMul","instMulNat","instOfNatNat"],"value_dag_size":109,"value_refs":["DecidableRel","Eq.symm","Finset.card","Finset.sum","Finset.univ","Fintype","HMul.hMul","Membership.mem","Nat","Nat.instAddCommMonoid","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.sum_degrees_eq_twice_card_edges","Subtype.fintype","Sym2","Sym2.instFintype","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add","reducibility":null,"statement_dag_size":44,"type_refs":["AddCommMonoid","Eq","Fin","Fin.fintype","Fin.val","Finset.range","Finset.sum","Finset.univ","Nat"],"value_dag_size":50,"value_refs":["AddCommMonoid","Eq.symm","Fin","Fin.fintype","Fin.sum_univ_eq_sum_range","Fin.val","Finset.range","Finset.sum","Finset.univ","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph_add","reducibility":null,"statement_dag_size":81,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":86,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq.symm","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","two_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.exists_isTuranMaximal._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.exists_isTuranMaximal","reducibility":null,"statement_dag_size":43,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":242,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.exists_isTuranMaximal._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.exists_isTuranMaximal","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableRel","Eq","Exists","Fintype","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsExtremal"],"value_dag_size":47,"value_refs":["DecidableRel","Exists","Fintype","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsExtremal","SimpleGraph.exists_isExtremal_iff_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.isExtremal_top_free_iff_isTuranMaximal._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.isExtremal_top_free_iff_isTuranMaximal","reducibility":null,"statement_dag_size":47,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Fintype","Fintype.card","SimpleGraph","SimpleGraph.CliqueFree","SimpleGraph.Free","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":51,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Fintype","Fintype.card","SimpleGraph","SimpleGraph.CliqueFree","SimpleGraph.Free","SimpleGraph.cliqueFree_iff_top_free","SimpleGraph.completeAtomicBooleanAlgebra","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.mul_card_edgeFinset_turanGraph_le._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.mul_card_edgeFinset_turanGraph_le","reducibility":null,"statement_dag_size":66,"type_refs":["CommMagma.toMul","CommSemigroup.toCommMagma","HMod.hMod","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.instCommSemigroup","Nat.instMod","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","instHMod","instHMul","instHSub","instOfNatNat","instSubNat"],"value_dag_size":246,"value_refs":["Classical.byContradiction","CommMagma.toMul","CommSemigroup.toCommMagma","Eq","Eq.trans","False","False.casesOn","False.elim","HAdd.hAdd","HMod.hMod","HMul.hMul","HSub.hSub","LE.le","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_zero","Lean.Grind.Semiring.ofNat","Lean.Grind.Semiring.zero_mul","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Nat","Nat.ctorIdx","Nat.instCommSemigroup","Nat.instMod","Nat.instPreorder","Nat.le_zero_eq","Nat.mod_zero","Nat.not_le_eq","Nat.zero_sub","Not","OfNat.ofNat","Preorder.toLE","congr","congrArg","congrFun'","eq_false'","instAddNat","instHAdd","instHMod","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique"],"value_dag_size":50,"value_refs":["And","Eq","Finset","Finset.card","Finset.instSetLike","Nat","SetLike.coe","SimpleGraph","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.isNClique_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.not_cliqueFree_of_isTuranMaximal","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Finset.range","Finset.sum","HAdd.hAdd","HMod.hMod","HSub.hSub","Nat","Nat.instAddCommMonoid","Nat.instMod","Ne","OfNat.ofNat","instAddNat","instDecidableEqNat","instDecidableNot","instHAdd","instHMod","instHSub","instOfNatNat","instSubNat","ite"],"value_dag_size":1174,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","And.left","And.right","Distrib.rightDistribClass","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists.intro","Finset","Finset.Nonempty","Finset.card","Finset.card_filter","Finset.card_filter_add_card_filter_not","Finset.card_le_one_iff","Finset.card_range","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.one_le_card","Finset.range","Finset.sum","GT.gt","HAdd.hAdd","HMod.hMod","HMul.hMul","HSub.hSub","LE.le","LT.lt","Membership.mem","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","Nat","Nat.ModEq","Nat.ModEq.add_iff_left","Nat.ModEq.symm","Nat.ModEq.trans","Nat.add_mod_mod","Nat.eq_sub_of_add_eq'","Nat.eq_zero_or_pos","Nat.instAddCommMonoid","Nat.instAddSemigroup","Nat.instCanonicallyOrderedAdd","Nat.instDecidableModEq","Nat.instDistrib","Nat.instMod","Nat.instMulOneClass","Nat.instOrderedSub","Nat.instPartialOrder","Nat.mod_eq_of_lt","Nat.mod_lt","Nat.mod_zero","Nat.mul_add_mod_self_left","Ne","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._simp_1_2","add_assoc","congr","congrArg","congrFun'","eq_self","funext","id","instAddNat","instDecidableEqNat","instDecidableNot","instHAdd","instHMod","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat","ite","ite_congr","ite_not","le_antisymm","of_eq_true","one_add_mul","propext","rfl","zero_tsub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","GT.gt","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":641,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":34,"value_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":37,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":40,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Iff"],"value_dag_size":19,"value_refs":["Eq","Iff","eq_iff_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Iff","Not"],"value_dag_size":20,"value_refs":["Iff","Not","not_iff_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_eq_top","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.val","Fin.val_inj","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Turan","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.turanGraph_zero","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.val","Fin.val_inj","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.toFinset"],"value_dag_size":56,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mem_toFinset","Sym2.toFinset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two","reducibility":null,"statement_dag_size":42,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.booleanAlgebra","Finset.instSDiff","Finset.univ","Fintype","SDiff.sdiff"],"value_dag_size":48,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq.symm","Finset","Finset.booleanAlgebra","Finset.compl_eq_univ_sdiff","Finset.instSDiff","Finset.univ","Fintype","SDiff.sdiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.eventually_isContained_of_card_edgeFinset.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.eventually_isContained_of_card_edgeFinset","reducibility":"abbrev","statement_dag_size":154,"type_refs":["And","And.intro","DivInvMonoid.toDiv","Eq","Exists","Exists.intro","HDiv.hDiv","Membership.mem","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.Ici","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.extremalNumber","instHDiv","instOfNatNat"],"value_dag_size":229,"value_refs":["And","And.casesOn","And.intro","DivInvMonoid.toDiv","Eq","Exists","Exists.casesOn","Exists.intro","HDiv.hDiv","Membership.mem","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.Ici","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.extremalNumber","instHDiv","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.eventually_isContained_of_card_edgeFinset.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.eventually_isContained_of_card_edgeFinset","reducibility":"abbrev","statement_dag_size":374,"type_refs":["And","And.intro","DecidableRel","Exists","Exists.intro","Fin","Fin.fintype","Finset.card","GE.ge","HAdd.hAdd","HMul.hMul","IsEmpty","LE.le","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Real","Real.instAdd","Real.instLE","Real.instMul","Real.instNatCast","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.turanDensity","Sym2","Sym2.instFintype","instHAdd","instHMul","instOfNatNat"],"value_dag_size":825,"value_refs":["And","And.casesOn","And.intro","DecidableRel","Exists","Exists.casesOn","Exists.intro","Fin","Fin.fintype","Finset.card","GE.ge","HAdd.hAdd","HMul.hMul","IsEmpty","LE.le","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Real","Real.instAdd","Real.instLE","Real.instMul","Real.instNatCast","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.turanDensity","Sym2","Sym2.instFintype","instHAdd","instHMul","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.isEquivalent_extremalNumber._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.isEquivalent_extremalNumber","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LT.lt","Nat","Nat.choose","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq","LT.lt","Nat","Nat.choose","Nat.choose_eq_zero_iff","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.isGLB_turanDensity.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.isGLB_turanDensity","reducibility":"abbrev","statement_dag_size":155,"type_refs":["And","And.intro","DivInvMonoid.toDiv","Eq","Exists","Exists.intro","HDiv.hDiv","Membership.mem","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.Ici","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.extremalNumber","instHDiv","instOfNatNat"],"value_dag_size":234,"value_refs":["And","And.casesOn","And.intro","DivInvMonoid.toDiv","Eq","Exists","Exists.casesOn","Exists.intro","HDiv.hDiv","Membership.mem","Nat","Nat.cast","Nat.choose","Nat.instPreorder","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instNatCast","Set","Set.Ici","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.extremalNumber","instHDiv","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff","reducibility":null,"statement_dag_size":113,"type_refs":["And","DistribLattice.toLattice","Eq","Exists","Finset","Finset.instSetLike","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":120,"value_refs":["And","DistribLattice.toLattice","Exists","Finset","Finset.instSetLike","Finset.lt_sup_iff","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff.match_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff","reducibility":"abbrev","statement_dag_size":346,"type_refs":["And","And.intro","Classical.propDecidable","DistribLattice.toLattice","Exists","Exists.intro","Finset.card","Fintype","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","Sum","Sym2","Sym2.instFintype","completeBipartiteGraph","instDistribLatticeOfLinearOrder","instFintypeSum"],"value_dag_size":578,"value_refs":["And","And.casesOn","And.intro","Classical.propDecidable","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset.card","Fintype","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","Sum","Sym2","Sym2.instFintype","completeBipartiteGraph","instDistribLatticeOfLinearOrder","instFintypeSum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff.match_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.lt_zarankiewicz_iff","reducibility":"abbrev","statement_dag_size":373,"type_refs":["And","And.intro","DecidableRel","Exists","Exists.intro","Finset.card","Fintype","LE.le","LT.lt","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","Sum","Sym2","Sym2.instFintype","completeBipartiteGraph","instFintypeSum","instLTNat"],"value_dag_size":741,"value_refs":["And","And.casesOn","And.intro","DecidableRel","Exists","Exists.casesOn","Exists.intro","Finset.card","Fintype","LE.le","LT.lt","Nat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","Sum","Sym2","Sym2.instFintype","completeBipartiteGraph","instFintypeSum","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symm","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symm._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symm","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz","reducibility":null,"statement_dag_size":155,"type_refs":["And","Classical.propDecidable","Eq","Fin","Fin.fintype","Finset.card","Finset.filter","Finset.sup","Finset.univ","LE.le","Lattice.toSemilatticeSup","Nat","Nat.instLattice","Nat.instOrderBot","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Free","SimpleGraph.IsContained","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","SimpleGraph.zarankiewicz","Sum","Sym2","Sym2.instFintype","completeBipartiteGraph","instDecidableAnd","instDecidableEqFin","instDecidableEqSum","instDecidableNot","instFintypeSimpleGraphOfDecidableEq","instFintypeSum"],"value_dag_size":17,"value_refs":["Eq.refl","Nat","SimpleGraph.zarankiewicz"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_extremalNumber","reducibility":"abbrev","statement_dag_size":116,"type_refs":["And","And.intro","Fin","LE.le","Nat","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"],"value_dag_size":137,"value_refs":["And","And.casesOn","And.intro","Fin","LE.le","Nat","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff.match_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_le_iff","reducibility":"abbrev","statement_dag_size":122,"type_refs":["And","And.intro","LE.le","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","LE.le","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Membership.mem","Nat","SetLike.instMembership","Subtype"],"value_dag_size":58,"value_refs":["Eq.symm","Finset","Finset.card","Finset.instSetLike","Fintype","Fintype.card","Fintype.card_coe","Membership.mem","Nat","SetLike.instMembership","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"],"value_dag_size":60,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","SimpleGraph.mem_edgeFinset","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":"abbrev","statement_dag_size":116,"type_refs":["And","And.intro","Fin","LE.le","Nat","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"],"value_dag_size":137,"value_refs":["And","And.casesOn","And.intro","Fin","LE.le","Nat","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz","name":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq.match_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz.0.SimpleGraph.zarankiewicz_of_fintypeCard_eq","reducibility":"abbrev","statement_dag_size":122,"type_refs":["And","And.intro","LE.le","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","LE.le","SimpleGraph","SimpleGraph.Free","SimpleGraph.instLE","Sum","completeBipartiteGraph"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.Adj.card_commonNeighbors_lt_degree._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.Adj.card_commonNeighbors_lt_degree","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","DecidableEq","Finset","Finset.insert_subset_iff","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_commonNeighbors_le_degree_right._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_commonNeighbors_le_degree_right","reducibility":null,"statement_dag_size":91,"type_refs":["DecidableRel","Eq","Fintype","Fintype.card","LE.le","Membership.mem","Nat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.decidableMemCommonNeighbors","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","instLENat"],"value_dag_size":95,"value_refs":["DecidableRel","Fintype","Fintype.card","LE.le","Membership.mem","Nat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.card_commonNeighbors_le_degree_left","SimpleGraph.commonNeighbors","SimpleGraph.decidableMemCommonNeighbors","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_commonNeighbors_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_commonNeighbors_top","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_edgeFinset_top_eq_card_choose_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.card_edgeFinset_top_eq_card_choose_two","reducibility":null,"statement_dag_size":74,"type_refs":["Compl.compl","DecidableEq","Eq","Fintype","Fintype.card","Membership.mem","Nat","Nat.choose","OfNat.ofNat","Set","Set.Elem","Set.decidableCompl","Set.instCompl","Set.instMembership","Subtype.fintype","Sym2","Sym2.decidablePred_mem_diagSet","Sym2.diagSet","Sym2.instFintype","instOfNatNat"],"value_dag_size":79,"value_refs":["Compl.compl","DecidableEq","Eq.symm","Fintype","Fintype.card","Membership.mem","Nat","Nat.choose","OfNat.ofNat","Set","Set.Elem","Set.decidableCompl","Set.instCompl","Set.instMembership","Subtype.fintype","Sym2","Sym2.card_diagSet_compl","Sym2.decidablePred_mem_diagSet","Sym2.diagSet","Sym2.instFintype","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.complete_graph_degree._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.complete_graph_degree","reducibility":null,"statement_dag_size":37,"type_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","Top.top"],"value_dag_size":40,"value_refs":["BooleanAlgebra.toTop","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_eq_card_sub_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_eq_card_sub_one","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_eq_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_eq_zero","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_induce_of_neighborSet_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_induce_of_neighborSet_subset","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_le_of_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_le_of_le","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Fintype","Fintype.card","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Fintype","Fintype.card","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborSet_eq_degree","SimpleGraph.degree","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_lt_card_sub_one._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_lt_card_sub_one","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableRel","Fintype","Fintype.card","HSub.hSub","Iff","LT.lt","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniversal","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":918,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fintype","Fintype.card","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_sub_one_of_lt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniversal","SimpleGraph.degree","SimpleGraph.degree_eq_card_sub_one","SimpleGraph.degree_lt_card_verts","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_pos._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_pos","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set.Elem","SimpleGraph","SimpleGraph.card_neighborFinset_eq_degree","SimpleGraph.degree","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_pos_iff_exists_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.degree_pos_iff_exists_adj","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.card","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":34,"value_refs":["Finset","Finset.Nonempty","Finset.card","Finset.card_pos","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_edgeFinset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_edgeFinset","reducibility":null,"statement_dag_size":67,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq.symm","Finset","Finset.disjoint_coe","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_edgeFinset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_edgeFinset","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":82,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_incidenceFinset_of_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_incidenceFinset_of_disjoint","reducibility":null,"statement_dag_size":67,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq.symm","Finset","Finset.disjoint_coe","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_neighborFinset_of_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.disjoint_neighborFinset_of_disjoint","reducibility":null,"statement_dag_size":67,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq.symm","Finset","Finset.disjoint_coe","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.edgeFinset_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.edgeFinset_top","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.exists_maximal_degree_vertex._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.exists_maximal_degree_vertex","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableRel","Eq","Exists","Fintype","Membership.mem","Nat","Nonempty","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.maxDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"],"value_dag_size":713,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty.image","Finset.image","Finset.instSetLike","Finset.max","Finset.max_mem_image_coe","Finset.mem_image","Finset.univ","Finset.univ_nonempty","Fintype","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_exists","LinearOrder.toDecidableEq","Membership.mem","Nat","Nat.instLinearOrder","Nonempty","Not","OfNat.ofNat","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.maxDegree","SimpleGraph.maxDegree.eq_1","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","True.intro","WithBot","WithBot.decidableEq","WithBot.some","WithBot.unbotD","WithBot.unbotD_coe","congrArg","eq_false","eq_true","id","instDecidableEqNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.exists_minimal_degree_vertex._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.exists_minimal_degree_vertex","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableRel","Eq","Exists","Fintype","Membership.mem","Nat","Nonempty","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"],"value_dag_size":713,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty.image","Finset.image","Finset.instSetLike","Finset.mem_image","Finset.min","Finset.min_mem_image_coe","Finset.univ","Finset.univ_nonempty","Fintype","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_exists","LinearOrder.toDecidableEq","Membership.mem","Nat","Nat.instLinearOrder","Nonempty","Not","OfNat.ofNat","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.minDegree","SimpleGraph.minDegree.eq_1","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","True.intro","WithTop","WithTop.decidableEq","WithTop.some","WithTop.untopD","WithTop.untopD_coe","congrArg","eq_false","eq_true","id","instDecidableEqNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.filter_edgeFinset_toFinset_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.filter_edgeFinset_toFinset_subset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.filter_edgeFinset_toFinset_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.filter_edgeFinset_toFinset_subset","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":67,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_sym2_iff","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.incidenceFinset_eq_filter._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.incidenceFinset_eq_filter","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Iff","Membership.mem","Not","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":666,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.insert_neighborFinset_eq_univ","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.le_minDegree_induce_of_support_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.le_minDegree_induce_of_support_subset","reducibility":null,"statement_dag_size":56,"type_refs":["DecidableRel","Eq","Fintype","Nat","Ne","Nonempty","OfNat.ofNat","Set","Set.univ","SimpleGraph","SimpleGraph.Adj","SimpleGraph.minDegree","SimpleGraph.support","instOfNatNat"],"value_dag_size":62,"value_refs":["DecidableRel","Eq","Fintype","Nat","Ne","Nonempty","OfNat.ofNat","Set","Set.univ","SimpleGraph","SimpleGraph.Adj","SimpleGraph.minDegree","SimpleGraph.minDegree_eq_zero_iff_support_ne","SimpleGraph.support","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.le_minDegree_induce_of_support_subset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.le_minDegree_induce_of_support_subset","reducibility":null,"statement_dag_size":26,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Nonempty","Set","Set.instEmptyCollection","Set.univ"],"value_dag_size":26,"value_refs":["EmptyCollection.emptyCollection","Eq","Nonempty","Set","Set.empty_ne_univ","Set.instEmptyCollection","Set.univ","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Exists","Sym2","Sym2.mk"],"value_dag_size":35,"value_refs":["Exists","Sym2","Sym2.exists","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.map_edgeFinset_induce","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.maxDegree_eq_zero_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.maxDegree_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableRel","Eq","Fintype","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.maxDegree","instOfNatNat"],"value_dag_size":343,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fintype","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.degree","SimpleGraph.degree_eq_zero","SimpleGraph.degree_le_maxDegree","SimpleGraph.maxDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","eagerReduce","eq_false","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableRel","Eq","Exists","Fintype","Nat","Nonempty","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.minDegree","instOfNatNat"],"value_dag_size":229,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fintype","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_exists","Membership.mem","Nat","Nonempty","Not","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.degree","SimpleGraph.degree_eq_zero","SimpleGraph.exists_minimal_degree_vertex","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","True.intro","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableRel","Eq","Fintype","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.minDegree","instOfNatNat"],"value_dag_size":347,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fintype","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.degree","SimpleGraph.degree_eq_zero","SimpleGraph.minDegree","SimpleGraph.minDegree_le_degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","True","eagerReduce","eq_true","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff","reducibility":"abbrev","statement_dag_size":47,"type_refs":["Exists","Exists.intro","SimpleGraph","SimpleGraph.IsIsolated"],"value_dag_size":64,"value_refs":["Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.IsIsolated"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff_support_ne._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff_support_ne","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Membership.mem","Ne","Not","Set","Set.instMembership","Set.univ"],"value_dag_size":37,"value_refs":["Exists","Membership.mem","Ne","Not","Set","Set.instMembership","Set.ne_univ_iff_exists_notMem","Set.univ","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff_support_ne._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_eq_zero_iff_support_ne","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableRel","Eq","Exists","Fintype","Nat","Nonempty","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.minDegree","instOfNatNat"],"value_dag_size":60,"value_refs":["DecidableRel","Eq","Exists","Fintype","Nat","Nonempty","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsIsolated","SimpleGraph.minDegree","SimpleGraph.minDegree_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_lt_card.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.minDegree_lt_card","reducibility":"abbrev","statement_dag_size":175,"type_refs":["DecidableRel","Eq","Exists","Exists.intro","Fintype","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"],"value_dag_size":218,"value_refs":["DecidableRel","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.minDegree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_eq_empty._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_eq_empty","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_eq_erase_univ._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_eq_erase_univ","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","DecidableRel","Eq","Finset","Finset.erase","Finset.univ","Fintype","Iff","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniversal","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype"],"value_dag_size":1160,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finset.mem_univ","Finset.univ","Fintype","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniversal","SimpleGraph.insert_neighborFinset_eq_univ","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","SimpleGraph.notMem_neighborFinset_self","Subtype.fintype","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_inf._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_inf","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_nonempty._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_nonempty","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.Nonempty","Finset.instEmptyCollection","Ne"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.nonempty_iff_ne_empty","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sdiff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sdiff","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sup._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sup","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sup_of_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_sup_of_disjoint","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Finite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finite.0.SimpleGraph.neighborFinset_top","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Finsubgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Finsubgraph___unexpand_SimpleGraph_FinsubgraphHom_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":250,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Finsubgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph.«_aux_Mathlib_Combinatorics_SimpleGraph_Finsubgraph___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Finsubgraph_0_SimpleGraph_term_→fg__1»","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":234,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Finsubgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph.«term_→fg_»","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Finsubgraph.0.SimpleGraph","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":61,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.card_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.card_left","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Nat","Nat.succ"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Nat","Nat.succ","Nat.succ_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exist_not_adj_of_adj_inter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike","reducibility":null,"statement_dag_size":195,"type_refs":["And","DecidableEq","Exists","Finset","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Ne","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.IsFiveWheelLike","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1508,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Ne","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.isNClique_fst_left","SimpleGraph.IsFiveWheelLike.isNClique_left","SimpleGraph.IsFiveWheelLike.isNClique_right","SimpleGraph.IsFiveWheelLike.isNClique_snd_right","SimpleGraph.IsNClique.exists_not_adj_of_cliqueFree_succ","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exist_not_adj_of_adj_inter._proof_1_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exist_not_adj_of_adj_inter._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exist_not_adj_of_adj_inter","reducibility":null,"statement_dag_size":222,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instInter","Finset.instSetLike","Insert.insert","Inter.inter","Membership.mem","Nat","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsFiveWheelLike"],"value_dag_size":2002,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_insert","Finset.mem_inter","HAdd.hAdd","Iff","Insert.insert","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsFiveWheelLike.fst_notMem_right","SimpleGraph.IsFiveWheelLike.snd_notMem_left","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.fst_ne_snd","SimpleGraph.IsPathGraph3Compl.ne_fst","SimpleGraph.IsPathGraph3Compl.ne_snd","True","True.intro","congr","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","False","Ne"],"value_dag_size":57,"value_refs":["Eq","Eq.mp","Eq.symm","Eq.trans","False","Ne","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","Eq","False","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":303,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","Eq","False","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":310,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":73,"type_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSingleton","Finset.instUnion","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Union.union"],"value_dag_size":904,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_union","Finset.singleton_union","Finset.subset_iff","Finset.union_insert","Iff","Insert.insert","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","True","True.intro","Union.union","congrArg","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","Finset","Nat","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsPathGraph3Compl"],"value_dag_size":280,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":412,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.erase","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","HAdd.hAdd","Iff","Insert.insert","Inter.inter","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":412,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.erase","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","HAdd.hAdd","Iff","Insert.insert","Inter.inter","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":412,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.erase","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","HAdd.hAdd","Iff","Insert.insert","Inter.inter","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":414,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.erase","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","HAdd.hAdd","Iff","Insert.insert","Inter.inter","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":252,"type_refs":["And","DecidableEq","DecidableRel","Eq","Finset","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Insert.insert","Membership.mem","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","Union.union","instDecidableNot"],"value_dag_size":1864,"value_refs":["And","Classical.byContradiction","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_filter","Finset.mem_insert","Finset.mem_singleton","Finset.mem_union","Finset.singleton_union","Finset.union_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_left","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Ne","Not","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","True","True.intro","Union.union","congr","congrArg","eq_false","eq_true","id","instDecidableNot","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":242,"type_refs":["And","DecidableEq","DecidableRel","Eq","Finset","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Insert.insert","Membership.mem","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","Union.union","instDecidableNot"],"value_dag_size":1812,"value_refs":["And","Classical.byContradiction","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_filter","Finset.mem_insert","Finset.mem_singleton","Finset.mem_union","Finset.singleton_union","Finset.union_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_left","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Ne","Not","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","True","True.intro","Union.union","congr","congrArg","eq_false","eq_true","id","instDecidableNot","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":154,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Not","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike"],"value_dag_size":1102,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsFiveWheelLike.fst_notMem_right","SimpleGraph.IsFiveWheelLike.snd_notMem_left","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.ne_fst","SimpleGraph.IsPathGraph3Compl.ne_snd","True","True.intro","congr","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":"abbrev","statement_dag_size":56,"type_refs":["And","And.intro","Eq"],"value_dag_size":71,"value_refs":["And","And.casesOn","And.intro","Eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two.match_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":"abbrev","statement_dag_size":147,"type_refs":["And","And.intro","DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":164,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two.match_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":"abbrev","statement_dag_size":184,"type_refs":["And","And.intro","Finset","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":443,"value_refs":["And","And.casesOn","And.intro","Finset","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two.match_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.exists_isFiveWheelLike_succ_of_not_adj_le_two","reducibility":"abbrev","statement_dag_size":77,"type_refs":["And","And.intro","Ne"],"value_dag_size":124,"value_refs":["And","And.casesOn","And.intro","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":197,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instSingleton","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.IsFiveWheelLike","Singleton.singleton","Union.union","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":2976,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","Singleton.singleton","True","Union.union","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":240,"type_refs":["AddSemigroup.toAdd","DecidableEq","Eq","Finset","Finset.card","Finset.instSingleton","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.instAddSemigroup","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","SimpleGraph","SimpleGraph.IsFiveWheelLike","Singleton.singleton","Union.union","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1980,"value_refs":["AddSemigroup.toAdd","Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instAddSemigroup","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Preorder.toLE","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","Singleton.singleton","True","Union.union","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":95,"type_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Insert.insert","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","Union.union"],"value_dag_size":451,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_union","Finset.singleton_union","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","True","True.intro","Union.union","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":108,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instSingleton","Finset.instUnion","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.IsFiveWheelLike","Singleton.singleton","Union.union","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":3351,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_singleton","Finset.card_union_add_card_inter","Finset.decidableMem","Finset.insert_inter","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_singleton","Finset.mem_union","Finset.singleton_union","HAdd.hAdd","HMul.hMul","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instMul","Int.instNegInt","Inter.inter","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.card_left","SimpleGraph.IsFiveWheelLike.card_right","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsFiveWheelLike.fst_notMem_right","SimpleGraph.IsFiveWheelLike.snd_notMem_left","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.fst_ne_snd","SimpleGraph.IsPathGraph3Compl.ne_fst","SimpleGraph.IsPathGraph3Compl.ne_snd","Singleton.singleton","True","Union.union","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":270,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","DecidableRel","Eq","Finset","Finset.booleanAlgebra","Finset.card","Finset.decidableMem","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.univ","Fintype","Fintype.decidableForallFintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Inter.inter","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsFiveWheelLike","Singleton.singleton","Union.union","forall_prop_decidable","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":4912,"value_refs":["Bool","Bool.true","BooleanAlgebra.toCompl","Classical.byContradiction","Compl.compl","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.booleanAlgebra","Finset.card","Finset.card_insert_of_notMem","Finset.card_singleton","Finset.card_union_add_card_inter","Finset.decidableMem","Finset.filter","Finset.insert_inter","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_singleton","Finset.mem_union","Finset.singleton_union","Finset.union_insert","Finset.univ","Fintype","Fintype.decidableForallFintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Insert.insert","Int","Int.instNegInt","Inter.inter","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Ne","Neg.neg","Not","OfNat.ofNat","Or","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.card_left","SimpleGraph.IsFiveWheelLike.card_right","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsFiveWheelLike.fst_notMem_right","SimpleGraph.IsFiveWheelLike.snd_notMem_left","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","SimpleGraph.IsPathGraph3Compl.fst_ne_snd","SimpleGraph.IsPathGraph3Compl.ne_fst","SimpleGraph.IsPathGraph3Compl.ne_snd","Singleton.singleton","True","Union.union","congrArg","eagerReduce","eq_false","eq_true","forall_prop_decidable","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":81,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":86,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq.symm","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","two_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succ","reducibility":"abbrev","statement_dag_size":150,"type_refs":["And","DecidableEq","Exists","Exists.intro","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":188,"value_refs":["And","DecidableEq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.not_colorable_succ.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.not_colorable_succ","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Fin","HAdd.hAdd","Nat","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":76,"value_refs":["Fin","HAdd.hAdd","Nat","Nonempty.casesOn","Nonempty.intro","OfNat.ofNat","SimpleGraph","SimpleGraph.Colorable","SimpleGraph.Coloring","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.symm.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsFiveWheelLike.symm","reducibility":"abbrev","statement_dag_size":245,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.mk","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":347,"value_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.IsFiveWheelLike","SimpleGraph.IsFiveWheelLike.casesOn","SimpleGraph.IsFiveWheelLike.mk","SimpleGraph.IsNClique","SimpleGraph.IsPathGraph3Compl","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":317,"value_refs":["DecidableEq","Eq","Eq.ndrec","Eq.rec","Eq.symm","False","False.elim","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Nat","Not","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.IsNClique","SimpleGraph.IsNClique.insert","SimpleGraph.IsNClique.isClique"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique","reducibility":null,"statement_dag_size":115,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Ne","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique"],"value_dag_size":457,"value_refs":["And","And.left","And.right","DecidableEq","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","False","False.elim","Finset","Finset.erase","Finset.erase_insert_of_ne","Finset.insert_comm","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert_of_mem","Finset.mem_sdiff","Iff.mp","Insert.insert","Membership.mem","Nat","Ne","Not","SDiff.sdiff","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.IsNClique.insert_erase","Singleton.singleton","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase._simp_1_2","congrArg","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.IsNClique.insert_insert_erase","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","Ne","Not","SetLike.instMembership","Singleton.singleton"],"value_dag_size":48,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.instSingleton","Finset.notMem_singleton","Membership.mem","Ne","Not","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.colorable_iff_isCompleteMultipartite_of_maximal_cliqueFree.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.colorable_iff_isCompleteMultipartite_of_maximal_cliqueFree","reducibility":"abbrev","statement_dag_size":102,"type_refs":["HAdd.hAdd","Maximal","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.CliqueFree","SimpleGraph.instLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":140,"value_refs":["HAdd.hAdd","Maximal","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","SimpleGraph","SimpleGraph.CliqueFree","SimpleGraph.instLE","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.colorable_of_cliqueFree_lt_minDegree.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.colorable_of_cliqueFree_lt_minDegree","reducibility":"abbrev","statement_dag_size":230,"type_refs":["DecidableRel","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.instDiv","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.minDegree","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":367,"value_refs":["DecidableRel","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LT.lt","Nat","Nat.casesOn","Nat.instDiv","Nat.succ","Nat.zero","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.minDegree","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph","reducibility":null,"statement_dag_size":203,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","DecidableRel","Finset","Finset.booleanAlgebra","Finset.card","Finset.filter","Finset.instSetLike","Finset.sum","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Membership.mem","Nat","Nat.instAddCommMonoid","Not","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","instAddNat","instDecidableNot","instHAdd","instHMul","instHSub","instLENat","instMulNat","instSubNat"],"value_dag_size":1259,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","And","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","DecidableRel","Distrib.toMul","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Finset","Finset.booleanAlgebra","Finset.card","Finset.card_eq_sum_ones","Finset.filter","Finset.filter.congr_simp","Finset.filter_inter","Finset.instInter","Finset.instSetLike","Finset.instUnion","Finset.mem_inter._simp_1","Finset.mem_univ._simp_1","Finset.sum","Finset.sum_comm'","Finset.sum_congr","Finset.sum_le_sum","Finset.sum_mul","Finset.sum_union","Finset.union_compl","Finset.univ","Finset.univ_inter","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","HeytingAlgebra.toCompl","Iff","Inter.inter","IsOrderedAddMonoid.toAddLeftMono","LE.le","Membership.mem","Nat","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instIsOrderedAddMonoid","Nat.instMulOneClass","Nat.instNonUnitalNonAssocSemiring","Nat.instPreorder","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","Preorder.toLE","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.degree","SimpleGraph.mem_neighborFinset._simp_1","SimpleGraph.neighborFinset","SimpleGraph.neighborFinset_eq_filter","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Subtype.fintype","Trans.trans","True","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._simp_1_2","add_le_add","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","disjoint_compl_right","forall_congr","id","iff_self","implies_true","instAddNat","instDecidableNot","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat","instTransEq","of_eq_true","one_mul","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj","reducibility":null,"statement_dag_size":116,"type_refs":["DecidableRel","Finset","Finset.card","Finset.filter","Finset.instSetLike","HSub.hSub","LE.le","Membership.mem","Nat","Nat.instPreorder","Not","Preorder.toLE","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","instDecidableNot","instHSub","instLENat","instSubNat"],"value_dag_size":926,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_filter_add_card_filter_not","Finset.card_filter_le","Finset.filter","Finset.instSetLike","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","True","congrArg","eagerReduce","eq_true","id","instAddNat","instDecidableNot","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj","reducibility":null,"statement_dag_size":150,"type_refs":["BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","DecidableRel","Finset","Finset.booleanAlgebra","Finset.card","Finset.filter","Finset.instSetLike","Fintype","HSub.hSub","HeytingAlgebra.toCompl","LE.le","Membership.mem","Nat","Nat.instPreorder","Not","Preorder.toLE","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","instDecidableNot","instHSub","instLENat","instSubNat"],"value_dag_size":978,"value_refs":["BiheytingAlgebra.toHeytingAlgebra","Bool","Bool.true","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toCompl","Classical.byContradiction","Compl.compl","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.booleanAlgebra","Finset.card","Finset.card_filter_add_card_filter_not","Finset.card_filter_le","Finset.filter","Finset.instSetLike","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","HeytingAlgebra.toCompl","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","True","congrArg","eagerReduce","eq_true","id","instAddNat","instDecidableNot","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.SimpleGraph.sum_degree_le_of_le_not_adj","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0._aux_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike___unexpand_Fintype_card_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":240,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.«_aux_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike___macroRules__private_Mathlib_Combinatorics_SimpleGraph_FiveWheelLike_0_term‖_‖_1»","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":230,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.FiveWheelLike","name":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0.«term‖_‖»","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.FiveWheelLike.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":56,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":26,"type_refs":["ENat","Eq","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.egirth","Top.top","instTopENat"],"value_dag_size":35,"value_refs":["ENat","Eq","Eq.symm","SimpleGraph","SimpleGraph.IsAcyclic","SimpleGraph.egirth","SimpleGraph.egirth_eq_top","Top.top","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Ne","Ne.eq_def","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":54,"type_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENat","ENat.instNatCast","Eq","Nat","Nat.cast","Ne","Nonempty","Top.top","iInf","instCompleteLinearOrderENat","instTopENat"],"value_dag_size":56,"value_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENat","ENat.iInf_natCast_ne_top","ENat.instNatCast","Nat","Nat.cast","Ne","Nonempty","Top.top","iInf","instCompleteLinearOrderENat","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":25,"value_refs":["And","Eq.symm","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Exists","Subtype","Subtype.property","Subtype.val"],"value_dag_size":52,"value_refs":["Exists","Subtype","Subtype.exists'","Subtype.property","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Exists","Sigma","Sigma.fst","Sigma.snd"],"value_dag_size":53,"value_refs":["Exists","Sigma","Sigma.exists'","Sigma.fst","Sigma.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.exists_egirth_eq_length","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Girth","name":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.girth_eq_zero._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Girth.0.SimpleGraph.girth_eq_zero","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.girth","instLENat","instOfNatNat"],"value_dag_size":180,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.girth","eagerReduce","id","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le","reducibility":null,"statement_dag_size":72,"type_refs":["Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","Subtype.val"],"value_dag_size":186,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","Subtype.property","Subtype.val","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le","reducibility":null,"statement_dag_size":72,"type_refs":["Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","Subtype.val"],"value_dag_size":186,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","Subtype.property","Subtype.val","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","SetLike.coe"],"value_dag_size":30,"value_refs":["Eq.symm","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","Set.ncard_coe_finset","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","SetLike.coe"],"value_dag_size":30,"value_refs":["Eq.symm","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","Set.ncard_coe_finset","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":29,"type_refs":["Decidable","Eq","Exists","False","Not","dite"],"value_dag_size":33,"value_refs":["Decidable","Exists","False","Not","dite","dite_else_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":125,"type_refs":["Classical.propDecidable","Disjoint.notMem_of_mem_right","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.Subgraph.verts","Subtype.property","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph"],"value_dag_size":420,"value_refs":["Classical.byContradiction","Classical.propDecidable","Disjoint.notMem_of_mem_right","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","Set.instUnion","Set.mem_range","Set.mem_union","Set.range","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.Subgraph.verts","Subtype","Subtype.casesOn","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":48,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val"],"value_dag_size":57,"value_refs":["Eq.mpr_prop","Eq.refl","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":27,"type_refs":["Membership.mem","Set","Set.instMembership"],"value_dag_size":36,"value_refs":["Eq.mpr_prop","Eq.refl","Membership.mem","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":34,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val"],"value_dag_size":32,"value_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.property","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":46,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val"],"value_dag_size":55,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":289,"type_refs":["And","Classical.propDecidable","Disjoint.notMem_of_mem_right","Eq","Eq.mpr_prop","Eq.refl","Exists","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.Subgraph.verts","Subtype.mk","Subtype.property","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph"],"value_dag_size":1581,"value_refs":["And","Classical.byContradiction","Classical.propDecidable","Disjoint.notMem_of_mem_right","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","HEq.trans","Iff.mpr","Iff.of_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Or","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsBipartiteWith","SimpleGraph.IsBipartiteWith.disjoint","SimpleGraph.Subgraph.verts","Subtype","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","exists_prop_congr","heq_of_eq","id","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_isPerfectMatching_of_forall_ncard_le","reducibility":null,"statement_dag_size":29,"type_refs":["Decidable","Eq","Exists","False","Not","dite"],"value_dag_size":33,"value_refs":["Decidable","Exists","False","Not","dite","dite_else_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph","reducibility":"abbrev","statement_dag_size":74,"type_refs":["DecidablePred","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","Subtype.val"],"value_dag_size":185,"value_refs":["DecidablePred","Eq","False","Membership.mem","Not","Set","Set.Elem","Set.instMembership","Set.instUnion","Set.range","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.mk","Subtype.mk","Subtype.val","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_4","dite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","reducibility":null,"statement_dag_size":115,"type_refs":["DecidablePred","Eq","False","Lean.Grind.nestedDecidable","Membership.mem","Not","Set","Set.Elem","Set.instMembership","Set.instUnion","Set.range","Subtype","Subtype.mk","Union.union","dite"],"value_dag_size":423,"value_refs":["Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.Elem","Set.instMembership","Set.instUnion","Set.mem_range","Set.mem_union","Set.range","Subtype","Subtype.mk","True","True.intro","Union.union","dite","eq_false","eq_true","forall_not_of_not_exists","id","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","reducibility":null,"statement_dag_size":156,"type_refs":["DecidablePred","Eq","False","Lean.Grind.nestedDecidable","Membership.mem","Not","Set","Set.Elem","Set.instMembership","Subtype.mk","dite"],"value_dag_size":496,"value_refs":["Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.casesOn","Set","Set.Elem","Set.instMembership","Subtype.mk","True","True.intro","congrArg","dite","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","reducibility":null,"statement_dag_size":136,"type_refs":["DecidablePred","Eq","False","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype.mk","Subtype.val","dite"],"value_dag_size":360,"value_refs":["DecidablePred","Eq","Eq.mp","Eq.rec","False","False.elim","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","Subtype.mk","Subtype.val","dif_neg","dif_pos","dite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph","reducibility":null,"statement_dag_size":121,"type_refs":["DecidablePred","Eq","False","Membership.mem","Not","Set","Set.Elem","Set.instMembership","Std.Symm","Subtype.mk","dite"],"value_dag_size":128,"value_refs":["DecidablePred","Eq","False","Membership.mem","Not","Set","Set.Elem","Set.instMembership","Std.Symm.mk","Subtype.mk","_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.hall_subgraph._proof_2","dite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.union_eq_univ_of_forall_ncard_le._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.union_eq_univ_of_forall_ncard_le","reducibility":null,"statement_dag_size":54,"type_refs":["And","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":194,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","True","True.intro","Union.union","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hall","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.union_eq_univ_of_forall_ncard_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.union_eq_univ_of_forall_ncard_le","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","SetLike.coe"],"value_dag_size":30,"value_refs":["Eq.symm","Finset","Finset.card","Finset.instSetLike","Nat","Set.ncard","Set.ncard_coe_finset","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.IsHamiltonian.mono.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.IsHamiltonian.mono","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DecidableEq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle"],"value_dag_size":165,"value_refs":["DecidableEq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.IsHamiltonian.length_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.IsHamiltonian.length_support","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Fintype","Fintype.card","Inhabited","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.support"],"value_dag_size":1111,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","Fintype.card","Fintype.card_ne_zero","HAdd.hAdd","HMul.hMul","HSub.hSub","Inhabited","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.IsHamiltonian.length_eq","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instNonemptyOfInhabited","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.IsHamiltonian.toFinset_support._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.IsHamiltonian.toFinset_support","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":42,"value_refs":["Eq","Finset","Finset.eq_univ_iff_forall","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eq._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eq","reducibility":null,"statement_dag_size":84,"type_refs":["And","Eq","Fintype","Fintype.card","HSub.hSub","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.tail","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1136,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","Fintype.card","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.Nil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_tail_add_one","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eq","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Eq","Fintype","Fintype.card","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.length"],"value_dag_size":118,"value_refs":["And","And.casesOn","And.intro","Eq","Fintype","Fintype.card","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.length"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one","reducibility":null,"statement_dag_size":58,"type_refs":["And","DecidableEq","Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail"],"value_dag_size":63,"value_refs":["And","DecidableEq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","False","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.Nil"],"value_dag_size":38,"value_refs":["SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.Nil","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail","reducibility":"abbrev","statement_dag_size":76,"type_refs":["DecidableEq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.IsHamiltonianCycle.mk","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail"],"value_dag_size":115,"value_refs":["DecidableEq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.IsHamiltonianCycle.casesOn","SimpleGraph.Walk.IsHamiltonianCycle.mk","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail","reducibility":"abbrev","statement_dag_size":127,"type_refs":["And","And.intro","DecidableEq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail"],"value_dag_size":144,"value_refs":["And","And.casesOn","And.intro","DecidableEq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonian","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_rotate._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonianCycle_rotate","reducibility":null,"statement_dag_size":56,"type_refs":["And","DecidableEq","Eq","Fintype","Fintype.card","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.length"],"value_dag_size":63,"value_refs":["And","DecidableEq","Eq","Fintype","Fintype.card","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eq","SimpleGraph.Walk.length","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonian_iff_isPath_and_length_eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.Walk.isHamiltonian_iff_isPath_and_length_eq","reducibility":"abbrev","statement_dag_size":131,"type_refs":["And","And.intro","Eq","Fintype","Fintype.card","HSub.hSub","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","instHSub","instOfNatNat","instSubNat"],"value_dag_size":149,"value_refs":["And","And.casesOn","And.intro","Eq","Fintype","Fintype.card","HSub.hSub","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_bot_of_card_ne_one.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_bot_of_card_ne_one","reducibility":"abbrev","statement_dag_size":174,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DecidableEq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":245,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","DecidableEq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.completeAtomicBooleanAlgebra"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Fintype","Fintype.card","Nat","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":133,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fintype","Fintype.card","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_unsat","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Not","OfNat.ofNat","eagerReduce","id","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","False","Fintype","Fintype.card","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle","instOfNatNat"],"value_dag_size":251,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fintype","Fintype.card","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit.three_le_length","SimpleGraph.Walk.IsCycle.isCircuit","SimpleGraph.Walk.IsHamiltonianCycle","SimpleGraph.Walk.IsHamiltonianCycle.length_eq","SimpleGraph.Walk.IsHamiltonianCycle.toIsCycle","SimpleGraph.Walk.length","eagerReduce","id","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hamiltonian","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hamiltonian.0.SimpleGraph.not_isHamiltonian_of_card_eq_two","reducibility":"abbrev","statement_dag_size":102,"type_refs":["DecidableEq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle"],"value_dag_size":163,"value_refs":["DecidableEq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsHamiltonianCycle"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":106,"type_refs":["DecidableEq","HAdd.hAdd","LT.lt","List.idxOf","Membership.mem","Nat","OfNat.ofNat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":653,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","Subtype.property","Subtype.val","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":138,"type_refs":["DecidableEq","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":154,"value_refs":["DecidableEq","Eq.substr","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":176,"type_refs":["DFunLike.coe","DecidableEq","Fin","Fin.mk","Function.RightInverse","HAdd.hAdd","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instOfNatNat"],"value_dag_size":1927,"value_refs":["Bool","Bool.true","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.getElem_fin","Fin.instGetElemFinVal","Fin.mk","Fin.val","Function.LeftInverse","Function.LeftInverse.eq_1","Function.RightInverse","Function.RightInverse.eq_1","GetElem.getElem","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","Iff.mpr","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_idxOf","List.getElem_mem","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","RelHom","RelHom.coeFn_mk","RelHom.instFunLike","RelHom.mk","SemilatticeInf.toPartialOrder","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_5","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_6","SimpleGraph.Walk.pathGraphHomToSubgraph.eq_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_8","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_9","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_2","congrArg","congrFun","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":255,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":240,"value_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":156,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":85,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":68,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":389,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_15","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":70,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":407,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_14","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":275,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Fin.val","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":274,"value_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":319,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.instGetElemFinVal","Fin.mk","Fin.val","Function.LeftInverse","Function.RightInverse","GetElem.getElem","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_18","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":274,"value_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_6","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":276,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":275,"value_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_4","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":410,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Fin.val","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":426,"value_refs":["DFunLike.coe","DecidableEq","Eq.substr","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","Fin.val","Function.LeftInverse","Function.RightInverse","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_22","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":243,"type_refs":["DFunLike.coe","DecidableEq","Equiv","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Fin","Fin.mk","HAdd.hAdd","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom.instFunLike","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instOfNatNat"],"value_dag_size":8895,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Equiv","Equiv.coe_fn_mk","Equiv.instEquivLike","Equiv.mk","EquivLike.toFunLike","Exists","Exists.casesOn","False","False.elim","Fin","Fin.getElem_fin","Fin.instGetElemFinVal","Fin.mk","Fin.mk.inj","Fin.val","Function.LeftInverse","Function.LeftInverse.eq_1","Function.RightInverse","Function.RightInverse.eq_1","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq","HEq.trans","HMul.hMul","Iff","Iff.mp","Iff.mpr","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup.getElem_inj_iff","List.getD","List.getD_eq_getElem?_getD","List.getElem_mem","List.idxOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Option.getD_some","Option.some","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","RelHom","RelHom.coeFn_mk","RelHom.instFunLike","RelHom.mk","SemilatticeInf.toPartialOrder","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_12","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_6","SimpleGraph.Walk.IsPath.support_nodup","SimpleGraph.Walk.Nil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_getD_support","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_5","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_6","SimpleGraph.Walk.pathGraphHomToSubgraph.eq_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_iff","SimpleGraph.pathGraph","SimpleGraph.pathGraph_adj","Subtype","Subtype.mk","Subtype.mk.inj","Subtype.property","Subtype.val","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_14","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_15","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_16","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_17","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_18","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_19","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_20","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_21","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_3","congrArg","congrFun","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","funext","getElem?_pos","heq_eq_eq","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":160,"type_refs":["DFunLike.coe","DecidableEq","Fin","HAdd.hAdd","LT.lt","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":142,"value_refs":["DFunLike.coe","DecidableEq","Fin","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":184,"type_refs":["DFunLike.coe","DecidableEq","Fin","Fin.mk","Function.LeftInverse","HAdd.hAdd","List.idxOf","Membership.mem","Nat","OfNat.ofNat","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instOfNatNat"],"value_dag_size":2018,"value_refs":["Bool","Bool.true","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.getElem_fin","Fin.instGetElemFinVal","Fin.mk","Fin.val","Function.LeftInverse","Function.LeftInverse.eq_1","GetElem.getElem","HAdd.hAdd","HMul.hMul","Iff.mpr","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.Nodup.idxOf_getElem","List.getElem_mem","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","RelHom","RelHom.coeFn_mk","RelHom.instFunLike","RelHom.mk","SemilatticeInf.toPartialOrder","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.IsPath.support_nodup","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_5","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_6","SimpleGraph.Walk.pathGraphHomToSubgraph.eq_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.mk","Subtype.mk.inj","Subtype.property","Subtype.val","True","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_4","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_3","congrArg","congrFun","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":131,"type_refs":["DecidableEq","HAdd.hAdd","LT.lt","List.idxOf","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","Subtype.mk","Subtype.val","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":73,"value_refs":["DecidableEq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_2","SimpleGraph.Walk.toSubgraph","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":115,"type_refs":["DecidableEq","Fin.mk","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":114,"value_refs":["DecidableEq","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph","reducibility":null,"statement_dag_size":183,"type_refs":["DecidableEq","Fin","Fin.instGetElemFinVal","Fin.mk","Fin.val","GetElem.getElem","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_8","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":114,"value_refs":["DecidableEq","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List.idxOf","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_6","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph._proof_7","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph","reducibility":null,"statement_dag_size":142,"type_refs":["Fin","Fin.instGetElemFinVal","Fin.val","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":167,"value_refs":["Fin","Fin.instGetElemFinVal","Fin.val","GetElem.getElem","HAdd.hAdd","Iff.mpr","LT.lt","List","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph","reducibility":null,"statement_dag_size":98,"type_refs":["Fin","Fin.val","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":114,"value_refs":["Eq.substr","Fin","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph","reducibility":null,"statement_dag_size":243,"type_refs":["Fin","Fin.instGetElemFinVal","Fin.val","GetElem.getElem","HAdd.hAdd","Iff.mpr","LT.lt","List","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.pathGraph","Subtype","Subtype.mk","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1802,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","Fin","Fin.getElem_fin","Fin.instGetElemFinVal","Fin.isLt","Fin.val","GetElem.getElem","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSub.hSub","Iff","Iff.mpr","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coe_adj","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.pathGraphHomToSubgraph._proof_1","SimpleGraph.Walk.support","SimpleGraph.Walk.support_getElem_eq_getVert","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_getVert","SimpleGraph.pathGraph","SimpleGraph.pathGraph_adj","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.Walk.pathGraphHomToSubgraph._proof_3","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.cliqueFree_hasse_three._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.cliqueFree_hasse_three","reducibility":null,"statement_dag_size":39,"type_refs":["False","Preorder","SimpleGraph.Adj","SimpleGraph.hasse"],"value_dag_size":1146,"value_refs":["And","CovBy","CovBy.eq_1","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","LT.lt","Lean.Grind.Order.lt_eq_false_of_lt","Lean.Grind.Order.lt_trans","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Not","Or","Or.casesOn","Preorder","Preorder.toLE","Preorder.toLT","SimpleGraph.Adj","SimpleGraph.hasse","SimpleGraph.hasse_adj","True","True.intro","eq_true","id","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.cliqueFree_hasse_three.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.cliqueFree_hasse_three","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","OfNat.ofNat","Preorder","SetLike.coe","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.IsNClique.mk","SimpleGraph.hasse","instOfNatNat"],"value_dag_size":108,"value_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Nat","OfNat.ofNat","Preorder","SetLike.coe","SimpleGraph.IsClique","SimpleGraph.IsNClique","SimpleGraph.IsNClique.casesOn","SimpleGraph.IsNClique.mk","SimpleGraph.hasse","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasseDualIso._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasseDualIso","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","Or","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Adj","SimpleGraph.boxProd"],"value_dag_size":82,"value_refs":["And","Eq","Or","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Adj","SimpleGraph.boxProd","SimpleGraph.boxProd_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod","reducibility":null,"statement_dag_size":91,"type_refs":["And","CovBy","Eq","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.instPreorder","Prod.snd"],"value_dag_size":97,"value_refs":["And","CovBy","Eq","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.covBy_iff","Prod.fst","Prod.instPreorder","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Hasse","name":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Hasse.0.SimpleGraph.hasse_prod","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Or"],"value_dag_size":30,"value_refs":["Or","or_or_or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_eq_zero_iff","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","Membership.mem","OfNat.ofNat","Set","Set.indicator","Set.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":68,"value_refs":["Eq","Membership.mem","OfNat.ofNat","Set","Set.indicator","Set.indicator_apply_eq_zero","Set.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_eq_zero_iff","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["Eq","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","eq_false","one_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_mul_incMatrix_apply._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_mul_incMatrix_apply","reducibility":null,"statement_dag_size":45,"type_refs":["And","Decidable","Eq","instDecidableAnd","ite"],"value_dag_size":54,"value_refs":["And","Decidable","Eq.symm","instDecidableAnd","ite","ite_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_mul_incMatrix_apply._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_apply_mul_incMatrix_apply","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_transpose_mul_diag._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_transpose_mul_diag","reducibility":null,"statement_dag_size":10,"type_refs":["And","Eq"],"value_dag_size":12,"value_refs":["And","and_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_transpose_mul_diag._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.incMatrix_transpose_mul_diag","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.IncMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.IncMatrix.0.SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Init","name":"_private.Mathlib.Combinatorics.SimpleGraph.Init.0.initFn._@.Mathlib.Combinatorics.SimpleGraph.Init.3578731502._hygCtx._hyg.3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Init.0.initFn._@.Mathlib.Combinatorics.SimpleGraph.Init.3578731502._hygCtx._hyg","reducibility":"regular","statement_dag_size":3,"type_refs":["IO","Unit"],"value_dag_size":37,"value_refs":["Aesop.Frontend.declareRuleSetUnchecked","Aesop.RuleSetName","Array.forM","Array.mkArray1","Array.size","Bool.false","IO","IO.Error","Lean.Name","Lean.Name.mkStr1","Nat","OfNat.ofNat","instMonadEIO","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.dotProduct_mulVec_degMatrix._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.dotProduct_mulVec_degMatrix","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.sum","HSub.hSub","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHSub"],"value_dag_size":81,"value_refs":["Eq.symm","Finset","Finset.sum","Finset.sum_sub_distrib","HSub.hSub","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toAddCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'","reducibility":null,"statement_dag_size":75,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Finset","Finset.sum","HAdd.hAdd","instHAdd"],"value_dag_size":83,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","Finset","Finset.sum","Finset.sum_add_distrib","HAdd.hAdd","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj","reducibility":null,"statement_dag_size":149,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finset","Finset.instSetLike","Finset.sum","LE.le","Membership.mem","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero.toOfNat0"],"value_dag_size":157,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finset","Finset.instSetLike","Finset.sum","Finset.sum_eq_zero_iff_of_nonneg","LE.le","Membership.mem","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj","reducibility":null,"statement_dag_size":58,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub"],"value_dag_size":62,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub","propext","sub_eq_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"],"value_dag_size":55,"value_refs":["Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","OfNat.ofNat","One.toOfNat1","Real","Real.instOne","Real.instZero","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk","Zero.toOfNat0","ite"],"value_dag_size":308,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Real","Real.instOne","Real.instZero","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.eq","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.LapMatrix","name":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.LapMatrix.0.SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Embedding.complEquiv._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Embedding.complEquiv","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Iff","Not"],"value_dag_size":20,"value_refs":["Iff","Not","not_iff_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Hom.nonempty_hom_iff_exists_le_comap.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Hom.nonempty_hom_iff_exists_le_comap","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Nonempty","Nonempty.intro","SimpleGraph","SimpleGraph.Hom"],"value_dag_size":57,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro","SimpleGraph","SimpleGraph.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Hom.nonempty_hom_iff_exists_le_comap.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Hom.nonempty_hom_iff_exists_le_comap","reducibility":"abbrev","statement_dag_size":88,"type_refs":["Exists","Exists.intro","LE.le","SimpleGraph","SimpleGraph.comap","SimpleGraph.instLE"],"value_dag_size":113,"value_refs":["Exists","Exists.casesOn","Exists.intro","LE.le","SimpleGraph","SimpleGraph.comap","SimpleGraph.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Iso.map._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.Iso.map","reducibility":null,"statement_dag_size":65,"type_refs":["And","Eq","Exists","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map"],"value_dag_size":71,"value_refs":["And","Eq","Exists","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map","SimpleGraph.map_adj'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":81,"value_refs":["DFunLike.coe","Eq","Eq.symm","Equiv","Equiv.eq_symm_apply","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.comap_symm","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map","reducibility":"abbrev","statement_dag_size":234,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":475,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map","reducibility":"abbrev","statement_dag_size":230,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.Embedding.sym2Map","Function.instFunLikeEmbedding","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":317,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.Embedding.sym2Map","Function.instFunLikeEmbedding","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.edgeSet","Sym2","Sym2.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map","reducibility":"abbrev","statement_dag_size":124,"type_refs":["And","And.intro","DFunLike.coe","Eq","Function.Embedding","Function.instFunLikeEmbedding"],"value_dag_size":140,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Function.Embedding","Function.instFunLikeEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map.match_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.edgeSet_map","reducibility":"abbrev","statement_dag_size":124,"type_refs":["And","And.intro","DFunLike.coe","Eq","Function.Embedding","Function.instFunLikeEmbedding"],"value_dag_size":140,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Function.Embedding","Function.instFunLikeEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.induceHom_injective._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.induceHom_injective","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Function.Injective","Set","Set.Elem","Set.InjOn","Set.MapsTo","Set.MapsTo.restrict"],"value_dag_size":58,"value_refs":["Function.Injective","Set","Set.Elem","Set.InjOn","Set.MapsTo","Set.MapsTo.restrict","Set.MapsTo.restrict_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_adj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_adj","reducibility":null,"statement_dag_size":68,"type_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","Iff","Not","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":1324,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","Iff","Lean.Grind._simp_1","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Ne","Nonempty","Nonempty.intro","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_id._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_id","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","Exists","Iff","Not","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":830,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind._simp_1","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Ne","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","True","True.intro","congr","congrArg","eq_false","eq_of_heq","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_map._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.map_map","reducibility":null,"statement_dag_size":109,"type_refs":["And","Eq","Exists","Iff","Not","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":2368,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind._simp_1","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_swap12","Lean.Grind.true_imp_eq","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.neighborSet_map.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.neighborSet_map","reducibility":"abbrev","statement_dag_size":266,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Ne","Relation.Map","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map","SimpleGraph.neighborSet"],"value_dag_size":657,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Ne","Relation.Map","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.neighborSet_map.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.neighborSet_map","reducibility":"abbrev","statement_dag_size":180,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Set","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.neighborSet"],"value_dag_size":280,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Set","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.spanningCoe_induce_eq_self.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.spanningCoe_induce_eq_self","reducibility":"abbrev","statement_dag_size":189,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.induce","SimpleGraph.support","Subtype.val"],"value_dag_size":297,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.induce","SimpleGraph.support","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_comap_subset.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_comap_subset","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.support","SimpleGraph.support.match_1"],"value_dag_size":198,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.support","SimpleGraph.support.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_induce_subset_coe_preimage_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_induce_subset_coe_preimage_support","reducibility":"abbrev","statement_dag_size":157,"type_refs":["Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.Elem","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.induce","SimpleGraph.support","SimpleGraph.support.match_1"],"value_dag_size":210,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.Elem","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Adj","SimpleGraph.induce","SimpleGraph.support","SimpleGraph.support.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Maps.0.SimpleGraph.support_map","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.support"],"value_dag_size":40,"value_refs":["Exists","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_support","SimpleGraph.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.univ","True"],"value_dag_size":23,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_univ","Set.univ","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.ConnectedComponent.odd_matches_node_outside","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","Top.top"],"value_dag_size":40,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Ne","Or","Prod","Prod.mk","Quot","Quot.mk","Sym2.Rel"],"value_dag_size":627,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Ne","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":81,"type_refs":["And","Eq","Ne","Or","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":440,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_left","Ne","Not","Or","SimpleGraph","SimpleGraph.Adj","True","True.intro","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":77,"type_refs":["And","Eq","Iff","Ne","Not","Or","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":567,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Ne","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax"],"value_dag_size":46,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax","SimpleGraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsAlternating.sup_edge","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsClique.even_iff_exists_isMatching._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsClique.even_iff_exists_isMatching","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj","reducibility":null,"statement_dag_size":105,"type_refs":["And","Eq","Insert.insert","Membership.mem","Ne","Set","Set.instInsert","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.neighborSet","Singleton.singleton"],"value_dag_size":620,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Insert.insert","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","Set","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_singleton_iff","SimpleGraph","SimpleGraph.neighborSet","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":45,"value_refs":["Eq.symm","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.existsUnique_ne_adj","reducibility":"abbrev","statement_dag_size":66,"type_refs":["And","And.intro","Ne","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":82,"value_refs":["And","And.casesOn","And.intro","Ne","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.exists_cycle_toSubgraph_verts_eq_connectedComponentSupp._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.exists_cycle_toSubgraph_verts_eq_connectedComponentSupp","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Nat","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":59,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","False.elim","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Nat","Nat.ctorIdx","Not","OfNat.ofNat","eq_false'","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.other_adj_of_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.other_adj_of_adj","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LT.lt","Nat","OfNat.ofNat","Set.ncard","SimpleGraph","SimpleGraph.neighborSet","instLTNat","instOfNatNat"],"value_dag_size":267,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set.ncard","SimpleGraph","SimpleGraph.neighborSet","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.other_adj_of_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.other_adj_of_adj","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":45,"value_refs":["Eq.symm","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts","SimpleGraph.singletonSubgraph"],"value_dag_size":57,"value_refs":["LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts","SimpleGraph.singletonSubgraph","SimpleGraph.singletonSubgraph_le_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_deleteEdges","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles","reducibility":null,"statement_dag_size":58,"type_refs":["Finite","SDiff.sdiff","SimpleGraph","SimpleGraph.IsCycles","SimpleGraph.Reachable","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.toSubgraph","SimpleGraph.sdiff"],"value_dag_size":78,"value_refs":["Finite","PSigma","PSigma.mk","SimpleGraph","SimpleGraph.IsCycles","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux._unary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff"],"value_dag_size":48,"value_refs":["And","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff","SimpleGraph.sdiff_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux._unary","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux","reducibility":null,"statement_dag_size":66,"type_refs":["Finite","PSigma","SDiff.sdiff","SimpleGraph","SimpleGraph.IsCycles","SimpleGraph.Reachable","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.toSubgraph","SimpleGraph.sdiff"],"value_dag_size":2959,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.false","Bool.true","Classical.byContradiction","Classical.propDecidable","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toCoframe","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists.casesOn","ExistsUnique","False","Finite","Fintype","Fintype.card","Fintype.ofFinite","GeneralizedCoheytingAlgebra.toLattice","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","InvImage","LE.le","LT.lt","Lattice.toSemilatticeSup","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Max.max","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.card","Nat.card_eq_fintype_card","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Nonempty.intro","Nonempty.some","Not","OfNat.ofNat","Or","Or.casesOn","Order.Coframe.toCoheytingAlgebra","PSigma","PSigma.casesOn","PSigma.mk","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeSup.toPartialOrder","Set","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.reachable","SimpleGraph.Adj.symm","SimpleGraph.Adj.toWalk","SimpleGraph.IsCycles","SimpleGraph.IsCycles.existsUnique_ne_adj","SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj","SimpleGraph.Reachable","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.adj_sub","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Subgraph.spanningCoe_subgraphOfAdj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.length_lt","SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","SimpleGraph.Walk.Nil","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons_isPath_iff","SimpleGraph.Walk.length","SimpleGraph.Walk.mapLe","SimpleGraph.Walk.nil","SimpleGraph.Walk.not_nil_of_ne","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_snd","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.fromEdgeSet","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.instPartialOrder","SimpleGraph.sdiff","SimpleGraph.subgraphOfAdj","Singleton.singleton","Sym2","Sym2.mk","True","WellFounded.Nat.fix","_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.reachable_sdiff_toSubgraph_spanningCoe_aux._simp_1_1","congr","congrArg","congrFun'","dite","eagerReduce","eq_true","gt_iff_lt._simp_1","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","le_refl","le_sup_right._simp_2","of_decide_eq_true","of_eq_true","propext","sdiff_le_sdiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Nat","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":248,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","eagerReduce","eq_true","id","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","LE.le","LT.lt","Nat","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instLTNat","instOfNatNat"],"value_dag_size":357,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.toSimpleGraph._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.toSimpleGraph","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.toSimpleGraph.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.IsCycles.toSimpleGraph","reducibility":"abbrev","statement_dag_size":129,"type_refs":["Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.neighborSet","SimpleGraph.spanningCoe"],"value_dag_size":167,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.neighborSet","SimpleGraph.spanningCoe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph","reducibility":null,"statement_dag_size":111,"type_refs":["Eq","Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.verts","Subtype.mk"],"value_dag_size":117,"value_refs":["Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.coeSubgraph_adj","SimpleGraph.Subgraph.verts","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Subtype","Subtype.val","True"],"value_dag_size":43,"value_refs":["Membership.mem","Set","Set.instMembership","Subtype","Subtype.coe_prop","Subtype.val","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.coeSubgraph","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Exists","Nonempty"],"value_dag_size":23,"value_refs":["Exists","Nonempty","exists_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv","reducibility":null,"statement_dag_size":111,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Membership.mem","Or","Set","Set.Elem","Set.instMembership","Set.instUnion","Subtype","Subtype.mk","Subtype.val","Union.union"],"value_dag_size":457,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","False.elim","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.Elem","Set.instMembership","Set.instUnion","Set.mem_union","Subtype","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","Union.union","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Exists","Nonempty"],"value_dag_size":23,"value_refs":["Exists","Nonempty","exists_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Exists","True","True.intro"],"value_dag_size":16,"value_refs":["Exists","True","True.intro","exists_true_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Subtype","Subtype.val","True"],"value_dag_size":43,"value_refs":["Membership.mem","Set","Set.instMembership","Subtype","Subtype.coe_prop","Subtype.val","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.iSup._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.iSup","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.toEdge_preimage_singleton._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.toEdge_preimage_singleton","reducibility":null,"statement_dag_size":50,"type_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts","Subtype.val"],"value_dag_size":40,"value_refs":["Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts","Subtype.property"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.toEdge_preimage_singleton._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.toEdge_preimage_singleton","reducibility":null,"statement_dag_size":158,"type_refs":["Insert.insert","Membership.mem","Set","Set.Elem","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.preimage","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.fst_mem","SimpleGraph.Subgraph.Adj.snd_mem","SimpleGraph.Subgraph.IsMatching","SimpleGraph.Subgraph.IsMatching.toEdge","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.verts","Singleton.singleton","Subtype","Subtype.mk","Sym2","Sym2.mk"],"value_dag_size":974,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","Set","Set.Elem","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_preimage","Set.mem_singleton_iff","Set.preimage","SetLike.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.fst_mem","SimpleGraph.Subgraph.Adj.snd_mem","SimpleGraph.Subgraph.IsMatching","SimpleGraph.Subgraph.IsMatching.mem_coe_toEdge","SimpleGraph.Subgraph.IsMatching.toEdge","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.verts","Singleton.singleton","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.property","Subtype.val","Sym2","Sym2.Rel","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.toEdge_preimage_singleton._proof_1_2","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.verts_eq_biUnion_edgeSet.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.verts_eq_biUnion_edgeSet","reducibility":"abbrev","statement_dag_size":185,"type_refs":["Exists","Exists.intro","Membership.mem","Set","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.edgeSet","Sym2","Sym2.instSetLike"],"value_dag_size":274,"value_refs":["Exists","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.edgeSet","Sym2","Sym2.instSetLike"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.verts_eq_biUnion_edgeSet.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.verts_eq_biUnion_edgeSet","reducibility":"abbrev","statement_dag_size":100,"type_refs":["And","And.intro","Eq","Exists.intro","ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj"],"value_dag_size":180,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Exists","Insert.insert","Nat","Ne","OfNat.ofNat","Set","Set.instInsert","Set.instSingletonSet","Set.ncard","Singleton.singleton","instOfNatNat"],"value_dag_size":65,"value_refs":["And","Eq","Exists","Insert.insert","Nat","Ne","OfNat.ofNat","Set","Set.instInsert","Set.instSingletonSet","Set.ncard","Set.ncard_eq_two","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":23,"value_refs":["Eq.symm","Not","Or","imp_iff_not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Not","Or","imp_iff_not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":27,"type_refs":["EmptyCollection.emptyCollection","Eq","Not","Set","Set.Nonempty","Set.instEmptyCollection"],"value_dag_size":29,"value_refs":["EmptyCollection.emptyCollection","Eq","Not","Set","Set.Nonempty","Set.instEmptyCollection","Set.not_nonempty_iff_eq_empty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Membership.mem","Not","Set","Set.eq_empty_iff_forall_notMem","Set.instEmptyCollection","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax"],"value_dag_size":46,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax","SimpleGraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff"],"value_dag_size":48,"value_refs":["And","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff","SimpleGraph.sdiff_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","reducibility":null,"statement_dag_size":74,"type_refs":["And","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj"],"value_dag_size":262,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.imp_eq_of_eq_true_left","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","True","True.intro","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","Top.top"],"value_dag_size":40,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax"],"value_dag_size":46,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax","SimpleGraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff"],"value_dag_size":48,"value_refs":["And","Not","SDiff.sdiff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sdiff","SimpleGraph.sdiff_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating.match_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","reducibility":"abbrev","statement_dag_size":77,"type_refs":["And","Exists","Exists.intro","Ne","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":100,"value_refs":["And","Exists","Exists.casesOn","Exists.intro","Ne","SimpleGraph","SimpleGraph.Adj"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.toSubgraph_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsPerfectMatching.toSubgraph_iff","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.IsPerfectMatching"],"value_dag_size":37,"value_refs":["ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.IsPerfectMatching","SimpleGraph.Subgraph.isPerfectMatching_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.Iso.isMatching_map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.Iso.isMatching_map","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","SimpleGraph","SimpleGraph.Hom","SimpleGraph.Hom.comp","SimpleGraph.Subgraph","SimpleGraph.Subgraph.map"],"value_dag_size":88,"value_refs":["Eq.symm","SimpleGraph","SimpleGraph.Hom","SimpleGraph.Hom.comp","SimpleGraph.Subgraph","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.map_comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isMatching_iff_forall_degree._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isMatching_iff_forall_degree","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","ExistsUnique","Fintype","Nat","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.degree","SimpleGraph.Subgraph.neighborSet","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq","ExistsUnique","Fintype","Nat","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.degree","SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj","SimpleGraph.Subgraph.neighborSet","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","ExistsUnique","Fintype","Nat","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.degree","SimpleGraph.Subgraph.neighborSet","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq","ExistsUnique","Fintype","Nat","OfNat.ofNat","Set.Elem","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.degree","SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj","SimpleGraph.Subgraph.neighborSet","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.IsPerfectMatching"],"value_dag_size":37,"value_refs":["ExistsUnique","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.IsPerfectMatching","SimpleGraph.Subgraph.isPerfectMatching_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":91,"type_refs":["And","Eq","Iff","Ne","Not","Or","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.toSubgraph","Sym2.Rel"],"value_dag_size":1992,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Ne","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.toSubgraph","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax"],"value_dag_size":46,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instMax","SimpleGraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Max.max","Or","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instMax"],"value_dag_size":56,"value_refs":["Max.max","Or","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instMax","SimpleGraph.Subgraph.sup_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","LE.le","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.mapLe","SimpleGraph.Walk.toSubgraph","SimpleGraph.instLE"],"value_dag_size":77,"value_refs":["LE.le","SimpleGraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.adj_toSubgraph_mapLe","SimpleGraph.Walk.mapLe","SimpleGraph.Walk.toSubgraph","SimpleGraph.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Matching","name":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","Sym2","Sym2.mk"],"value_dag_size":82,"value_refs":["And","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons_isCycle_iff","SimpleGraph.Walk.edges","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Adj.diff_dist_adj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Adj.diff_dist_adj","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Reachable","SimpleGraph.dist","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":413,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_true_right","Nat","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.reachable","SimpleGraph.Reachable","SimpleGraph.Reachable.trans","SimpleGraph.dist","SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Adj.diff_dist_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Adj.diff_dist_adj","reducibility":null,"statement_dag_size":107,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.dist","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1183,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.dist","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_left._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_left","reducibility":null,"statement_dag_size":48,"type_refs":["HAdd.hAdd","LE.le","Nat","Not","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","instAddNat","instHAdd","instLENat"],"value_dag_size":357,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable","True","eagerReduce","eq_false","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_left._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_left","reducibility":null,"statement_dag_size":59,"type_refs":["ENat","ENat.instNatCast","HAdd.hAdd","LE.le","NatCast.natCast","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","instAddENat","instHAdd","instLEENat"],"value_dag_size":435,"value_refs":["Classical.byContradiction","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_trans","Lean.Grind.Order.lt_le_trans","Lean.Grind.Order.lt_of_not_le","Lean.Grind.Order.lt_unsat","Lean.Grind.imp_eq_of_eq_true_left","Nat.cast","NatCast.natCast","Not","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Reachable.coe_dist_eq_edist","SimpleGraph.Reachable.symm","SimpleGraph.Reachable.trans","SimpleGraph.dist","SimpleGraph.edist","SimpleGraph.edist_triangle","Std.IsLinearOrder.toIsLinearPreorder","True","congr","congrArg","eq_true","id","instAddENat","instHAdd","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instLinearOrderENat","instPreorderENat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_right._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_right","reducibility":null,"statement_dag_size":48,"type_refs":["HAdd.hAdd","LE.le","Nat","Not","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","instAddNat","instHAdd","instLENat"],"value_dag_size":410,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable","True","eagerReduce","eq_false","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_right._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Reachable.dist_triangle_right","reducibility":null,"statement_dag_size":59,"type_refs":["ENat","ENat.instNatCast","HAdd.hAdd","LE.le","NatCast.natCast","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.dist","instAddENat","instHAdd","instLEENat"],"value_dag_size":435,"value_refs":["Classical.byContradiction","ENat","ENat.instNatCast","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_trans","Lean.Grind.Order.lt_le_trans","Lean.Grind.Order.lt_of_not_le","Lean.Grind.Order.lt_unsat","Lean.Grind.imp_eq_of_eq_true_left","Nat.cast","NatCast.natCast","Not","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Reachable.coe_dist_eq_edist","SimpleGraph.Reachable.symm","SimpleGraph.Reachable.trans","SimpleGraph.dist","SimpleGraph.edist","SimpleGraph.edist_triangle","Std.IsLinearOrder.toIsLinearPreorder","True","congr","congrArg","eq_true","id","instAddENat","instHAdd","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instLinearOrderENat","instPreorderENat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.dist","instLTNat","instOfNatNat"],"value_dag_size":288,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.dist","True","eagerReduce","eq_true","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":431,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.tail","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":189,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.tail","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.tail","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":182,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.tail","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":167,"type_refs":["And","Eq","LE.le","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","instLENat","instLTNat","instOfNatNat"],"value_dag_size":621,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":178,"type_refs":["And","Eq","HAdd.hAdd","LE.le","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":622,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","SimpleGraph.dist","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj_ne","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instLTNat","instOfNatNat"],"value_dag_size":56,"value_refs":["LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.not_nil_iff_lt_length","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_top","reducibility":null,"statement_dag_size":35,"type_refs":["ENat","Eq","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","Top.top","instTopENat"],"value_dag_size":39,"value_refs":["ENat","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","SimpleGraph.edist_ne_top_iff_reachable","Top.top","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two","reducibility":null,"statement_dag_size":52,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","LE.le","OfNat.ofNat","One.toOfNat1","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edist","instAddMonoidWithOneENat","instLEENat"],"value_dag_size":56,"value_refs":["AddMonoidWithOne.toOne","ENat","Eq","LE.le","OfNat.ofNat","One.toOfNat1","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edist","SimpleGraph.edist_le_one_iff_adj_or_eq","instAddMonoidWithOneENat","instLEENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.ball_two","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable","reducibility":null,"statement_dag_size":44,"type_refs":["EmptyCollection.emptyCollection","Eq","InfSet.sInf","Membership.mem","Nat","Nat.instInfSet","OfNat.ofNat","Or","Set","Set.instEmptyCollection","Set.instMembership","instOfNatNat"],"value_dag_size":46,"value_refs":["EmptyCollection.emptyCollection","Eq","InfSet.sInf","Membership.mem","Nat","Nat.instInfSet","Nat.sInf_eq_zero","OfNat.ofNat","Or","Set","Set.instEmptyCollection","Set.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_comm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_comm","reducibility":null,"statement_dag_size":66,"type_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENat","ENat.instNatCast","Eq","InfSet.sInf","Nat.cast","Set.range","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist","instCompleteLinearOrderENat"],"value_dag_size":72,"value_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENat","ENat.instNatCast","Eq.symm","InfSet.sInf","Nat.cast","Set.range","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist","SimpleGraph.edist_eq_sInf","instCompleteLinearOrderENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_eq_two_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_eq_two_iff","reducibility":null,"statement_dag_size":42,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","OfNat.ofNat","One.toOfNat1","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edist","instAddMonoidWithOneENat"],"value_dag_size":53,"value_refs":["AddMonoidWithOne.toOne","ENat","Eq","Eq.symm","OfNat.ofNat","One.toOfNat1","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edist","SimpleGraph.edist_eq_one_iff_adj","instAddMonoidWithOneENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_eq_two_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_eq_two_iff","reducibility":null,"statement_dag_size":152,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LE.le","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder"],"value_dag_size":159,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LE.le","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Or","Order.le_one_iff","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_ne_top_iff_reachable._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_ne_top_iff_reachable","reducibility":null,"statement_dag_size":88,"type_refs":["BoundedOrder.toOrderTop","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toLattice","CompleteSemilatticeInf.toInfSet","Eq","Lattice.toSemilatticeInf","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Top.top","iInf"],"value_dag_size":92,"value_refs":["BoundedOrder.toOrderTop","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toLattice","CompleteSemilatticeInf.toInfSet","Eq","Lattice.toSemilatticeInf","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Top.top","iInf","iInf_eq_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_ne_top_iff_reachable._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.edist_ne_top_iff_reachable","reducibility":null,"statement_dag_size":22,"type_refs":["ENat","ENat.instNatCast","Eq","False","Nat","Nat.cast","Top.top","instTopENat"],"value_dag_size":22,"value_refs":["ENat","ENat.instNatCast","ENat.natCast_ne_top","Eq","Nat","Nat.cast","Top.top","eq_false","instTopENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.exists_walk_of_edist_eq_coe.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.exists_walk_of_edist_eq_coe","reducibility":"abbrev","statement_dag_size":112,"type_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.intro","Nat.cast","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"],"value_dag_size":142,"value_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Nat.cast","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.length_eq_dist_of_subwalk._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.length_eq_dist_of_subwalk","reducibility":null,"statement_dag_size":200,"type_refs":["And","Eq","False","HAdd.hAdd","LE.le","LT.lt","Nat","Nat.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.dist","instAddNat","instHAdd","instLENat"],"value_dag_size":686,"value_refs":["And","Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instPartialOrder","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.dist","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.mem_ball_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.mem_ball_top","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.mem_ball_top._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.mem_ball_top","reducibility":null,"statement_dag_size":35,"type_refs":["ENat","Eq","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","Top.top","instTopENat"],"value_dag_size":39,"value_refs":["ENat","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","SimpleGraph.edist_ne_top_iff_reachable","Top.top","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.nonempty_of_pos_dist._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.nonempty_of_pos_dist","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Nonempty","Set.Nonempty","Set.range"],"value_dag_size":26,"value_refs":["Nonempty","Set.Nonempty","Set.range","Set.range_nonempty_iff_nonempty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.nonempty_of_pos_dist._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.nonempty_of_pos_dist","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Nonempty","Set.Nonempty","Set.univ"],"value_dag_size":16,"value_refs":["Nonempty","Set.Nonempty","Set.nonempty_iff_univ_nonempty","Set.univ","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff","reducibility":null,"statement_dag_size":93,"type_refs":["AddMonoidWithOne.toOne","And","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","ENat","EmptyCollection.emptyCollection","Eq","LE.le","Ne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","instAddMonoidWithOneENat","instCompleteLinearOrderENat"],"value_dag_size":330,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And","Classical.byContradiction","CommSemiring.toSemiring","CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","ENat","ENat.instSuccAddOrder","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","MulZeroClass.toZero","Ne","NeZero.one","Not","OfNat.ofNat","One.toOfNat1","Order.one_le_iff_pos","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","SimpleGraph.edist_eq_zero_iff","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id","instAddMonoidWithOneENat","instCanonicallyOrderedAddENat","instCommSemiringENat","instCompleteLinearOrderENat","instIsBotZeroClass","instLEENat","instLTENat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNontrivialENat","instZeroLEOneClassENat","pos_iff_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff","reducibility":null,"statement_dag_size":68,"type_refs":["AddMonoidWithOne.toOne","And","ENat","EmptyCollection.emptyCollection","Eq","Ne","Not","OfNat.ofNat","One.toOfNat1","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","instAddMonoidWithOneENat"],"value_dag_size":230,"value_refs":["AddMonoidWithOne.toOne","And","Bool","Bool.true","Classical.byContradiction","CommSemiring.toGrindCommSemiring","ENat","ENat.instNatCast","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Int","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.eq_normS","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_not","Lean.RArray.leaf","Nat","NatCast.natCast","Ne","Not","OfNat.ofNat","One.toOfNat1","Set","Set.instEmptyCollection","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","SimpleGraph.edist_eq_one_iff_adj","True","eagerReduce","eq_true","id","instAddMonoidWithOneENat","instCommSemiringENat","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Metric","name":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.two_lt_edist_iff","reducibility":null,"statement_dag_size":76,"type_refs":["And","ENat","ENat.instNatCast","Eq","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Not","OfNat.ofNat","Set.Nonempty","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":81,"value_refs":["And","ENat","ENat.instNatCast","Eq","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Not","OfNat.ofNat","Set.Nonempty","SimpleGraph","SimpleGraph.Adj","SimpleGraph.commonNeighbors","SimpleGraph.edist","SimpleGraph.edist_eq_two_iff","instOfNatAtLeastTwo","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.Subgraph.spanningCoe_sup_edge_le._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.Subgraph.spanningCoe_sup_edge_le","reducibility":null,"statement_dag_size":75,"type_refs":["Max.max","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":2321,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.eq_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Max.max","Ne","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.adj_sub","SimpleGraph.Subgraph.adj_congr_of_sym2","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.edge","SimpleGraph.edge_adj","SimpleGraph.instMax","SimpleGraph.sup_adj","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","and_true","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","id","implies_congr","of_eq_true","true_and","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.adj_edge._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.adj_edge","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Iff","Not","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph.Adj","SimpleGraph.edge","Sym2.Rel"],"value_dag_size":1428,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Ne","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Set","SimpleGraph","SimpleGraph.edgeSet","Sym2"],"value_dag_size":40,"value_refs":["Eq","Eq.symm","Set","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSet_inj","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq","reducibility":null,"statement_dag_size":74,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Eq","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val","iSup"],"value_dag_size":81,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Eq.symm","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val","iSup","iSup_subtype''"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.biSup_fromEdgeSet_singleton_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","SDiff.sdiff","Set","Set.iUnion","Set.instSDiff"],"value_dag_size":46,"value_refs":["Eq.symm","SDiff.sdiff","Set","Set.iUnion","Set.iUnion_sdiff","Set.instSDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.card_edgeFinset_replaceVertex_of_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.card_edgeFinset_replaceVertex_of_adj","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.incidenceSet","Sym2","True"],"value_dag_size":34,"value_refs":["LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.incidenceSet","SimpleGraph.incidenceSet_subset","Sym2","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.incidenceSet","Sym2","True"],"value_dag_size":34,"value_refs":["LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.incidenceSet","SimpleGraph.incidenceSet_subset","Sym2","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.deleteEdges_edge._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.deleteEdges_edge","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","Set.instUnion","Union.union"],"value_dag_size":46,"value_refs":["LE.le","SDiff.sdiff","Set","Set.instLE","Set.instSDiff","Set.instUnion","Set.sdiff_subset_iff","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.disjoint_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.disjoint_edge","reducibility":null,"statement_dag_size":79,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2"],"value_dag_size":88,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Order.Frame.toHeytingAlgebra","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edgeSet","SimpleGraph.edgeSet","SimpleGraph.instPartialOrder","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj","reducibility":null,"statement_dag_size":114,"type_refs":["And","Eq","Iff","Membership.mem","Not","Or","Prod","Prod.mk","Quot","Quot.mk","Set","Set.image","Set.instMembership","Set.instSingletonSet","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet","Singleton.singleton","Sym2.Rel"],"value_dag_size":2492,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","Set","Set.image","Set.instMembership","Set.instSingletonSet","Set.mem_image","Set.mem_singleton_iff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet","Singleton.singleton","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","heq_eq_eq","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_adj","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":99,"type_refs":["And","Eq","Iff","Membership.mem","Not","Or","Prod","Prod.mk","Quot","Quot.mk","Set","Set.image","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet","Sym2.Rel"],"value_dag_size":1199,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","Set","Set.image","Set.instMembership","Set.mem_image","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edgeSet_replaceVertex_of_not_adj","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","Sym2","Sym2.mk"],"value_dag_size":59,"value_refs":["And","Eq","Membership.mem","Or","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.incidenceSet","SimpleGraph.mk'_mem_incidenceSet_iff","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edge_le_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edge_le_iff","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Ne","Or","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":587,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Ne","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_symm","SimpleGraph.edge","SimpleGraph.edge_adj","True","True.intro","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edge_le_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.edge_le_iff","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.replaceVertex._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.replaceVertex","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.replaceVertex_self._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.replaceVertex_self","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Classical.or_iff_not_imp_left","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq","reducibility":null,"statement_dag_size":74,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Eq","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val","iSup"],"value_dag_size":81,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Eq.symm","Membership.mem","Set","Set.Elem","Set.instMembership","Subtype.val","iSup","iSup_subtype''"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Exists","Sym2","Sym2.mk"],"value_dag_size":35,"value_refs":["Exists","Sym2","Sym2.exists","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sSup_edge_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sdiff_edge._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Operations.0.SimpleGraph.sdiff_edge","reducibility":null,"statement_dag_size":53,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","HeytingAlgebra.toOrderBot","Not","Order.Frame.toHeytingAlgebra","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.instPartialOrder"],"value_dag_size":57,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","HeytingAlgebra.toOrderBot","Not","Order.Frame.toHeytingAlgebra","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edge","SimpleGraph.edge","SimpleGraph.instPartialOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Path.cons_isCycle._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Path.cons_isCycle","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.isCycle_cycleBypass._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.isCycle_cycleBypass","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil"],"value_dag_size":51,"value_refs":["And","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCircuit_def","SimpleGraph.Walk.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.isCycle_cycleBypass.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.isCycle_cycleBypass","reducibility":"abbrev","statement_dag_size":78,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.cons"],"value_dag_size":439,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List.Nodup","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsCircuit.casesOn","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.IsTrail.casesOn","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2","absurd","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.ne_bot.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.ne_bot","reducibility":"abbrev","statement_dag_size":78,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.cons"],"value_dag_size":439,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List.Nodup","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsCircuit.casesOn","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.IsTrail.casesOn","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2","absurd","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.three_le_length._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.three_le_length","reducibility":null,"statement_dag_size":80,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":657,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.length_cons","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.three_le_length.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCircuit.three_le_length","reducibility":"abbrev","statement_dag_size":201,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":1385,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List.Nodup","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsCircuit.casesOn","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.IsTrail.casesOn","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2","absurd","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support","reducibility":null,"statement_dag_size":88,"type_refs":["DecidableEq","Eq","List.count","List.head?","List.tail","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instBEqOfDecidableEq","instOfNatNat"],"value_dag_size":1417,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsCharPIntOfNatNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.count","List.count_tail","List.head?","List.le_count_tail","List.tail","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.instBEq","Option.instDecidableEq","Option.instLawfulBEq","Option.some","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem","reducibility":null,"statement_dag_size":39,"type_refs":["LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":66,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.support_ne_nil","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem","reducibility":null,"statement_dag_size":58,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLENat","instLTNat","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem","reducibility":null,"statement_dag_size":58,"type_refs":["LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":156,"value_refs":["Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","List","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem._proof_1_2","eq_true","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.count_support_of_mem","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableEq","Eq","List","List.count","List.head?","List.instMembership","List.tail","Membership.mem","Nat","Ne","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instBEqOfDecidableEq","instOfNatNat"],"value_dag_size":1970,"value_refs":["And","And.casesOn","BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPIntOfNatNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","List.count_eq_zero","List.count_tail","List.head?","List.instMembership","List.le_count_tail","List.tail","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.instBEq","Option.instDecidableEq","Option.instLawfulBEq","Option.some","Option.some.inj","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instLENat","instLawfulBEq","instNatCastInt","instNatCastNat","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_endpoint_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_endpoint_iff","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":361,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_endpoint_iff._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_endpoint_iff","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":386,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'","reducibility":null,"statement_dag_size":78,"type_refs":["And","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1718,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1393,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn'","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":2948,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn","reducibility":null,"statement_dag_size":34,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.snd"],"value_dag_size":36,"value_refs":["SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.adj_snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn","reducibility":null,"statement_dag_size":98,"type_refs":["And","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":803,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_injOn","reducibility":null,"statement_dag_size":111,"type_refs":["And","Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1119,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":85,"type_refs":["GE.ge","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":752,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":85,"type_refs":["GE.ge","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1037,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","False","GE.ge","HSub.hSub","LE.le","Nat","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1536,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":76,"type_refs":["GE.ge","HAdd.hAdd","HSub.hSub","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":347,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","GE.ge","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":76,"type_refs":["GE.ge","HAdd.hAdd","HSub.hSub","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":304,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","GE.ge","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","False","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":584,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_neg","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":45,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","Nat.sub_le_iff_le_add","instAddNat","instHAdd","instHSub","instLENat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.isPath_take._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.isPath_take","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","False","HSub.hSub","LT.lt","Min.min","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLTNat","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":1263,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMin","Int.instNegInt","Int.instSub","Int.min_def","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_min","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Min.min","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","id","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List.Nodup","List.tail","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support"],"value_dag_size":46,"value_refs":["List.Nodup","List.tail","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.nodup_tail_support_reverse","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq","Eq.symm","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate","reducibility":null,"statement_dag_size":49,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":260,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate","reducibility":null,"statement_dag_size":60,"type_refs":["HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":699,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.snd_ne_penultimate","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","False","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":645,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.transfer","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","Sym2","Sym2.mk"],"value_dag_size":82,"value_refs":["And","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons_isCycle_iff","SimpleGraph.Walk.edges","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.disjoint_edges_of_disjoint_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.disjoint_edges_of_disjoint_support","reducibility":null,"statement_dag_size":207,"type_refs":["And","Eq","Exists","List","List.instMembership","List.tail","Membership.mem","Nat","Ne","OfNat.ofNat","Or","Prod","Prod.mk","Quot.mk","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.support","Sym2","Sym2.Rel","instOfNatNat"],"value_dag_size":991,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","List","List.instMembership","List.tail","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj.ne","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.length_eq_one_of_mem_edges","SimpleGraph.Walk.adj_of_mem_edges","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.support","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_true","false_or","forall_congr","id","implies_congr","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.disjoint_edges_of_disjoint_support._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.disjoint_edges_of_disjoint_support","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.Disjoint","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["List","List.Disjoint","List.disjoint_left","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.eq_snd_of_mem_edges._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.eq_snd_of_mem_edges","reducibility":null,"statement_dag_size":125,"type_refs":["Eq","List","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","Or","Prod","Prod.mk","Prod.swap","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","Sym2","Sym2.mk","instOfNatNat"],"value_dag_size":657,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.intro_with_eq","Lean.Grind.or_assoc","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.fst_mem_support_of_mem_edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.snd","SimpleGraph.Walk.support","SimpleGraph.Walk.tail","Sym2","Sym2.Rel","Sym2.mk","True","True.casesOn","True.intro","congr","congrArg","eq_false","eq_self","eq_true","heq_eq_eq","id","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_length_le_add_of_ne._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_length_le_add_of_ne","reducibility":null,"statement_dag_size":112,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","List","List.Sublist","List.instAppend","List.instMembership","List.reverse","List.tail","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHAppendOfAppend","instLENat"],"value_dag_size":1375,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Sublist","List.Sublist.length_le","List.dropLast","List.instAppend","List.instMembership","List.length","List.length_append","List.length_dropLast","List.length_pos_of_mem","List.length_reverse","List.reverse","List.tail","List.tail_reverse","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":null,"statement_dag_size":269,"type_refs":["And","Classical.propDecidable","Eq","Exists","List","List.instMembership","Membership.mem","Nat","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil"],"value_dag_size":1688,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.exists_and_left","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.true_imp_eq","List","List.instMembership","Membership.mem","Nat","Ne","Not","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.trans","SimpleGraph.Walk.append","SimpleGraph.Walk.isSubwalk_takeUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","True","True.intro","congrArg","eq_false","eq_self","eq_true","false_or","forall_congr","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":null,"statement_dag_size":126,"type_refs":["Classical.propDecidable","Eq","List","List.instMembership","Membership.mem","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil"],"value_dag_size":330,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","List","List.instMembership","Membership.mem","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.take_spec","True","True.intro","congr","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":null,"statement_dag_size":187,"type_refs":["And","Classical.propDecidable","Eq","Exists","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support"],"value_dag_size":1530,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.exists_and_left","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.true_imp_eq","List","List.instMembership","Membership.mem","Nat","Not","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.trans","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.isSubwalk_dropUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","True","True.intro","congrArg","eq_self","eq_true","false_or","forall_congr","funext","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","False","List","List.instMembership","List.tail","Membership.mem","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support"],"value_dag_size":1178,"value_refs":["And","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.not_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.Nodup","List.cons","List.dropLast","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.mem_reverse","List.nil","List.nodup_append","List.nodup_cons","List.reverse","List.reverse_append","List.reverse_concat","List.reverse_cons","List.reverse_nil","List.tail","List.tail_reverse","Membership.mem","Ne","Not","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.support_nodup","SimpleGraph.Walk.cons_tail_support","SimpleGraph.Walk.dropLast_support_concat","SimpleGraph.Walk.reverse","SimpleGraph.Walk.support","SimpleGraph.Walk.support_reverse","True","True.intro","congrArg","eq_self","eq_true","id","implies_congr","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":null,"statement_dag_size":67,"type_refs":["LT.lt","Nat","Ne","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","instLTNat","instOfNatNat"],"value_dag_size":621,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Ne","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.eq_of_length_le_one","SimpleGraph.Walk.length","SimpleGraph.Walk.length_reverse","SimpleGraph.Walk.reverse","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_of_ne","reducibility":"abbrev","statement_dag_size":204,"type_refs":["And","And.intro","Exists","Exists.intro","List","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"],"value_dag_size":442,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_sublist_of_ne.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.exists_isCycle_sublist_of_ne","reducibility":"abbrev","statement_dag_size":405,"type_refs":["And","And.intro","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.reverse"],"value_dag_size":1194,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append","SimpleGraph.Walk.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff","reducibility":null,"statement_dag_size":50,"type_refs":["HSub.hSub","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","instHSub","instLENat","instSubNat"],"value_dag_size":699,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.reverse","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HSub.hSub","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instSubNat"],"value_dag_size":1038,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_end_iff","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","HSub.hSub","Iff","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1071,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_start_iff_of_not_nil._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_start_iff_of_not_nil","reducibility":null,"statement_dag_size":42,"type_refs":["LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat"],"value_dag_size":242,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_start_iff_of_not_nil._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_eq_start_iff_of_not_nil","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":117,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":111,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Not","OfNat.ofNat","eagerReduce","id","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":754,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":752,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":680,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":71,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":845,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HSub.hSub","Nat","Not","OfNat.ofNat","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1372,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":289,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":155,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","LE.le","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_eq_add_le","Nat.ToInt.of_diseq","Nat.decLe","NatCast.natCast","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff","reducibility":null,"statement_dag_size":55,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":134,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.getVert_injOn_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":82,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","LT.lt","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","OfNat.ofNat","True","True.intro","eq_true","id","instAddNat","instHAdd","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.isCycle_append._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.isCycle_append","reducibility":null,"statement_dag_size":107,"type_refs":["LT.lt","List.Disjoint","List.tail","Nat","OfNat.ofNat","Or","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.support","Sym2.Rel","instLTNat","instOfNatNat"],"value_dag_size":827,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.leaf","List.Disjoint","List.Disjoint.symm","List.tail","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Prod","Quot","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.disjoint_edges_of_disjoint_support","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.support","Sym2","Sym2.Rel","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.isCycle_append._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.isCycle_append","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","instLTNat","instOfNatNat"],"value_dag_size":495,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.nil","SimpleGraph.Walk.nil_append_iff","SimpleGraph.Walk.nil_nil","True","congr","congrArg","eagerReduce","eq_true","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.length_eq_one_of_mem_edges._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.length_eq_one_of_mem_edges","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","HSub.hSub","List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","Sym2","Sym2.mk","instHSub","instOfNatNat","instSubNat"],"value_dag_size":948,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.mk","Quot","Quot.mk","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.length_edges","Sym2","Sym2.Rel","Sym2.mk","True","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.mem_support_iff_exists_append.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.mem_support_iff_exists_append","reducibility":"abbrev","statement_dag_size":253,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.append"],"value_dag_size":517,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.append"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.nil_iff_eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.nil_iff_eq","reducibility":"abbrev","statement_dag_size":84,"type_refs":["SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.nil","SimpleGraph.Walk.nil"],"value_dag_size":353,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.casesOn","SimpleGraph.Walk.Nil.nil","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.of_append_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.of_append_left","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.of_cons._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.of_cons","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.reverse._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.reverse","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.tail._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsPath.tail","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.disjoint_edges_takeUntil_dropUntil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.disjoint_edges_takeUntil_dropUntil","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.edges","Sym2","instHAppendOfAppend"],"value_dag_size":74,"value_refs":["Eq.symm","HAppend.hAppend","List","List.instAppend","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.edges","SimpleGraph.Walk.edges_append","Sym2","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.isPath_iff_isSubwalk_imp_not_isCycle._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.isPath_iff_isSubwalk_imp_not_isCycle","reducibility":null,"statement_dag_size":52,"type_refs":["Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsSubwalk"],"value_dag_size":233,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.not_nil","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","True","True.intro","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.isPath_iff_isSubwalk_imp_not_isCycle.match_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.isPath_iff_isSubwalk_imp_not_isCycle","reducibility":"abbrev","statement_dag_size":212,"type_refs":["Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":679,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.of_cons._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.of_cons","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.reverse._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsTrail.reverse","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.bypass.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.bypass.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.bypass.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.bypass.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.bypass.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.bypass.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isCycle_iff","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isPath_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.cons_isPath_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.support"],"value_dag_size":43,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.isPath_def","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.darts_cycleBypass_sublist_darts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.darts_cycleBypass_sublist_darts","reducibility":"abbrev","statement_dag_size":61,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":310,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.edges_cycleBypass_sublist_edges.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.edges_cycleBypass_sublist_edges","reducibility":"abbrev","statement_dag_size":61,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":310,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.endpoint_notMem_support_takeUntil._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.endpoint_notMem_support_takeUntil","reducibility":null,"statement_dag_size":98,"type_refs":["DecidableEq","LE.le","LT.lt","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","instLENat","instLTNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.endpoint_notMem_support_takeUntil._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.endpoint_notMem_support_takeUntil","reducibility":null,"statement_dag_size":102,"type_refs":["DecidableEq","Eq","False","LE.le","LT.lt","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","instLENat","instLTNat"],"value_dag_size":390,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_length._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_length","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat"],"value_dag_size":531,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_length.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_length","reducibility":"abbrev","statement_dag_size":200,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length"],"value_dag_size":461,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_length._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_length","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat"],"value_dag_size":531,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_length.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_length","reducibility":"abbrev","statement_dag_size":200,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.length"],"value_dag_size":461,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.length"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCircuit_rotate._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCircuit_rotate","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil"],"value_dag_size":51,"value_refs":["And","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCircuit_def","SimpleGraph.Walk.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length","reducibility":null,"statement_dag_size":41,"type_refs":["LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":90,"value_refs":["Eq.trans","HAdd.hAdd","LT.lt","List.length","Nat","Nat.zero_lt_succ._simp_1","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","instAddNat","instHAdd","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length","reducibility":null,"statement_dag_size":58,"type_refs":["HSub.hSub","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_le._simp_1","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length","reducibility":null,"statement_dag_size":207,"type_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.trans","False","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_le._simp_1","Nat.zero_lt_succ._simp_1","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_true"],"value_dag_size":845,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.mk","Fin.mk.inj","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.le_add_ge","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.sub_le._simp_1","Nat.zero_lt_succ._simp_1","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._proof_1_5","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","GetElem.getElem","Iff.mpr","LT.lt","List","List.head","List.instGetElemNatLtLength","List.length","List.length_pos_iff","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.symm","GetElem.getElem","Iff.mpr","LT.lt","List","List.head","List.head_eq_getElem_zero","List.instGetElemNatLtLength","List.length","List.length_pos_iff","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length","reducibility":"abbrev","statement_dag_size":140,"type_refs":["And","And.intro","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","instLENat","instOfNatNat"],"value_dag_size":168,"value_refs":["And","And.casesOn","And.intro","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.length","SimpleGraph.Walk.snd","SimpleGraph.Walk.tail","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_rotate._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isCycle_rotate","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":65,"value_refs":["And","List.Nodup","List.tail","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.isCycle_def","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.take"],"value_dag_size":165,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.take","True","congrArg","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":174,"type_refs":["Eq","False","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instLTNat"],"value_dag_size":2216,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List","List.instGetElemNatLtLength","List.length","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instLinearOrder","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.hcongr_8","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.hcongr_5","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.take","SimpleGraph.Walk.take_getVert","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_8","cast","cast_heq","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","min_def","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":76,"type_refs":["LT.lt","List.length","Nat","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instLTNat"],"value_dag_size":743,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List.length","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.nil_drop_iff","SimpleGraph.Walk.support","SimpleGraph.Walk.take","SimpleGraph.Walk.take_length","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","min_def","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":50,"type_refs":["LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat"],"value_dag_size":109,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":47,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":401,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_3","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":78,"type_refs":["LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instLENat","instLTNat"],"value_dag_size":149,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":60,"type_refs":["LE.le","LT.lt","List.length","Min.min","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat","instMinNat"],"value_dag_size":121,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.length","Min.min","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instMinNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":59,"type_refs":["LT.lt","List.length","Min.min","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat","instMinNat"],"value_dag_size":630,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List.length","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instLinearOrder","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_6","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","min_def","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instLTNat"],"value_dag_size":1127,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List","List.instGetElemNatLtLength","List.length","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instLinearOrder","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.take","SimpleGraph.Walk.take_getVert","True","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_7","congrArg","eagerReduce","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","min_def","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_nil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_nil","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.nil","True"],"value_dag_size":26,"value_refs":["SimpleGraph","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.nil","SimpleGraph.Walk.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_append._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_append","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_append._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_append","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","instHAppendOfAppend"],"value_dag_size":45,"value_refs":["And","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","List.nodup_append'","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_cons._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_cons","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":45,"value_refs":["List.Nodup","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsTrail","SimpleGraph.Walk.edges","SimpleGraph.Walk.isTrail_def","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_cons._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isTrail_cons","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.not_nil_of_isCycle_cons._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.not_nil_of_isCycle_cons","reducibility":null,"statement_dag_size":48,"type_refs":["Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons"],"value_dag_size":455,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsCircuit.three_le_length","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.isCircuit","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.length_cons","SimpleGraph.Walk.not_nil_iff_lt_length","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Paths","name":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.support_cycleBypass_sublist_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.support_cycleBypass_sublist_support","reducibility":"abbrev","statement_dag_size":61,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":310,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.length_boxProd.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.length_boxProd","reducibility":"abbrev","statement_dag_size":161,"type_refs":["Prod","Prod.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.boxProd","Unit"],"value_dag_size":636,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Prod","Prod.mk","Prod.mk.noConfusion","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.boxProd","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1","reducibility":null,"statement_dag_size":131,"type_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.ofBoxProdLeft.match_1","SimpleGraph.boxProd","Unit","Unit.unit"],"value_dag_size":128,"value_refs":["Eq.refl","Prod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.ofBoxProdLeft.match_1","SimpleGraph.boxProd","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1","reducibility":null,"statement_dag_size":169,"type_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.ofBoxProdLeft.match_1","SimpleGraph.boxProd","Unit"],"value_dag_size":164,"value_refs":["Eq.refl","Prod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.ofBoxProdLeft.match_1","SimpleGraph.boxProd","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft.match_1","reducibility":"abbrev","statement_dag_size":121,"type_refs":["Prod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.boxProd","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.ofBoxProdLeft.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft_boxProdLeft.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdLeft_boxProdLeft","reducibility":"abbrev","statement_dag_size":75,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":355,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdRight_boxProdRight.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.Walk.ofBoxProdRight_boxProdRight","reducibility":"abbrev","statement_dag_size":75,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":355,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","or_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdAssoc","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":60,"value_refs":["Disjoint","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjUnion","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet._simp_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProdFintypeNeighborSet","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd_adj_left._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd_adj_left","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","False","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":21,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.irrefl","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd_adj_right._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.boxProd_adj_right","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","False","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":21,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.irrefl","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":31,"value_refs":["Eq","Eq.symm","Ne","Not","not_ne_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":null,"statement_dag_size":35,"type_refs":["ENat","Eq","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","Top.top","instTopENat"],"value_dag_size":39,"value_refs":["ENat","Ne","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.edist","SimpleGraph.edist_ne_top_iff_reachable","Top.top","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.boxProd"],"value_dag_size":69,"value_refs":["And","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.boxProd","SimpleGraph.reachable_boxProd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd.match_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":"abbrev","statement_dag_size":161,"type_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.intro","Nat.cast","Prod","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.boxProd","SimpleGraph.edist"],"value_dag_size":191,"value_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Nat.cast","Prod","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.boxProd","SimpleGraph.edist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd.match_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":"abbrev","statement_dag_size":145,"type_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.intro","Nat.cast","Prod","Prod.fst","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"],"value_dag_size":175,"value_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Nat.cast","Prod","Prod.fst","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd.match_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.edist_boxProd","reducibility":"abbrev","statement_dag_size":145,"type_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.intro","Nat.cast","Prod","Prod.snd","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"],"value_dag_size":175,"value_refs":["ENat","ENat.instNatCast","Eq","Exists","Exists.casesOn","Exists.intro","Nat.cast","Prod","Prod.snd","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.edist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":39,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborSet","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd","reducibility":null,"statement_dag_size":75,"type_refs":["And","Eq","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd"],"value_dag_size":80,"value_refs":["And","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd","Set.mem_prod","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.neighborSet_boxProd","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.reachable_boxProd.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.reachable_boxProd","reducibility":"abbrev","statement_dag_size":80,"type_refs":["Nonempty.intro","Prod","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.boxProd"],"value_dag_size":92,"value_refs":["Nonempty.casesOn","Nonempty.intro","Prod","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk","SimpleGraph.boxProd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.reachable_boxProd.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.reachable_boxProd","reducibility":"abbrev","statement_dag_size":130,"type_refs":["And","And.intro","Nonempty.intro","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"],"value_dag_size":236,"value_refs":["And","And.casesOn","And.intro","Nonempty.casesOn","Nonempty.intro","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Reachable","SimpleGraph.Walk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":70,"value_refs":["Eq.refl","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":68,"value_refs":["Eq.refl","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","False","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":802,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","False.elim","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","SimpleGraph.sum._sparseCasesOn_1","SimpleGraph.sum._sparseCasesOn_1.else_eq","SimpleGraph.sum._sparseCasesOn_2","SimpleGraph.sum._sparseCasesOn_2.else_eq","SimpleGraph.sum.match_1","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_4","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1","reducibility":"abbrev","statement_dag_size":102,"type_refs":["Eq","False","Sum","Sum.inl","Sum.inr"],"value_dag_size":347,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_4","absurd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inl"],"value_dag_size":101,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Prod","name":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Prod.0.SimpleGraph.sum.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inr"],"value_dag_size":103,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound","reducibility":null,"statement_dag_size":74,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":77,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound._sparseCasesOn_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound.match_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.Mathlib.Meta.Positivity.evalInitialBound","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity","reducibility":null,"statement_dag_size":105,"type_refs":["HMul.hMul","HPow.hPow","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instZero","Zero.toOfNat0","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":335,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","Decidable.decide","DistribLattice.toLattice","Eq","Eq.refl","HMul.hMul","HPow.hPow","Iff.mp","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","LT.lt.trans_le","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Monoid.toNPow","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.instAtLeastTwoHAddOfNat","Nat.instDecidablePredOdd","Nat.instNeZeroSucc","Nat.instSemiring","Nat.ofNat_pos._simp_1","NonAssocSemiring.toAddCommMonoidWithOne","Odd","Odd.pow_pos_iff","OfNat.ofNat","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.instAddGroup","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Zero.toOfNat0","id","instDistribLatticeOfLinearOrder","instHMul","instHPow","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","of_decide_eq_true","of_eq_true","pos_of_mul_pos_right","pow_pos"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity","reducibility":null,"statement_dag_size":133,"type_refs":["DecidableEq","Finpartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.instDiv","Nat.instMonoid","Nonempty","OfNat.ofNat","SzemerediRegularity.stepBound","instHDiv","instHMul","instHPow","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":220,"value_refs":["Bool","Bool.true","DecidableEq","Eq.refl","Finpartition","Finpartition.parts","Finpartition.parts_nonempty","Finset","Finset.Nonempty.card_pos","Finset.Nonempty.ne_empty","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Finset.univ_nonempty","Fintype","Fintype.card","HMul.hMul","HPow.hPow","LE.le","LE.le.trans'","Monoid.toNPow","NPow.toPow","Nat","Nat.decLe","Nat.div_pos","Nat.instCommSemigroup","Nat.instMonoid","Nat.instMulLeftMono","Nat.instPreorder","Nonempty","OfNat.ofNat","Preorder.toLE","SzemerediRegularity.stepBound","SzemerediRegularity.stepBound_pos","covariant_swap_mul_of_covariant_mul","eq_true_of_decide","id","instHMul","instHPow","instLENat","instMulNat","instOfNatNat","le_refl","mul_le_mul'","of_eq_true","pow_le_pow_left'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card","reducibility":null,"statement_dag_size":72,"type_refs":["DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Finset","Finset.sum","GroupWithZero.toDivInvMonoid","HDiv.hDiv","Semiring.toAddCommMonoid","instHDiv"],"value_dag_size":80,"value_refs":["DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","Finset","Finset.sum","Finset.sum_div","GroupWithZero.toDivInvMonoid","HDiv.hDiv","Semiring.toAddCommMonoid","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card","reducibility":null,"statement_dag_size":61,"type_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","instDistribOfSemiring","instHAdd","instHDiv"],"value_dag_size":68,"value_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","add_div","instDistribOfSemiring","instHAdd","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.add_div_le_sum_sq_div_card","reducibility":null,"statement_dag_size":64,"type_refs":["Distrib.toMul","Eq","Finset","Finset.sum","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"],"value_dag_size":72,"value_refs":["Distrib.toMul","Eq.symm","Finset","Finset.sum","Finset.sum_mul","HMul.hMul","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","instHMul"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termA_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Delaborator.Delab"],"value_dag_size":411,"value_refs":["Applicative.toPure","Bind.bind","Bind.kleisliRight","IO.RealWorld","Lean.Core.CoreM","Lean.Core.instMonadQuotationCoreM","Lean.Expr","Lean.Expr.isConstOf","Lean.MacroScope","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instMonadMetaM","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.PrettyPrinter.Delaborator.Context","Lean.PrettyPrinter.Delaborator.DelabM","Lean.PrettyPrinter.Delaborator.State","Lean.PrettyPrinter.Delaborator.SubExpr.getExpr","Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM","Lean.PrettyPrinter.Delaborator.whenNotPPOption","Lean.PrettyPrinter.Delaborator.whenPPOption","Lean.PrettyPrinter.Delaborator.withOverApp","Lean.SourceInfo","Lean.Syntax.Term","Lean.Syntax.atom","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.getPPExplicit","Lean.getPPNotation","Lean.instMonadQuotationOfMonadFunctorOfMonadLift","List.cons","List.nil","Mathlib.Notation3.MatchState","Mathlib.Notation3.MatchState.empty","Mathlib.Notation3.isType'","Mathlib.Notation3.matchApp","Mathlib.Notation3.matchExpr","Mathlib.Notation3.matchFVar","Mathlib.Notation3.natLitMatcher","Mathlib.Notation3.withHeadRefIfTagAppFns","Monad.toBind","Nat","OfNat.ofNat","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadFunctor","ReaderT.instMonadLift","StateRefT'","StateRefT'.instMonad","StateRefT'.instMonadFunctor","StateRefT'.instMonadLift","instOfNatNat"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Delaborator.Delab"],"value_dag_size":334,"value_refs":["Applicative.toPure","Bind.bind","Bind.kleisliRight","IO.RealWorld","Lean.Core.CoreM","Lean.Core.instMonadQuotationCoreM","Lean.Expr","Lean.Expr.isConstOf","Lean.MacroScope","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instMonadMetaM","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.PrettyPrinter.Delaborator.Context","Lean.PrettyPrinter.Delaborator.DelabM","Lean.PrettyPrinter.Delaborator.State","Lean.PrettyPrinter.Delaborator.SubExpr.getExpr","Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM","Lean.PrettyPrinter.Delaborator.whenNotPPOption","Lean.PrettyPrinter.Delaborator.whenPPOption","Lean.PrettyPrinter.Delaborator.withOverApp","Lean.SourceInfo","Lean.Syntax.Term","Lean.Syntax.atom","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.getPPExplicit","Lean.getPPNotation","Lean.instMonadQuotationOfMonadFunctorOfMonadLift","List.cons","List.nil","Mathlib.Notation3.MatchState","Mathlib.Notation3.MatchState.empty","Mathlib.Notation3.isType'","Mathlib.Notation3.matchApp","Mathlib.Notation3.matchExpr","Mathlib.Notation3.matchFVar","Mathlib.Notation3.withHeadRefIfTagAppFns","Monad.toBind","Nat","OfNat.ofNat","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadFunctor","ReaderT.instMonadLift","StateRefT'","StateRefT'.instMonad","StateRefT'.instMonadFunctor","StateRefT'.instMonadLift","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termA_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":428,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.Syntax.node3","Lean.Syntax.node5","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":409,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.Syntax.node3","Lean.Syntax.node5","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.termA","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":45,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Bound","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.termM","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":45,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Chunk___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Chunk_0_SzemerediRegularity_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Delaborator.Delab"],"value_dag_size":336,"value_refs":["Applicative.toPure","Bind.bind","Bind.kleisliRight","IO.RealWorld","Lean.Core.CoreM","Lean.Core.instMonadQuotationCoreM","Lean.Expr","Lean.Expr.isConstOf","Lean.MacroScope","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instMonadMetaM","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.PrettyPrinter.Delaborator.Context","Lean.PrettyPrinter.Delaborator.DelabM","Lean.PrettyPrinter.Delaborator.State","Lean.PrettyPrinter.Delaborator.SubExpr.getExpr","Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM","Lean.PrettyPrinter.Delaborator.whenNotPPOption","Lean.PrettyPrinter.Delaborator.whenPPOption","Lean.PrettyPrinter.Delaborator.withOverApp","Lean.SourceInfo","Lean.Syntax.Term","Lean.Syntax.atom","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.getPPExplicit","Lean.getPPNotation","Lean.instMonadQuotationOfMonadFunctorOfMonadLift","List.cons","List.nil","Mathlib.Notation3.MatchState","Mathlib.Notation3.MatchState.empty","Mathlib.Notation3.isType'","Mathlib.Notation3.matchApp","Mathlib.Notation3.matchExpr","Mathlib.Notation3.matchFVar","Mathlib.Notation3.withHeadRefIfTagAppFns","Monad.toBind","Nat","OfNat.ofNat","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadFunctor","ReaderT.instMonadLift","StateRefT'","StateRefT'.instMonad","StateRefT'.instMonadFunctor","StateRefT'.instMonadLift","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Chunk___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Chunk_0_SzemerediRegularity_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":417,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.Syntax.node3","Lean.Syntax.node5","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.abs_density_star_sub_density_le_eps","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":343,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Not","OfNat.ofNat","One.toOfNat1","Rat.cast","Real","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRatCast","Real.instSub","Real.lattice","Real.linearOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.nonuniformWitness","SzemerediRegularity.star","abs","id","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1956,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Bool","Bool.false","CommRing.toRing","CommSemiring.toSemiring","DecidableEq","DecidableRel","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsStrictOrderedRing.toPosMulStrictMono","LE","LE.le","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","Mul","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Ne","Ne.symm","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","Not.intro","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Rat.cast","Real","Real.commRing","Real.instAddGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.partialOrder","Real.semiring","Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul","Rel.edgeDensity","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.IsUniform.symm","SimpleGraph.edgeDensity","SimpleGraph.nonuniformWitness","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","SzemerediRegularity.biUnion_star_subset_nonuniformWitness","SzemerediRegularity.star","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_eps_mul_card_nonuniformWitness_le_card_star","abs","congrArg","div_pos","eq_of_heq","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.average_density_near_total_density","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":468,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRatCast","Real.instSub","Real.lattice","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SzemerediRegularity.chunk","abs","id","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1046,"value_refs":["AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddZero.toAdd","AddZeroClass.toAddZero","And","And.intro","Bool","Bool.true","DecidableEq","DecidableRel","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toNPow","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoidWithZero","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SzemerediRegularity.chunk","SzemerediRegularity.stepBound","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps","abs","abs_sub_le_iff","congrArg","covariant_swap_add_of_covariant_add","div_le_div₀","id","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","le_refl","pow_pos","propext","sub_le_iff_le_add","sub_le_iff_le_add'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":262,"type_refs":["DecidableEq","DecidableRel","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSDiff","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instDiv","Nat.instMonoid","Ne","Not","OfNat.ofNat","Real","Real.instField","Real.instIsStrictOrderedRing","Real.linearOrder","SDiff.sdiff","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.nonuniformWitness","SzemerediRegularity.star","SzemerediRegularity.stepBound","id","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":2780,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toNSMul","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","And","And.casesOn","And.intro","And.left","And.right","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Finpartition","Finpartition.IsEquipartition","Finpartition.atomise","Finpartition.biUnion_filter_atomise","Finpartition.card_filter_atomise_le_two_pow","Finpartition.card_nonuniformWitnesses_le","Finpartition.card_parts_equitabilise_subset_le","Finpartition.equitabilise","Finpartition.nonuniformWitness_mem_nonuniformWitnesses","Finpartition.nonuniformWitnesses","Finpartition.parts","Finset","Finset.Nonempty","Finset.biUnion","Finset.card","Finset.card_biUnion_le","Finset.card_le_card","Finset.decidableEq","Finset.decidableNonempty","Finset.filter","Finset.filter.congr_simp","Finset.filter_subset","Finset.instDecidableLE","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_sdiff","Finset.sum","Finset.sum_const","Finset.sum_le_sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSMul.hSMul","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toIsOrderedRing","LE.le","LE.le.trans","Membership.mem","Monoid.toNPow","MonoidWithZero.toMonoid","NPow.toPow","NSMul.toSMul","Nat","Nat.instAddCommMonoid","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instCommSemigroup","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instIsStrictOrderedRing","Nat.instMonoid","Nat.instMonoidWithZero","Nat.instMulLeftMono","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instTransLe","Nat.instZeroLEOneClass","Nat.one_le_ofNat._simp_1","Nat.sub_le_sub_right","Ne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instField","Real.instIsStrictOrderedRing","Real.linearOrder","SDiff.sdiff","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.instDecidableIsUniform","SimpleGraph.nonuniformWitness","SimpleGraph.nonuniformWitness_subset","SzemerediRegularity.card_aux₁","SzemerediRegularity.card_aux₂","SzemerediRegularity.chunk","SzemerediRegularity.star","SzemerediRegularity.star.eq_1","SzemerediRegularity.stepBound","Trans.simple","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_7","congr","congrArg","congrFun'","covariant_swap_mul_of_covariant_mul","dif_neg","dif_pos","dite","forall_congr","funext","id","instAddNat","instDecidableAnd","instDecidableEqNat","instDecidableNot","instHAdd","instHDiv","instHMul","instHPow","instHSMul","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","instSMulOfMul","instSubNat","le_imp_le_of_le_of_le","le_refl","mul_le_mul'","of_eq_true","pow_le_pow_right₀","propext","smul_eq_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":450,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SzemerediRegularity.chunk","id","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":3556,"value_refs":["AddCommGroup.toAddGroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And","Bool","CommGroupWithZero.toDivisionCommMonoid","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemigroup.toCommMagma","DecidableEq","DecidableRel","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists.intro","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.nonempty_of_mem_parts","Finpartition.ofSubset","Finpartition.ofSubset_parts","Finpartition.parts","Finset","Finset.Nonempty","Finset.biUnion","Finset.card","Finset.card_pos","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mul_sum","Finset.product","Finset.sum","Finset.sum_congr","Finset.sum_div","Finset.sum_le_sum","Finset.sup","Finset.sup_eq_biUnion","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeSup","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_mul._simp_1","Nat.cast_nonneg","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_pos","Nat.cast_sum","Nat.cast_zero","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instLinearOrderedCommMonoidWithZero","Nat.instMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","Rat","Rat.cast","Rat.cast_div","Rat.cast_le_natCast._simp_1","Rat.cast_mul","Rat.cast_natCast","Rat.cast_sum","Rat.instDiv","Rat.instDivisionRing","Rat.instField","Rat.instLE","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSemigroup","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Rel.card_interedges_finpartition","Rel.interedges","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","SProd.sprod","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semigroup.toMul","Semiring.toAddCommMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_def","SimpleGraph.edgeDensity_le_one","SimpleGraph.interedges","SimpleGraph.interedges.eq_1","SubNegMonoid.toSub","SzemerediRegularity.chunk","SzemerediRegularity.stepBound","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.le_sum_card_subset_chunk_parts","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_le_m_div_m_add_one_sq","cast","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_div","div_le_one_of_le₀","div_mul_eq_mul_div","div_pos","forall_congr","funext","id","implies_congr","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_div_iff₀","le_of_lt","mul_assoc","mul_comm","mul_div_left_comm","mul_le_mul","mul_le_mul_of_nonneg_right","mul_le_of_le_one_right","mul_mul_mul_comm","mul_nonneg","mul_pos","one_mul","pow_pos","propext","rfl","sq","sub_le_sub_iff_left","sub_mul","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":407,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SzemerediRegularity.chunk","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":4138,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommMonoid.toMonoid","CommRing.toRing","CommSemiring.toSemiring","DecidableEq","DecidableRel","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.biUnion_parts","Finpartition.parts","Finset","Finset.Subset.refl","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.mul","Int.negOfNat","Int.ofNat","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsOrderedRing.toZeroLEOneClass","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_add","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Meta.Positivity.nonneg_of_isNat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.const_pos","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.Common.zero_pow","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NNRat.rawCast","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_mul","Nat.cast_one","Nat.cast_pow","Nat.cast_pow._simp_1","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommMonoid","Nat.instCommSemiring","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul","Nat.ofNat_pos._simp_1","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Nonempty","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.snd","Rat","Rat.addCommMonoid","Rat.cast","Rat.cast_div._simp_1","Rat.cast_le._simp_1","Rat.cast_le_natCast._simp_1","Rat.cast_ofNat","Rat.cast_pow","Rat.cast_sum._simp_1","Rat.instDiv","Rat.instDivisionRing","Rat.instLE","Rat.instNatCast","Rat.instOfNat","Rat.instPreorder","Rat.natCast_le_cast._simp_1","Rat.rawCast","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_le_one","SimpleGraph.edgeDensity_nonneg","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","SzemerediRegularity.card_chunk","SzemerediRegularity.chunk","SzemerediRegularity.m_pos","SzemerediRegularity.stepBound","Trans.trans","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.density_sub_eps_le_sum_density_div_card","add_le_add","cast","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_le_div_of_nonneg_left","div_le_div_of_nonneg_right","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTransEq","instTransEq_1","instTransLE","le_of_lt","le_refl","le_total","le_trans","mul_le_mul_of_nonneg_right","mul_pow","of_eq_true","pow_le_pow_left₀","pow_nonneg","pow_pos","propext","rfl","sq_le","sq_nonneg","sub_le_sub_left","sub_nonneg","sub_nonpos_of_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform","reducibility":null,"statement_dag_size":156,"type_refs":["AddLeftMono","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","ExistsAddOfLE","HPow.hPow","LE.le","Lattice.toSemilatticeInf","LinearOrder","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","OfNat.ofNat","PartialOrder.toPreorder","PosMulMono","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring","Semiring.toMonoid","True","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHPow","instMulZeroClassOfSemiring","instOfNatNat"],"value_dag_size":161,"value_refs":["AddLeftMono","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ExistsAddOfLE","HPow.hPow","LE.le","Lattice.toSemilatticeInf","LinearOrder","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","OfNat.ofNat","PartialOrder.toPreorder","PosMulMono","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring","Semiring.toMonoid","Zero.toOfNat0","eq_true","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHPow","instMulZeroClassOfSemiring","instOfNatNat","pow_two_nonneg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform","reducibility":null,"statement_dag_size":63,"type_refs":["CommMonoid","CommMonoid.toMonoid","Eq","HMul.hMul","HPow.hPow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","instHMul","instHPow"],"value_dag_size":70,"value_refs":["CommMonoid","CommMonoid.toMonoid","Eq.symm","HMul.hMul","HPow.hPow","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","instHMul","instHPow","mul_pow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_chunk_not_uniform","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":462,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Ne","Nonempty","Not","OfNat.ofNat","One.toOfNat1","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRatCast","Real.instSub","Real.lattice","Real.linearOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SzemerediRegularity.chunk","SzemerediRegularity.star","abs","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1896,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","DecidableEq","DecidableRel","DivInvMonoid.toDiv","DivisionRing.toRatCast","DivisionRing.toRing","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toDivisionRing","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finpartition.sup_parts","Finset","Finset.Subset.refl","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSProd","Finset.instSetLike","Finset.product","Finset.sum","Finset.sup","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","LE.le","LT.lt","LT.lt.ne'","Lattice.toSemilatticeSup","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.cast","Nat.cast_pow","Nat.instAddCommMonoid","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPartialOrder","Nat.instPreorder","Nat.instZeroLEOneClass","Nat.one_le_ofNat._simp_1","Ne","NonAssocSemiring.toAddCommMonoidWithOne","Nonempty","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat","Rat.addGroup","Rat.cast","Rat.cast_abs._simp_1","Rat.cast_sub._simp_1","Rat.instLattice","Rat.instSub","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.lattice","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SProd.sprod","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity.congr_simp","SimpleGraph.nonuniformWitness","SimpleGraph.nonuniformWitness_spec","SzemerediRegularity.card_chunk","SzemerediRegularity.chunk","SzemerediRegularity.m_pos","SzemerediRegularity.star","SzemerediRegularity.star_subset_chunk","SzemerediRegularity.stepBound","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.abs_density_star_sub_density_le_eps","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.average_density_near_total_density","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._simp_1_2","abs","cast","congr","congrArg","congrFun'","ge_iff_le._simp_1","id","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","le_of_lt","of_eq_true","pow_le_pow_of_le_one","pow_one","pow_right_comm","rfl","sq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":596,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","Real.lattice","Real.linearOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.nonuniformWitness","SzemerediRegularity.chunk","SzemerediRegularity.star","abs","id","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":17027,"value_refs":["AddGroup.toSubtractionMonoid","And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","DecidableRel","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Field.toGrindField","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.ext","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.product","Finset.sum","Finset.sum_congr","Finset.univ","Fintype","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.instNegInt","IntCast.intCast","Inv.inv","IsStrictOrderedRing","LE.le","Lattice.toSemilatticeSup","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.inv","Lean.Grind.CommRing.eq_int_module","Lean.Grind.CommRing.eq_norm","Lean.Grind.CommRing.inv_int_eq'","Lean.Grind.CommRing.le_cancel_var","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.le_mul","Lean.Grind.CommRing.le_norm","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_cancel_var","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_mul","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_le_combine","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.le_of_eq","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_trans_k","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toIntModule","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Ne","Neg.neg","NegZeroClass.toNeg","Not","OfNat.ofNat","One.one","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat.cast","RatCast.ratCast","Real","Real.decidableLE","Real.instAdd","Real.instAddCommMonoid","Real.instAddGroup","Real.instDivInvMonoid","Real.instField","Real.instIntCast","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instSub","Real.lattice","Real.linearOrder","Real.partialOrder","Real.semiring","SemilatticeSup.toMax","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.nonuniformWitness","Std.IsLinearOrder.toIsLinearPreorder","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","SzemerediRegularity.chunk","SzemerediRegularity.star","abs","abs.eq_1","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing","ite","ite_cond_eq_false","ite_cond_eq_true","max_def","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.edgeDensity_star_not_uniform","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instLattice","Finset.instOrderBot","Finset.sup","Lattice.toSemilatticeSup"],"value_dag_size":51,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.biUnion","Finset.instLattice","Finset.instOrderBot","Finset.sup","Finset.sup_eq_biUnion","Lattice.toSemilatticeSup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.eps_le_card_star_div","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":360,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Ne","Nonempty","Not","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instField","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.linearOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SzemerediRegularity.star","instHDiv","instHMul","instHPow","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":3511,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","Decidable.decide","DecidableEq","DecidableRel","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.nonempty_of_mem_parts","Finpartition.parts","Finset","Finset.Nonempty.card_pos","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Int","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","LT.lt.ne'","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.to_eq","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsRat.to_isNNRat","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_le_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_sub","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNNRat","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.add_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.without_one_mul","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","Mul","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_pos","Nat.cast_pos'","Nat.cast_zero","Nat.decLe","Nat.decLt","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mul","Nat.one_le_ofNat._simp_1","Nat.rawCast","Ne","NeZero.charZero_one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","Nonempty","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instSemigroup","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Right.add_pos_of_nonneg_of_pos","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semigroup.toMul","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.le_card_nonuniformWitness","SimpleGraph.nonuniformWitness","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul","SzemerediRegularity.hundred_le_m","SzemerediRegularity.one_le_m_coe","SzemerediRegularity.pow_mul_m_le_card_part","SzemerediRegularity.star","SzemerediRegularity.stepBound","Trans.trans","True","True.intro","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_eps_mul_card_nonuniformWitness_le_card_star","cast","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_div","div_le_div_of_nonneg_right","div_le_div₀","div_le_iff₀","div_le_one","div_le_one_of_le₀","div_nonneg","eq_self","eq_true","eq_true_of_decide","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTransEq","instTransEq_1","instTransLE","inv_anti₀","inv_le_one_of_one_le₀","le_div_iff₀'","le_of_lt","le_of_not_gt","le_refl","mul_assoc","mul_comm","mul_comm_div","mul_div_assoc","mul_div_assoc'","mul_div_left_comm","mul_le_mul","mul_le_mul_of_nonneg_left","mul_le_mul_of_nonneg_right","mul_le_of_le_one_right","mul_nonneg","mul_pos","neg_neg_of_pos","of_eq_true","one_div","one_sub_div","pow_pos","propext","rfl","sub_le_sub_left","sub_nonneg_of_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.le_sum_card_subset_chunk_parts","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":245,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.sup","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","Lattice.toSemilatticeSup","Membership.mem","Nat","Nat.cast","Nat.instDiv","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SzemerediRegularity.chunk","SzemerediRegularity.stepBound","id","instHAdd","instHDiv","instHMul"],"value_dag_size":897,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","CommMagma.toMul","CommSemigroup.toCommMagma","DecidableEq","DecidableRel","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.symm","Eq.trans","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.ofSubset","Finpartition.ofSubset_parts","Finpartition.parts","Finpartition.sum_card_parts","Finset","Finset.card","Finset.card_nsmul_le_sum","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.sum","Finset.sup","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","Lattice.toSemilatticeSup","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.cast","Nat.cast_add._simp_1","Nat.cast_le","Nat.cast_le._simp_1","Nat.cast_mul","Nat.cast_nonneg'","Nat.cast_one","Nat.instAddCommMonoid","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SzemerediRegularity.card_le_m_add_one_of_mem_chunk_parts","SzemerediRegularity.chunk","SzemerediRegularity.coe_m_add_one_pos","SzemerediRegularity.m_le_card_of_mem_chunk_parts","SzemerediRegularity.stepBound","cast","congrArg","div_le_iff₀","id","instAddNat","instHAdd","instHDiv","instHMul","instLENat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","mul_div_assoc'","mul_le_mul","mul_right_comm","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.m_add_one_div_m_le_one_add","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":280,"type_refs":["DecidableEq","DivInvMonoid.toDiv","Finpartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","SzemerediRegularity.stepBound","instHAdd","instHDiv","instHMul","instHPow","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":2384,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","DecidableEq","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toInv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toDivisionRing","Field.toSemifield","Finpartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","Int.ofNat","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsOrderedRing.toZeroLEOneClass","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNNRat_add","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.NormNum.isRat_le_true","Mathlib.Meta.NormNum.one_natPow","Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.coeff_one","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_congr","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_bit0","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_nat","Mathlib.Tactic.Ring.Common.pow_one","Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.of_eq","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_pos'","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instInv","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SzemerediRegularity.hundred_div_ε_pow_five_le_m","SzemerediRegularity.stepBound","Trans.trans","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","add_le_add","add_pos_of_pos_of_nonneg","congrArg","covariant_swap_add_of_covariant_add","div_eq_mul_inv","div_le_div_of_nonneg_right","div_pos","id","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTransEq_1","instTransLE","le_of_lt","le_refl","mul_le_mul_of_nonneg_left","ne_of_gt","one_div_div","one_div_le_one_div_of_le","pow_le_pow_left₀","pow_nonneg","pow_pos","rfl","same_add_div"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_eps_mul_card_nonuniformWitness_le_card_star","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":331,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Ne","Not","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instField","Real.instIsStrictOrderedRing","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.linearOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.nonuniformWitness","SzemerediRegularity.star","id","instHDiv","instHMul","instHPow","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":2811,"value_refs":["AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommMagma.toMul","CommMonoid.toMonoid","CommRing.toNonUnitalCommRing","CommSemigroup.toCommMagma","Decidable.decide","DecidableEq","DecidableRel","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Even.pow_nonneg","Exists.intro","Field.toDivisionRing","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.nonempty_of_mem_parts","Finpartition.parts","Finset","Finset.Nonempty","Finset.biUnion","Finset.card","Finset.card_le_card","Finset.card_pos","Finset.card_sdiff_of_subset","Finset.instLattice","Finset.instOrderBot","Finset.instSDiff","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toIsOrderedRing","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.IsNatPowT.bit0","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isNat_pow","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_mul._simp_1","Nat.cast_nonneg","Nat.cast_nonneg'","Nat.cast_pos'","Nat.cast_pow._simp_1","Nat.cast_sub","Nat.decLe","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instMonoid","Nat.instNeZeroSucc","Nat.instNonUnitalSemiring","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemiring","Nat.instStarOrderedRing","Nat.instStarRing","Nat.succ","Nat.succ_le_iff","Ne","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toAddCommGroup","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instCommMonoid","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMonoidWithZero","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instSemigroup","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","SDiff.sdiff","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semigroup.toMul","SemilatticeInf.toPartialOrder","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.le_card_nonuniformWitness","SimpleGraph.nonuniformWitness","StarOrderedRing.toExistsAddOfLE","SubNegMonoid.toSub","SzemerediRegularity.biUnion_star_subset_nonuniformWitness","SzemerediRegularity.pow_mul_m_le_card_part","SzemerediRegularity.star","SzemerediRegularity.stepBound","Trans.trans","True","True.intro","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star","cast","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_div","div_le_iff₀'","div_le_one_of_le₀","div_pow","eq_self","eq_true","even_two_mul","id","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instSubNat","instTransEq","instTransEq_1","instTransLE","le_div_iff₀","le_mul_of_one_le_left","le_of_lt","le_of_mul_le_mul_left","mul_assoc","mul_div_assoc","mul_div_right_comm","mul_le_mul_of_nonneg_left","mul_le_mul_of_nonneg_right","mul_nonneg","mul_pos","mul_pow","mul_right_comm","of_decide_eq_true","of_eq_true","one_le_div","one_le_sq_iff₀","one_le_two","one_mul","pow_le_pow_of_le_one","pow_mul","pow_pos","pow_right_comm","pow_succ","propext","sq","sub_le_comm","sub_le_sub_left","sub_mul","tsub_add_cancel_of_le","zero_lt_two"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.one_sub_le_m_div_m_add_one_sq","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":285,"type_refs":["DecidableEq","DivInvMonoid.toDiv","Finpartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","SzemerediRegularity.stepBound","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1282,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.existsAddOfLE","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bool","CommGroupWithZero.toDivisionCommMonoid","CommGroupWithZero.toGroupWithZero","CommRing.toCommSemiring","CommRing.toRing","CommSemiring.toSemiring","DecidableEq","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.refl","Eq.symm","Field.toSemifield","Finpartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.univ","Fintype","Fintype.card","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","LT.lt.ne'","Lattice.toSemilatticeInf","Mathlib.Meta.NormNum.IsNat.to_eq","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instMonoid","Nat.instNeZeroSucc","Nat.ofNat_pos._simp_1","NonAssocSemiring.toAddCommMonoidWithOne","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddMonoid","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SzemerediRegularity.coe_m_add_one_pos","SzemerediRegularity.hundred_div_ε_pow_five_le_m","SzemerediRegularity.stepBound","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","add_sub_cancel_right","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_div","div_pos","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_add_of_nonneg_right","le_div_iff₀'","le_trans","mul_one","mul_pos","of_eq_true","one_div_div","one_div_le","one_pow","one_sub_div","pow_pos","propext","sq_nonneg","sub_le_sub_iff_left","sub_sq","zero_le_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_card_subset_chunk_parts_le","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":279,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.sup","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","Lattice.toSemilatticeSup","Membership.mem","Nat","Nat.cast","Nat.instDiv","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instZero","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SzemerediRegularity.chunk","SzemerediRegularity.stepBound","Zero.toOfNat0","id","instHAdd","instHDiv","instHMul"],"value_dag_size":870,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Bool","CommMagma.toMul","CommSemigroup.toCommMagma","DecidableEq","DecidableRel","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.card_biUnion_le_card_mul","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.sup","Finset.sup_eq_biUnion","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","Lattice.toSemilatticeSup","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toMulOneClass","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_add._simp_1","Nat.cast_le._simp_1","Nat.cast_mul._simp_1","Nat.cast_nonneg'","Nat.cast_one","Nat.instDiv","Nat.instPreorder","Nat.mono_cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SzemerediRegularity.card_le_m_add_one_of_mem_chunk_parts","SzemerediRegularity.chunk","SzemerediRegularity.m_le_card_of_mem_chunk_parts","SzemerediRegularity.stepBound","Zero.toOfNat0","add_pos'","cast","congrArg","id","instAddNat","instHAdd","instHDiv","instHMul","instLENat","instMulNat","instMulZeroClassOfSemiring","instOfNatNat","le_div_iff₀","le_of_lt","mul_div_assoc'","mul_le_mul","mul_nonneg","mul_right_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":null,"statement_dag_size":461,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.biUnion","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.product","Finset.sum","Finset.univ","Fintype","Fintype.card","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instMonoid","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","Rat.cast","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRatCast","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SzemerediRegularity.chunk","id","instHAdd","instHDiv","instHMul","instHPow","instLENat","instMulNat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":3798,"value_refs":["AddCommMonoidWithOne.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.addLeftReflectLE_of_addLeftMono","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Bool","CommGroupWithZero.toDivisionCommMonoid","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommSemigroup.toCommMagma","DecidableEq","DecidableRel","Distrib.rightDistribClass","Distrib.toMul","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.intro","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.nonempty_of_mem_parts","Finpartition.ofSubset","Finpartition.parts","Finset","Finset.Nonempty","Finset.biUnion","Finset.biUnion_nonempty","Finset.card","Finset.card_pos","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mul_sum","Finset.product","Finset.sum","Finset.sum_congr","Finset.sum_div","Finset.sum_le_sum","Finset.sup","Finset.sup_eq_biUnion","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff.mpr","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LT.lt","Lattice.toSemilatticeSup","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LinearOrderedCommMonoidWithZero.toPosMulStrictMono","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toMul","MulOne.toOne","MulOneClass.toMulOne","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_mul","Nat.cast_mul._simp_1","Nat.cast_nonneg","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_pos","Nat.cast_pos'","Nat.cast_sum","Nat.cast_zero","Nat.instAddCommMonoid","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instLinearOrderedCommMonoidWithZero","Nat.instMonoid","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instPreorder","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Nonempty","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.snd","Rat","Rat.cast","Rat.cast_div","Rat.cast_le_natCast._simp_1","Rat.cast_mul","Rat.cast_natCast","Rat.cast_sum","Rat.instDiv","Rat.instDivisionRing","Rat.instField","Rat.instLE","Rat.instMul","Rat.instNatCast","Rat.instOfNat","Rat.semiring","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemigroup","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSemigroup","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Rel.card_interedges_finpartition","Rel.edgeDensity","Rel.edgeDensity.eq_1","Rel.interedges","Right.add_pos_of_nonneg_of_pos","Ring.toAddGroupWithOne","Ring.toSemiring","SProd.sprod","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semigroup.toMul","Semiring.toAddCommMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity.eq_1","SimpleGraph.edgeDensity_le_one","SzemerediRegularity.chunk","SzemerediRegularity.stepBound","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.eps_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0.SzemerediRegularity.Positivity.m_pos","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.m_add_one_div_m_le_one_add","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_card_subset_chunk_parts_le","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_6","add_le_add_iff_left","add_mul","cast","congr","congrArg","congrFun'","contravariant_lt_of_covariant_le","covariant_swap_add_of_covariant_add","div_div","div_le_iff₀","div_mul_eq_mul_div","div_pos","forall_congr","funext","id","implies_congr","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instIsLeftCancelAddOfAddLeftReflectLE","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_mul_of_one_le_right","le_of_lt","le_trans","mul_assoc","mul_comm","mul_div_left_comm","mul_le_mul","mul_le_mul_of_nonneg_right","mul_le_of_le_one_right","mul_mul_mul_comm","mul_nonneg","mul_pos","one_le_div","one_mul","pow_pos","propext","rfl","sq","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.termM","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":48,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.card_parts_equitabilise._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.card_parts_equitabilise","reducibility":null,"statement_dag_size":67,"type_refs":["DecidablePred","Disjoint","Eq","Finset","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":74,"value_refs":["DecidablePred","Disjoint","Finset","Finset.disjoint_filter","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","IsBotZeroClass","LE.le","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero","Zero.toOfNat0"],"value_dag_size":56,"value_refs":["Eq","IsBotZeroClass","LE.le","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero","Zero.toOfNat0","le_zero_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Ne","Ne.eq_def","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":63,"value_refs":["Eq.symm","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSDiff","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff"],"value_dag_size":54,"value_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSDiff","Finset.sdiff_eq_empty_iff_subset","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise.0.Finpartition.equitabilise_aux","reducibility":null,"statement_dag_size":31,"type_refs":["Bot.bot","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instOrderBot","Finset.instPartialOrder","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":34,"value_refs":["Bot.bot","EmptyCollection.emptyCollection","Eq.symm","Finset","Finset.bot_eq_empty","Finset.instEmptyCollection","Finset.instOrderBot","Finset.instPartialOrder","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":28,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity","reducibility":"regular","statement_dag_size":93,"type_refs":["DecidableEq","DecidableRel","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Real","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype"],"value_dag_size":172,"value_refs":["DecidableEq","DecidableRel","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSProd","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Prod.fst","Prod.snd","Real","SProd.sprod","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","Subtype.val","SzemerediRegularity.chunk","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","reducibility":null,"statement_dag_size":113,"type_refs":["DecidableEq","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Prod.fst","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":145,"value_refs":["And","And.left","DecidableEq","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Finset.univ","Fintype","Iff.mp","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership","Subtype","Subtype.property","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","reducibility":null,"statement_dag_size":113,"type_refs":["DecidableEq","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Prod.snd","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":149,"value_refs":["And","And.left","And.right","DecidableEq","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Finset.univ","Fintype","Iff.mp","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership","Subtype","Subtype.property","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs.congr_simp","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","reducibility":null,"statement_dag_size":198,"type_refs":["DecidableEq","DecidableRel","Eq","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Real","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs"],"value_dag_size":396,"value_refs":["Decidable","DecidableEq","DecidableRel","Eq","Eq.ndrec","Eq.rec","Eq.refl","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Pi.instSubsingleton","Prod","Real","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subsingleton.elim","Subtype","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","instSubsingletonDecidable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","reducibility":null,"statement_dag_size":186,"type_refs":["DecidableEq","DecidableRel","Eq","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSProd","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Prod.fst","Prod.snd","Real","SProd.sprod","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","Subtype.val","SzemerediRegularity.chunk","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_2"],"value_dag_size":106,"value_refs":["DecidableEq","DecidableRel","Eq.refl","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Real","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity","reducibility":null,"statement_dag_size":168,"type_refs":["DecidableEq","DecidableRel","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.attach","Finset.biUnion","Finset.decidableEq","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Prod","Real","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","SzemerediRegularity.increment","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","instDecidableEqProd"],"value_dag_size":2315,"value_refs":["And","And.intro","And.left","And.right","DecidableEq","DecidableRel","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","Finpartition","Finpartition.IsEquipartition","Finpartition.bind._proof_2","Finpartition.bind_parts","Finpartition.disjoint","Finpartition.le","Finpartition.nonempty_of_mem_parts","Finpartition.parts","Finset","Finset.Nonempty","Finset.attach","Finset.biUnion","Finset.decidableEq","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Iff.mpr","Iff.of_eq","Membership.mem","Ne","Not","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","Real","Set.PairwiseDisjoint.elim_finset","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","Subtype.mk","Subtype.val","SzemerediRegularity.chunk","SzemerediRegularity.increment","SzemerediRegularity.increment._proof_1","True","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_9","congr","congrArg","congrFun'","exists_prop_congr","forall_congr","funext","id","implies_congr","instDecidableEqProd","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","Finset","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Finset","Finset.attach","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","True"],"value_dag_size":60,"value_refs":["Finset","Finset.attach","Finset.instSetLike","Finset.mem_attach","Membership.mem","SetLike.instMembership","Subtype","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs_increment","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.increment_isEquipartition._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.increment_isEquipartition","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Exists","HAdd.hAdd","Membership.mem","Nat","Nat.instOne","OfNat.ofNat","Or","Set","Set.EquitableOn","Set.instMembership","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":73,"value_refs":["Eq","Exists","HAdd.hAdd","Membership.mem","Nat","Nat.instOne","OfNat.ofNat","Or","Set","Set.EquitableOn","Set.equitableOn_iff_exists_eq_eq_add_one","Set.instMembership","instAddNat","instHAdd","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity","reducibility":null,"statement_dag_size":134,"type_refs":["DecidableEq","DecidableRel","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.attach","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.offDiag","Finset.univ","Fintype","Membership.mem","Prod","Real","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs"],"value_dag_size":2403,"value_refs":["And","And.left","And.right","DecidableEq","DecidableRel","Disjoint","Eq","Eq.mp","Eq.mpr","Eq.trans","Exists.casesOn","False","Finpartition","Finpartition.IsEquipartition","Finpartition.disjoint","Finpartition.le","Finpartition.nonempty_of_mem_parts","Finpartition.parts","Finset","Finset.Nonempty","Finset.attach","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Finset.univ","Fintype","Function.onFun","Membership.mem","Ne","Not","Prod","Prod.casesOn","Prod.ext","Prod.fst","Prod.mk","Prod.snd","Real","SProd.sprod","Set","Set.Pairwise","Set.PairwiseDisjoint","Set.PairwiseDisjoint.elim_finset","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Subtype","Subtype.casesOn","Subtype.ext","Subtype.mk","Subtype.val","SzemerediRegularity.chunk","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs._simp_1_3","congrArg","forall_congr","funext","id","implies_congr","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.pairwiseDisjoint_distinctPairs","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment_0_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Delaborator.Delab"],"value_dag_size":334,"value_refs":["Applicative.toPure","Bind.bind","Bind.kleisliRight","IO.RealWorld","Lean.Core.CoreM","Lean.Core.instMonadQuotationCoreM","Lean.Expr","Lean.Expr.isConstOf","Lean.MacroScope","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instMonadMetaM","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.PrettyPrinter.Delaborator.Context","Lean.PrettyPrinter.Delaborator.DelabM","Lean.PrettyPrinter.Delaborator.State","Lean.PrettyPrinter.Delaborator.SubExpr.getExpr","Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM","Lean.PrettyPrinter.Delaborator.whenNotPPOption","Lean.PrettyPrinter.Delaborator.whenPPOption","Lean.PrettyPrinter.Delaborator.withOverApp","Lean.SourceInfo","Lean.Syntax.Term","Lean.Syntax.atom","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.getPPExplicit","Lean.getPPNotation","Lean.instMonadQuotationOfMonadFunctorOfMonadLift","List.cons","List.nil","Mathlib.Notation3.MatchState","Mathlib.Notation3.MatchState.empty","Mathlib.Notation3.isType'","Mathlib.Notation3.matchApp","Mathlib.Notation3.matchExpr","Mathlib.Notation3.matchFVar","Mathlib.Notation3.withHeadRefIfTagAppFns","Monad.toBind","Nat","OfNat.ofNat","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadFunctor","ReaderT.instMonadLift","StateRefT'","StateRefT'.instMonad","StateRefT'.instMonadFunctor","StateRefT'.instMonadLift","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment___macroRules__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Increment_0_termM_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":403,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.Syntax.node3","Lean.Syntax.node5","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Increment","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.termM","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":45,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_biUnion_offDiag_le'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_biUnion_offDiag_le'","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableRel","Eq","Finset","Finset.card","HDiv.hDiv","HMul.hMul","Nat.cast","Prod","Rat","Rat.instDiv","Rat.instMul","Rat.instNatCast","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.interedges","instHDiv","instHMul"],"value_dag_size":85,"value_refs":["DecidableRel","Eq.symm","Finset","Finset.card","HDiv.hDiv","HMul.hMul","Nat.cast","Prod","Rat","Rat.instDiv","Rat.instMul","Rat.instNatCast","SimpleGraph","SimpleGraph.Adj","SimpleGraph.card_interedges_div_card","SimpleGraph.edgeDensity","SimpleGraph.interedges","instHDiv","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.card_interedges_sparsePairs_le'","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","Finset","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.IsEquipartition.sum_nonUniforms_lt","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.card","Finset.instSProd","HMul.hMul","Nat","Prod","SProd.sprod","instHMul","instMulNat"],"value_dag_size":62,"value_refs":["Eq.symm","Finset","Finset.card","Finset.card_product","Finset.instSProd","HMul.hMul","Nat","Prod","SProd.sprod","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","LT.lt","Monoid.toNPow","NPow.toPow","Nat","Nat.instDiv","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":361,"value_refs":["CommMonoid.toMonoid","Eq","Eq.mpr","Eq.symm","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","IsOrderedAddMonoid.toAddLeftMono","LE.le","LT.lt","LT.lt.trans_le","LinearOrderedCommMonoidWithZero.toPosMulStrictMono","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMonoid","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instCommMonoid","Nat.instCommSemigroup","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instMonoid","Nat.instMonoidWithZero","Nat.instMulLeftMono","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instOne","Nat.instPartialOrder","Nat.instPreorder","Nat.instZeroLEOneClass","Nat.mul_div_le","Nat.mul_lt_mul_of_pos_left","Nat.mul_lt_mul_of_pos_right","Nat.mul_succ","Nat.sub_lt","Nat.succ","Nat.succ_pos'","OfNat.ofNat","Preorder.toLE","add_le_add","congrArg","covariant_swap_add_of_covariant_add","covariant_swap_mul_of_covariant_mul","id","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat","le_refl","mul_pow","pow_le_pow_left'","pow_pos","sq","zero_lt_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.Finpartition.nonUniforms_bot","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.not_isUniform_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.regularityReduced_anti.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.regularityReduced_anti","reducibility":"abbrev","statement_dag_size":531,"type_refs":["And","And.intro","DecidableEq","DecidableRel","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.intro","Field","Field.toDivisionRing","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","Rat.cast","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.regularityReduced","instDistribLatticeOfLinearOrder"],"value_dag_size":2274,"value_refs":["And","And.casesOn","And.intro","DecidableEq","DecidableRel","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.casesOn","Exists.intro","Field","Field.toDivisionRing","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","Rat.cast","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.regularityReduced","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.regularityReduced_mono.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.regularityReduced_mono","reducibility":"abbrev","statement_dag_size":531,"type_refs":["And","And.intro","DecidableEq","DecidableRel","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.intro","Field","Field.toDivisionRing","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","Rat.cast","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.regularityReduced","instDistribLatticeOfLinearOrder"],"value_dag_size":2274,"value_refs":["And","And.casesOn","And.intro","DecidableEq","DecidableRel","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.casesOn","Exists.intro","Field","Field.toDivisionRing","Finpartition","Finpartition.parts","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","Ne","PartialOrder.toPreorder","Preorder.toLE","Rat.cast","SemilatticeInf.toPartialOrder","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","SimpleGraph.regularityReduced","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","or_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":83,"type_refs":["And","DecidableRel","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges"],"value_dag_size":89,"value_refs":["And","DecidableRel","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges","SimpleGraph.mem_interedges_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform","name":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","Finset","Finset.instSetLike","Finset.mem_offDiag","Finset.offDiag","Membership.mem","Ne","Prod","Prod.fst","Prod.snd","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Star","name":"_private.Mathlib.Combinatorics.SimpleGraph.Star.0.SimpleGraph.degree_starGraph_of_ne_center._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Star.0.SimpleGraph.degree_starGraph_of_ne_center","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Ne","SimpleGraph.Adj","SimpleGraph.starGraph"],"value_dag_size":131,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_left","Ne","Not","Or","SimpleGraph.Adj","SimpleGraph.starGraph","SimpleGraph.starGraph_adj","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborFinset_def","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":50,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Fintype","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":55,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.mem_compl","Fintype","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborFinset_def","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl","reducibility":null,"statement_dag_size":40,"type_refs":["And","Compl.compl","Eq","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instCompl"],"value_dag_size":44,"value_refs":["And","Compl.compl","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.compl_adj","SimpleGraph.instCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_neighborFinset_union_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.card_neighborFinset_union_eq","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborFinset_def","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.ediam_eq_two._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.ediam_eq_two","reducibility":null,"statement_dag_size":152,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LE.le","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder"],"value_dag_size":159,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LE.le","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Or","Order.le_one_iff","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.matrix_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.matrix_eq","reducibility":null,"statement_dag_size":40,"type_refs":["And","Compl.compl","Eq","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.instCompl"],"value_dag_size":44,"value_refs":["And","Compl.compl","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.compl_adj","SimpleGraph.instCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.matrix_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.matrix_eq","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":44,"value_refs":["Eq.symm","Finset","Fintype","Set.Elem","Set.toFinset","SimpleGraph","SimpleGraph.neighborFinset","SimpleGraph.neighborFinset_def","SimpleGraph.neighborSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":62,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Fintype","Inter.inter","Set","Set.Elem","Set.instInter","Set.toFinset"],"value_dag_size":75,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.instInter","Fintype","Inter.inter","Set","Set.Elem","Set.instInter","Set.toFinset","Set.toFinset_inter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset"],"value_dag_size":36,"value_refs":["Eq.symm","Finset.card","Fintype","Fintype.card","Nat","Set","Set.Elem","Set.toFinset","Set.toFinset_card"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":50,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Fintype","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":55,"value_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Finset","Finset.booleanAlgebra","Finset.instSetLike","Finset.mem_compl","Fintype","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Ne","Ne.eq_def","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","True","True.intro"],"value_dag_size":16,"value_refs":["True","True.intro","forall_true_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.bot_strongly_regular","reducibility":null,"statement_dag_size":34,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","False","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":37,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","False","SimpleGraph","SimpleGraph.Adj","SimpleGraph.bot_adj","SimpleGraph.completeAtomicBooleanAlgebra","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.compl_neighborFinset_sdiff_inter_eq._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.compl_neighborFinset_sdiff_inter_eq","reducibility":null,"statement_dag_size":126,"type_refs":["BooleanAlgebra.toCompl","Compl.compl","DecidableEq","DecidableRel","Eq","Finset","Finset.booleanAlgebra","Finset.instInter","Finset.instSDiff","Finset.instSingleton","Finset.instUnion","Fintype","Inter.inter","Membership.mem","SDiff.sdiff","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Singleton.singleton","Subtype.fintype","Union.union"],"value_dag_size":1189,"value_refs":["And","And.casesOn","BooleanAlgebra.toCompl","Classical.byContradiction","Compl.compl","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.booleanAlgebra","Finset.ext","Finset.instInsert","Finset.instInter","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_inter","Finset.mem_sdiff","Finset.mem_singleton","Finset.singleton_union","Finset.union_singleton","Fintype","Iff","Insert.insert","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","Set","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","SimpleGraph.neighborSet.memDecidable","Singleton.singleton","Subtype.fintype","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.StronglyRegular","name":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.conway_99","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph","reducibility":"regular","statement_dag_size":61,"type_refs":["DecidableRel","Exists","Fintype","Nat","OfNat.ofNat","ProofWanted","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsSRGWith","instOfNatNat"],"value_dag_size":61,"value_refs":["DecidableRel","Exists","Fintype","Nat","OfNat.ofNat","ProofWanted.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsSRGWith","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.IsInduced.induce_top_verts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.IsInduced.induce_top_verts","reducibility":"abbrev","statement_dag_size":140,"type_refs":["And","And.intro","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.verts","Top.top"],"value_dag_size":223,"value_refs":["And","And.casesOn","And.intro","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.verts","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.adj_congr_of_sym2._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.adj_congr_of_sym2","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.adj_congr_of_sym2._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.adj_congr_of_sym2","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq","reducibility":null,"statement_dag_size":111,"type_refs":["Eq","Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.verts","Subtype.mk"],"value_dag_size":117,"value_refs":["Exists","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coeSubgraph","SimpleGraph.Subgraph.coeSubgraph_adj","SimpleGraph.Subgraph.verts","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq","reducibility":null,"statement_dag_size":88,"type_refs":["And","Eq","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.restrict","SimpleGraph.Subgraph.verts","Subtype.val"],"value_dag_size":94,"value_refs":["And","Membership.mem","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.restrict","SimpleGraph.Subgraph.restrict_adj","SimpleGraph.Subgraph.verts","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.coeSubgraph_restrict_eq","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.comap_monotone._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.comap_monotone","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.comap_monotone._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.comap_monotone","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.toFinset","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.mem_toFinset","Set.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_pos_iff_exists_adj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_pos_iff_exists_adj","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fintype","Fintype.card","LT.lt","Nat","Nonempty","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":33,"value_refs":["Fintype","Fintype.card","Fintype.card_pos_iff","LT.lt","Nat","Nonempty","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_pos_iff_exists_adj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.degree_pos_iff_exists_adj","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists","Nonempty","Subtype"],"value_dag_size":24,"value_refs":["Exists","Nonempty","Subtype","nonempty_subtype","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteEdges","Sym2","Sym2.mk"],"value_dag_size":58,"value_refs":["And","Membership.mem","Not","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.deleteEdges","SimpleGraph.deleteEdges_adj","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_coe_eq","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_deleteEdges._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_deleteEdges","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_deleteEdges._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_deleteEdges","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_inter_edgeSet_right_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_inter_edgeSet_right_eq","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_le_of_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_le_of_le","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_le_of_le._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteEdges_le_of_le","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True","UsesSetNotationForOrder"],"value_dag_size":29,"value_refs":["LE.le","Preorder","Preorder.toLE","UsesSetNotationForOrder","eq_true","subset_rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_adj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_adj","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_deleteVerts._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_deleteVerts","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_deleteVerts._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_deleteVerts","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.disjoint_verts_iff_disjoint._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.disjoint_verts_iff_disjoint","reducibility":null,"statement_dag_size":137,"type_refs":["Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","CompletelyDistribLattice.toCompleteDistribLattice","Disjoint","HeytingAlgebra.toOrderBot","Iff","LE.le","Membership.mem","Order.Frame.toHeytingAlgebra","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.instCompletelyDistribLattice","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts"],"value_dag_size":543,"value_refs":["Bot.bot","BoundedOrder.toOrderBot","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","CompletelyDistribLattice.toCompleteDistribLattice","Disjoint","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HeytingAlgebra.toOrderBot","Iff","LE.le","Lattice.toSemilatticeInf","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Order.Frame.toHeytingAlgebra","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instCompleteAtomicBooleanAlgebra","Set.instDistribLattice","Set.instEmptyCollection","Set.instLE","Set.instMembership","Set.mem_empty_iff_false","Set.subset_def","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.instBot","SimpleGraph.Subgraph.instCompletelyDistribLattice","SimpleGraph.Subgraph.instPartialOrder","SimpleGraph.Subgraph.verts","SimpleGraph.Subgraph.verts_bot","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.ext.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.ext","reducibility":"abbrev","statement_dag_size":70,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.mk","Std.Symm"],"value_dag_size":113,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.casesOn","SimpleGraph.Subgraph.mk","Std.Symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.induce_mono._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.induce_mono","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.induce_self_verts._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.induce_self_verts","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instCompletelyDistribLattice._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instCompletelyDistribLattice","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Exists"],"value_dag_size":37,"value_refs":["Classical.skolem","Exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instFintypeOfDecidableEqOfDecidableRelAdj._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instFintypeOfDecidableEqOfDecidableRelAdj","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","Std.Symm"],"value_dag_size":27,"value_refs":["Std.Symm","propext","symm_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instSupSet._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.instSupSet","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj"],"value_dag_size":34,"value_refs":["SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.isInduced_iff_exists_eq_induce_top.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.isInduced_iff_exists_eq_induce_top","reducibility":"abbrev","statement_dag_size":100,"type_refs":["Eq","Exists","Exists.intro","Set","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","Top.top"],"value_dag_size":128,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Set","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.le_induce_union._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.le_induce_union","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_le_iff_le_comap","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_sup._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_sup","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_sup._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_sup","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":40,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts"],"value_dag_size":54,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.verts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":41,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.verts"],"value_dag_size":137,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.edge_vert","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Subgraph.verts","True","_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_3","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":41,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.verts"],"value_dag_size":171,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.adj_symm","SimpleGraph.Subgraph.edge_vert","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Subgraph.verts","True","_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_3","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":144,"type_refs":["And","Eq","Eq.refl","Exists","Iff","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.verts","Subtype","Subtype.mk"],"value_dag_size":1678,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Iff.mpr","Iff.of_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.exists_and_right","Lean.Grind.forall_forall_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.Elem","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.adj_symm","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.coe_adj","SimpleGraph.Subgraph.edge_vert","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Subgraph.verts","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._proof_1_5","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","exists_prop_congr","false_or","forall_congr","funext","id","implies_congr","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":83,"type_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map"],"value_dag_size":89,"value_refs":["And","DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","SimpleGraph","SimpleGraph.Adj","SimpleGraph.map","SimpleGraph.map_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.spanningCoe_coe","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Or","Prod.mk","Sym2.Rel"],"value_dag_size":48,"value_refs":["And","Eq","Or","Prod.mk","Sym2.Rel","Sym2.rel_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.subgraphOfAdj_eq_induce","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.support_subset_verts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.support_subset_verts","reducibility":"abbrev","statement_dag_size":129,"type_refs":["Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.support","SimpleGraph.Subgraph.support.match_1"],"value_dag_size":178,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Prod","Prod.mk","Set","Set.instMembership","Set.ofPred","SetRel","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.support","SimpleGraph.Subgraph.support.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.card_neighborSet_toSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.card_neighborSet_toSubgraph","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborFinset","SimpleGraph.neighborSet"],"value_dag_size":56,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set.Elem","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.mem_neighborFinset","SimpleGraph.neighborFinset","SimpleGraph.neighborSet","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","True"],"value_dag_size":18,"value_refs":["True","forall₂_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_singletonSubgraph._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_singletonSubgraph","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_singletonSubgraph._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_singletonSubgraph","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_subgraphOfAdj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_subgraphOfAdj","reducibility":null,"statement_dag_size":106,"type_refs":["DFunLike.coe","Iff","Membership.mem","RelHom","RelHom.instFunLike","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Hom.map_adj","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.verts","SimpleGraph.subgraphOfAdj"],"value_dag_size":1746,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","FunLike","HEq.refl","Iff","Insert.insert","LE.le","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","RelHom","RelHom.instFunLike","Set","Set.image","Set.image_congr","Set.instInsert","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.mem_image","Set.mem_insert_iff","Set.mem_singleton_iff","Set.singleton_subset_iff","Set.subset_insert","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Hom.map_adj","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.map_verts","SimpleGraph.Subgraph.verts","SimpleGraph.subgraphOfAdj","SimpleGraph.subgraphOfAdj_verts","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","heq_of_eq","id","implies_congr","of_eq_false","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_subgraphOfAdj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.map_subgraphOfAdj","reducibility":null,"statement_dag_size":100,"type_refs":["DFunLike.coe","Iff","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Hom.map_adj","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.map","SimpleGraph.subgraphOfAdj"],"value_dag_size":4476,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","FunLike","HEq","HEq.refl","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","RelHom","RelHom.instFunLike","Relation.Map","Relation.Map.eq_1","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Hom.map_adj","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.map","SimpleGraph.Subgraph.map_adj","SimpleGraph.subgraphOfAdj","SimpleGraph.subgraphOfAdj_adj","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","heq_eq_eq","heq_of_eq","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Iff"],"value_dag_size":19,"value_refs":["Eq","Iff","eq_iff_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_le_of_adj._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_le_of_adj","reducibility":null,"statement_dag_size":51,"type_refs":["LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.adj_sub","SimpleGraph.Subgraph.verts","SimpleGraph.subgraphOfAdj"],"value_dag_size":482,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Insert.insert","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Set","Set.instInsert","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_singleton_iff","Set.subset_def","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.fst_mem","SimpleGraph.Subgraph.Adj.snd_mem","SimpleGraph.Subgraph.adj_sub","SimpleGraph.Subgraph.verts","SimpleGraph.subgraphOfAdj","SimpleGraph.subgraphOfAdj_verts","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_le_of_adj._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_le_of_adj","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.adj_sub","SimpleGraph.subgraphOfAdj"],"value_dag_size":604,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Not","Or","Or.casesOn","Prod","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.adj_sub","SimpleGraph.subgraphOfAdj","SimpleGraph.subgraphOfAdj_adj","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","eq_false","eq_of_heq","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_symm._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_symm","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_symm._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.subgraphOfAdj_symm","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.support_subgraphOfAdj._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.support_subgraphOfAdj","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Subgraph","name":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.support_subgraphOfAdj._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.support_subgraphOfAdj","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.colorable_sum.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.colorable_sum","reducibility":"abbrev","statement_dag_size":66,"type_refs":["And","And.intro","Nat","SimpleGraph","SimpleGraph.Colorable"],"value_dag_size":82,"value_refs":["And","And.casesOn","And.intro","Nat","SimpleGraph","SimpleGraph.Colorable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl"],"value_dag_size":244,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_8","cast","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl"],"value_dag_size":236,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","cast","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":81,"type_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.rec","Bool.true","Eq","False","Nat.beq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","Sum.inr","True"],"value_dag_size":257,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","Sum.inr","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_8","cast","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":81,"type_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.rec","Bool.true","Eq","False","Nat.beq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","Sum.inr","True"],"value_dag_size":249,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","Sum.inr","cast","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inr"],"value_dag_size":244,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inr","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_8","cast","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inr"],"value_dag_size":236,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.nestedProof","SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inr","cast","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":481,"type_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","DFunLike.coe","Eq","False.elim","LE.le","Membership.mem","Prod","Prod.mk","Quot","Quot.mk","RelEmbedding","Set","Set.Elem","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.instLE","SimpleGraph.sum","SimpleGraph.symm","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","Sym2","Sym2.Rel","instFunLikeOrderEmbedding","noConfusion_of_Nat","symm"],"value_dag_size":2737,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.rec","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","HEq.trans","Iff","LE.le","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Nat.beq","Not","Or","Prod","Prod.mk","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","RelEmbedding","Set","Set.Elem","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.edgeSetSumEquiv.match_1.congr_eq_1","SimpleGraph.edgeSetSumEquiv.match_1.congr_eq_2","SimpleGraph.edgeSetSumEquiv.match_1.congr_eq_3","SimpleGraph.edgeSetSumEquiv.match_1.congr_eq_4","SimpleGraph.instLE","SimpleGraph.sum","SimpleGraph.symm","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.property","Subtype.val","Sum","Sum.casesOn","Sum.inl","Sum.inr","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_10","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_11","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_12","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_13","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_14","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_15","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_8","cast","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","heq_of_eq","id","instFunLikeOrderEmbedding","noConfusion_of_Nat","of_eq_true","symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv._proof_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv","reducibility":null,"statement_dag_size":47,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum"],"value_dag_size":55,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","SimpleGraph.symm","Sum","symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1","reducibility":null,"statement_dag_size":191,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"],"value_dag_size":187,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1","reducibility":null,"statement_dag_size":191,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"],"value_dag_size":187,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1","reducibility":null,"statement_dag_size":193,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"],"value_dag_size":189,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1.eq_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1","reducibility":null,"statement_dag_size":193,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"],"value_dag_size":189,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetSumEquiv.match_1","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.edgeSetSumEquiv.match_1","reducibility":"abbrev","statement_dag_size":165,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.sum","Sum","Sum.inl","Sum.inr"],"value_dag_size":1,"value_refs":["SimpleGraph.edgeSetSumEquiv.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.not_connected_sum._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.not_connected_sum","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected"],"value_dag_size":25,"value_refs":["And","Nonempty","SimpleGraph","SimpleGraph.Connected","SimpleGraph.Preconnected","SimpleGraph.connected_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.not_connected_sum._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.not_connected_sum","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","False","Nonempty","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.sum","Sum"],"value_dag_size":43,"value_refs":["Nonempty","SimpleGraph","SimpleGraph.Preconnected","SimpleGraph.not_preconnected_sum","SimpleGraph.sum","Sum","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":70,"value_refs":["Eq.refl","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":68,"value_refs":["Eq.refl","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","False","SimpleGraph.sum.match_1","Sum","Sum.inl","Sum.inr"],"value_dag_size":802,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","False.elim","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","SimpleGraph.sum._sparseCasesOn_1","SimpleGraph.sum._sparseCasesOn_1.else_eq","SimpleGraph.sum._sparseCasesOn_2","SimpleGraph.sum._sparseCasesOn_2.else_eq","SimpleGraph.sum.match_1","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_5","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1","reducibility":"abbrev","statement_dag_size":102,"type_refs":["Eq","False","Sum","Sum.inl","Sum.inr"],"value_dag_size":347,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_5","absurd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inl"],"value_dag_size":101,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Sum","name":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter._sparseCasesOn_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.splitter","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Nat.hasNotBit","Sum","Sum.ctorIdx","Sum.inr"],"value_dag_size":103,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Even","Nat","Nat.instSemiring","Not","Odd","instAddNat"],"value_dag_size":27,"value_refs":["Eq.symm","Even","Nat","Nat.instSemiring","Nat.not_even_iff_odd","Not","Odd","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.card_filter_odd_degree","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Not","Or","imp_iff_not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.fintypeEdgeSet._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.fintypeEdgeSet","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.mk","Membership.mem","Multiset","Multiset.Nodup","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instSetLike","Finset.mem_mk","Finset.mk","Membership.mem","Multiset","Multiset.Nodup","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.fintypeEdgeSet._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.fintypeEdgeSet","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.mem_edges_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsEulerian.mem_edges_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.succ","Nat.succ_le_iff","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":182,"type_refs":["And","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Even","HAdd.hAdd","Iff","List.countP","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Prod","Quot","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.Mem.decidable","Sym2.Rel","Sym2.instSetLike","instAddNat","instDecidableOr","instHAdd","instOfNatNat"],"value_dag_size":838,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","False.elim","HAdd.hAdd","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_and","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_eq_of_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_decide_eq_false","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.leaf","List.countP","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Prod","Quot","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.Mem.decidable","Sym2.Rel","Sym2.instSetLike","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableOr","instHAdd","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":159,"type_refs":["And","Decidable.decide","DecidableEq","Eq","Even","HAdd.hAdd","Iff","List.countP","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Prod","Quot","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.Mem.decidable","Sym2.Rel","Sym2.instSetLike","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":2076,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.eq_congr'","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_and","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_eq_of_eq_true_right","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.countP","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ctorIdx","Nat.even_add","Nat.even_iff","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Prod","Quot","SetLike.instMembership","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2","Sym2.Mem.decidable","Sym2.Rel","Sym2.instSetLike","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_self","eq_true","false_and","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Trails","name":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":84,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":62,"type_refs":["DecidableEq","DecidableRel","Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.cliqueFinset"],"value_dag_size":69,"value_refs":["DecidableEq","DecidableRel","Finset","Finset.instSetLike","Fintype","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.cliqueFinset","SimpleGraph.mem_cliqueFinset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":61,"value_refs":["Finset","Finset.instSetLike","Finset.mem_sym2_iff","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":72,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True"],"value_dag_size":77,"value_refs":["DecidableEq","Finset","Finset.insert_subset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":57,"type_refs":["And","Decidable","Eq","Finset","Finset.bipartiteBelow","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":65,"value_refs":["And","Decidable","Finset","Finset.bipartiteBelow","Finset.instSetLike","Finset.mem_bipartiteBelow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueSet"],"value_dag_size":43,"value_refs":["Finset","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueSet","SimpleGraph.mem_cliqueSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.instDecidable._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.instDecidable","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","LE.le","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instLENat","instOfNatNat"],"value_dag_size":66,"value_refs":["Eq","Finset","Finset.card","Finset.card_le_one","Finset.instSetLike","LE.le","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.instDecidable._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.instDecidable","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Set","Set.instInter","SetLike.coe"],"value_dag_size":50,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.coe_inter","Finset.instInter","Finset.instSetLike","Inter.inter","Set","Set.instInter","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.FarFromTriangleFree.lt_half._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.FarFromTriangleFree.lt_half","reducibility":null,"statement_dag_size":69,"type_refs":["DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","HDiv.hDiv","HMul.hMul","Inv.inv","InvOneClass.toInv","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul"],"value_dag_size":75,"value_refs":["DivInvMonoid.toDiv","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq.symm","HDiv.hDiv","HMul.hMul","Inv.inv","InvOneClass.toInv","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","div_eq_inv_mul","instHDiv","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":57,"type_refs":["And","Decidable","Eq","Finset","Finset.bipartiteBelow","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":65,"value_refs":["And","Decidable","Finset","Finset.bipartiteBelow","Finset.instSetLike","Finset.mem_bipartiteBelow","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"],"value_dag_size":60,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","SimpleGraph.mem_edgeFinset","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.card","Nat","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":32,"value_refs":["Finset","Finset.Nonempty","Finset.card","Finset.card_ne_zero","Nat","Ne","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":62,"type_refs":["DecidableEq","DecidableRel","Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.cliqueFinset"],"value_dag_size":69,"value_refs":["DecidableEq","DecidableRel","Finset","Finset.instSetLike","Fintype","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.cliqueFinset","SimpleGraph.mem_cliqueFinset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":84,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.LocallyLinear.card_edgeFinset","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":61,"value_refs":["Finset","Finset.instSetLike","Finset.mem_sym2_iff","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":61,"value_refs":["Finset","Finset.instSetLike","Finset.mem_sym2_iff","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Sym2.IsDiag","Sym2.mk"],"value_dag_size":26,"value_refs":["Eq","Sym2.IsDiag","Sym2.mk","Sym2.mk_isDiag_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":68,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":74,"value_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_triple_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Membership.mem","Or","SetLike.instMembership","Sym2","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_22","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_23","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_24","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueSet"],"value_dag_size":43,"value_refs":["Finset","Membership.mem","Nat","Set","Set.instMembership","SimpleGraph","SimpleGraph.IsNClique","SimpleGraph.cliqueSet","SimpleGraph.mem_cliqueSet_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":84,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":88,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":27,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.adj_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph","reducibility":null,"statement_dag_size":166,"type_refs":["DecidableEq","DecidableRel","Finset","Finset.card","Finset.instPartialOrder","Finset.instSetLike","Fintype","HSub.hSub","Inter.inter","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Set","Set.Pairwise","Set.Subsingleton","Set.instInter","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.CliqueFree","SimpleGraph.cliqueFinset","SimpleGraph.edgeFinset","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","Sym2","Sym2.instFintype","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":3556,"value_refs":["And","And.casesOn","And.intro","And.left","And.right","Classical.choose","Classical.choose_spec","Decidable.byContradiction","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.attach","Finset.card","Finset.card_attach","Finset.card_sdiff_of_subset","Finset.decidableMem","Finset.exists_ne_map_eq_of_card_lt_of_maps_to","Finset.instInsert","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert._simp_1","Finset.mem_singleton._simp_1","Fintype","Fintype.decidableExistsFintype","Function.Injective.ne","HSub.hSub","Iff.mp","Insert.insert","Inter.inter","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Tactic.Push.not_and_eq","Mathlib.Tactic.Push.not_exists._simp_1","Membership.mem","Nat","Nat.decLe","Nat.instLinearOrder","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","Set","Set.Pairwise","Set.Subsingleton","Set.instInter","Set.instMembership","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.CliqueFree","SimpleGraph.IsNClique","SimpleGraph.cliqueFinset","SimpleGraph.edgeFinset","SimpleGraph.edgeFinset_mono","SimpleGraph.edgeSet","SimpleGraph.fintypeEdgeSet","SimpleGraph.instLE","SimpleGraph.is3Clique_iff","SimpleGraph.is3Clique_triple_iff","SimpleGraph.mem_cliqueFinset_iff","Singleton.singleton","Subtype","Subtype.casesOn","Subtype.mk","Subtype.property","Subtype.val","Subtype.val_injective","Sym2","Sym2.eq_iff","Sym2.instDecidableEq","Sym2.instFintype","Sym2.mk","True","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_5","binderNameHint","congr","congrArg","eq_self","forall_congr","id","implies_congr","instDecidableAnd","instDecidableNot","instHSub","instLENat","instOfNatNat","instSubNat","not_le._simp_1","of_eq_true","or_true","propext","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","Sym2"],"value_dag_size":60,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.instMembership","SimpleGraph","SimpleGraph.edgeFinset","SimpleGraph.edgeSet","SimpleGraph.mem_edgeFinset","Sym2","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.farFromTriangleFree_of_disjoint_triangles_aux","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","Sym2","Sym2.mk"],"value_dag_size":44,"value_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.mem_edgeSet","Sym2","Sym2.mk","propext"]}
+{"definition_height":22,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":"regular","statement_dag_size":26,"type_refs":["DecidableRel","Finset","Real","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":97,"value_refs":["DecidableRel","Finset","Finset.card","Finset.filter","HMul.hMul","HSub.hSub","LT.lt","Nat.cast","Rat.cast","Real","Real.decidableLT","Real.instLT","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","instHMul","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices.congr_simp","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","reducibility":null,"statement_dag_size":84,"type_refs":["DecidableRel","Eq","Finset","Real","SimpleGraph","SimpleGraph.Adj","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices"],"value_dag_size":259,"value_refs":["Decidable","DecidableRel","Eq","Eq.ndrec","Eq.rec","Eq.refl","Finset","Pi.instSubsingleton","Real","SimpleGraph","SimpleGraph.Adj","Subsingleton.elim","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","instSubsingletonDecidable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableRel","Eq","Finset","Finset.card","Finset.filter","HMul.hMul","HSub.hSub","LT.lt","Nat.cast","Rat.cast","Real","Real.decidableLT","Real.instLT","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","instHMul","instHSub"],"value_dag_size":37,"value_refs":["DecidableRel","Eq.refl","Finset","Real","SimpleGraph","SimpleGraph.Adj","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_badVertices_le","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":117,"type_refs":["DecidableRel","Finset","Finset.card","HMul.hMul","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Rat.cast","Real","Real.instField","Real.instLE","Real.instMul","Real.instNatCast","Real.instRatCast","Real.linearOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1344,"value_refs":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","And","And.right","CommRing.toRing","CommSemiring.toSemiring","Decidable.byContradiction","DecidableRel","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivisionRing.toRing","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toDivisionRing","Field.toSemifield","Finset","Finset.Subset.rfl","Finset.card","Finset.filter","Finset.filter_subset","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toCharZero","LE.le","LE.le.trans","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nat.cast_one","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.one_le_ofNat._simp_1","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Rat","Rat.cast","Rat.cast_le_natCast._simp_1","Rat.instDivisionRing","Rat.instLE","Rat.instNatCast","Rat.instOfNat","Real","Real.commRing","Real.decidableLE","Real.decidableLT","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.lattice","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.IsUniform.pos","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_le_one","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.edgeDensity_badVertices_le","abs","abs_sub_lt_iff","cast","congrArg","id","inferInstance","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_mul_of_one_le_left","mul_le_of_le_one_right","not_le._simp_1","of_eq_true","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":99,"type_refs":["DecidableRel","Finset","Finset.card","HMul.hMul","HSub.hSub","LE.le","Nat.cast","Prod","Rat.cast","Real","Real.instLE","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","Rel.interedges","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","instHMul","instHSub"],"value_dag_size":680,"value_refs":["AddCommMonoidWithOne.toAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","And","And.right","Classical.propDecidable","CommMagma.toMul","CommRing.toNonUnitalCommRing","DecidableRel","Eq","Eq.mpr","Eq.refl","Finset","Finset.biUnion","Finset.card","Finset.card_biUnion_le","Finset.card_le_card","Finset.card_map","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.instUsesSetNotationForOrder","Finset.map","Finset.mem_filter","Finset.sum","Finset.sum_congr","Finset.sum_le_card_nsmul","Function.Embedding.mk","HMul.hMul","HSMul.hSMul","HSub.hSub","Iff.mp","Iff.mpr","IsOrderedAddMonoid.toAddLeftMono","IsStrictOrderedRing.toCharZero","LE.le","LE.le.trans","LT.lt","LT.lt.le","Membership.mem","NSMul.toSMul","Nat","Nat.cast","Nat.cast_le","Nat.cast_sum","Nat.instAddCommMonoid","Nat.instPreorder","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocCommSemiring.toCommMagma","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.nat_isScalarTower","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.mk","Prod.mk_right_injective","Rat.cast","Real","Real.commRing","Real.decidableLT","Real.instAddCommMonoid","Real.instIsOrderedAddMonoid","Real.instIsStrictOrderedRing","Real.instLT","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZeroLEOneClass","Real.partialOrder","Real.semiring","Rel.interedges","Rel.interedges_eq_biUnion","Ring.toAddGroupWithOne","Ring.toSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le._simp_1_2","congrArg","congrFun'","id","instDecidableEqProd","instHMul","instHSMul","instHSub","instLENat","mul_comm","smul_mul_assoc","subset_of_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le","reducibility":null,"statement_dag_size":68,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","HMul.hMul","HSMul.hSMul","NSMul.toSMul","Nat","Nat.cast","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instHSMul"],"value_dag_size":74,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toNSMul","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq.symm","HMul.hMul","HSMul.hSMul","NSMul.toSMul","Nat","Nat.cast","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instHSMul","nsmul_eq_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.edgeDensity_badVertices_le","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":122,"type_refs":["DecidableRel","Finset","HMul.hMul","HSub.hSub","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Rat.cast","Real","Real.instLE","Real.instMul","Real.instNatCast","Real.instRatCast","Real.instSub","Real.instZero","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","instHMul","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":1273,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","DecidableRel","Distrib.toAdd","Distrib.toMul","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Field.toSemifield","Finset","Finset.card","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toCharZero","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_nonpos","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg'","Nat.cast_zero","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Rat","Rat.cast","Rat.cast_div","Rat.cast_mul","Rat.cast_natCast","Rat.instDiv","Rat.instMul","Rat.instNatCast","Real","Real.commRing","Real.instAddCommMonoid","Real.instAddCommSemigroup","Real.instAddGroup","Real.instAddMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_def","SimpleGraph.interedges","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.card_interedges_badVertices_le","congr","congrArg","congrFun'","covariant_swap_add_of_covariant_add","div_le_of_le_mul₀","id","inferInstance","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","mul_comm","mul_nonneg","rfl","sub_nonneg_of_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":304,"type_refs":["DecidableEq","DecidableRel","Finset","Finset.card","Finset.filter","Finset.image","Finset.instSDiff","Finset.instSProd","Finset.instSetLike","Finset.instUnion","HMul.hMul","HPow.hPow","LE.le","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Prod","Prod.fst","Prod.mk","Prod.snd","Rat.cast","Real","Real.instField","Real.instLE","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instRatCast","Real.linearOrder","SDiff.sdiff","SProd.sprod","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.edgeDensity","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card.match_1","instDecidableEqProd","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":3802,"value_refs":["AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","And","And.casesOn","And.right","CommMagma","CommMagma.toMul","CommRing.toNonUnitalCommRing","CommRing.toRing","CommSemiring.toSemiring","DecidableEq","DecidableRel","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionRing.toDivInvMonoid","DivisionRing.toDivisionSemiring","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Eq.trans_le","False","Field.toDivisionRing","Field.toSemifield","Finset","Finset.card","Finset.card_image_of_injective","Finset.filter","Finset.filter_subset","Finset.image","Finset.instSDiff","Finset.instSProd","Finset.instSetLike","Finset.instUnion","GroupWithZero.toMonoidWithZero","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub","HSub.hSub","Int","Int.negOfNat","Int.ofNat","Int.rawCast","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toCharZero","IsStrictOrderedRing.toMulPosStrictMono","LE.le","LT.lt","LT.lt.le","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Tactic.Linarith.add_lt_of_le_of_neg","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_nonneg","Nat.cast_nonneg'","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.fst","Prod.mk","Prod.mk_right_injective","Prod.snd","Rat","Rat.cast","Rat.cast_div","Rat.cast_mul","Rat.cast_natCast","Rat.instDiv","Rat.instMul","Rat.instNatCast","Real","Real.commRing","Real.decidableLT","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivisionRing","Real.instField","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","SDiff.sdiff","SProd.sprod","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsUniform","SimpleGraph.IsUniform.pos","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_def","SimpleGraph.interedges","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Union.union","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card.match_1","abs","abs_sub_lt_iff","and_or_left","congr","congrArg","congrFun'","false_or","id","inferInstance","instDecidableEqProd","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","le_of_not_gt","le_trans","mul_comm","mul_le_mul","mul_le_mul_of_nonneg_left","mul_le_of_le_div₀","mul_nonneg","or_and_left","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":null,"statement_dag_size":13,"type_refs":["And","Eq","False","Not"],"value_dag_size":13,"value_refs":["And","Not","and_not_self","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Prod","Prod.mk"],"value_dag_size":39,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting","reducibility":null,"statement_dag_size":68,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":74,"value_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_triple_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":240,"type_refs":["And","DecidableEq","DecidableRel","Finset","Finset.biUnion","Finset.filter","Finset.image","Finset.instPartialOrder","Finset.instSDiff","Finset.instSProd","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.mk","Prod.snd","Real","SDiff.sdiff","SProd.sprod","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper.match_1","instDecidableAnd","instDecidableEqProd"],"value_dag_size":2282,"value_refs":["And","And.intro","DecidableEq","DecidableRel","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.trans","Exists","Finset","Finset.biUnion","Finset.filter","Finset.filter_congr","Finset.image","Finset.instSDiff","Finset.instSProd","Finset.instSetLike","Finset.instUnion","Iff.of_eq","Membership.mem","Not","Or","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","Real","SDiff.sdiff","SProd.sprod","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.badVertices","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_11","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_12","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_9","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper.match_1","congr","congrArg","congrFun'","forall_congr","funext","id","implies_congr","instDecidableAnd","instDecidableEqProd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":83,"type_refs":["And","DecidableRel","Eq","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges"],"value_dag_size":89,"value_refs":["And","DecidableRel","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.interedges","SimpleGraph.mem_interedges_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Prod","Prod.mk"],"value_dag_size":68,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph","reducibility":null,"statement_dag_size":186,"type_refs":["DecidableEq","Disjoint","Eq","Finset","Finset.instInsert","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Prod","Prod.mk","SetLike.instMembership","Singleton.singleton"],"value_dag_size":621,"value_refs":["And","DecidableEq","Disjoint","Eq","Eq.mp","Eq.trans","Finset","Finset.instInsert","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Insert.insert","LE.le","Membership.mem","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_6","congr","congrArg","forall_congr","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":216,"type_refs":["And","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Or","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":1350,"value_refs":["And","Classical.byContradiction","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","SetLike.instMembership","True","True.intro","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["And","Eq","Finset","Finset.Subset.antisymm_iff","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triple_eq_triple_of_mem","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._proof_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._sparseCasesOn_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._sparseCasesOn_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound.match_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound.match_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound","reducibility":"abbrev","statement_dag_size":207,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","OfNat.ofNat","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":486,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.Mathlib.Meta.Positivity.evalTriangleRemovalBound._sparseCasesOn_6","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph","reducibility":null,"statement_dag_size":58,"type_refs":["HDiv.hDiv","HMul.hMul","LE.le","LT.lt","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":519,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommMonoidWithOne.toAddMonoidWithOne","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Distrib.toAdd","Distrib.toMul","Eq","Eq.mp","Eq.mpr","Eq.symm","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff.mpr","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","LE.le","LT.lt","LT.lt.trans_le","Nat","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddSemigroup","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instIsOrderedAddMonoid","Nat.instLinearOrder","Nat.instMod","Nat.instMulOneClass","Nat.instNeZeroSucc","Nat.instNonAssocSemiring","Nat.instPartialOrder","Nat.instPreorder","Nat.instSemigroup","Nat.mod_add_div","Nat.mod_lt","Nat.mul_le_mul_left","Nat.one_le_div_iff","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Semigroup.toMul","addRightReflectLE_of_addLeftReflectLE","add_assoc","add_comm","add_lt_add_iff_right","add_right_comm","congrArg","congrFun'","contravariant_lt_of_covariant_le","contravariant_swap_add_of_contravariant_add","covariant_swap_add_of_covariant_add","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instIsRightCancelAddOfAddRightReflectLE","instLENat","instLTNat","instMulNat","instOfNatAtLeastTwo","instOfNatNat","mul_assoc","mul_one","propext","two_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.card_bound","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph","reducibility":null,"statement_dag_size":222,"type_refs":["DecidableEq","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","HDiv.hDiv","HMul.hMul","LE.le","Membership.mem","Nat","Nat.cast","Nat.ceil","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instFloorRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instRing","Real.linearOrder","Real.partialOrder","Real.semiring","SetLike.instMembership","SzemerediRegularity.bound","instHDiv","instHMul","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":877,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddZero.toZero","AddZeroClass.toAddZero","Bool","CharP.cast_eq_zero","CharP.ofCharZero","CommGroupWithZero.toGroupWithZero","DecidableEq","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq","Eq.refl","Eq.symm","Eq.trans","Exists.intro","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.IsEquipartition.average_le_card_part","Finpartition.card_parts_le_card","Finpartition.parts","Finset","Finset.Nonempty.card_pos","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","Fintype.card_eq_zero","Fintype.card_pos","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","Iff.mpr","IsEmpty","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toPosMulMono","IsStrictOrderedRing.toMulPosStrictMono","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","LT.lt.le","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.Positivity.pos_of_isNat","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulPosReflectLE.toMulPosReflectLT","MulPosStrictMono.toMulPosReflectLE","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.ble","Nat.cast","Nat.cast_le._simp_1","Nat.cast_mul._simp_1","Nat.cast_nonneg._simp_1","Nat.cast_pos'","Nat.ceil","Nat.instAtLeastTwoHAddOfNat","Nat.instDiv","Nat.instNeZeroSucc","Nat.instPreorder","Nat.mono_cast","NeZero.charZero_one","NonAssocSemiring.toAddCommMonoidWithOne","Nonempty","OfNat.ofNat","Or","Or.casesOn","Or.inl","Or.inr","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Real","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instPreorder","Real.instRing","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","SzemerediRegularity.bound","Trans.trans","True","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.aux","cast","congrArg","congrFun'","div_le_div₀","div_le_iff₀'","instHDiv","instHMul","instLENat","instLTNat","instMulNat","instMulZeroClassOfSemiring","instOfNatAtLeastTwo","instOfNatNat","instTransLE","isEmpty_or_nonempty","le_of_lt","le_refl","mul_le_mul_of_nonneg_left","mul_pos","of_eq_true","zero_div"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.regularityReduced_edges_card_aux.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.regularityReduced_edges_card_aux","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Finset","Prod","Prod.mk"],"value_dag_size":45,"value_refs":["Finset","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.regularityReduced_edges_card_aux.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.regularityReduced_edges_card_aux","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Prod","Prod.mk"],"value_dag_size":39,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Removal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.triangle_removal_aux","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph","reducibility":null,"statement_dag_size":290,"type_refs":["DecidableEq","DecidableRel","DivInvMonoid.toDiv","Finpartition","Finpartition.IsEquipartition","Finpartition.parts","Finset","Finset.card","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","LT.lt","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.ceil","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","Real","Real.instDivInvMonoid","Real.instField","Real.instFloorRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instRing","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.cliqueFinset","SimpleGraph.regularityReduced","SimpleGraph.regularityReduced.instDecidableRel_adj","SimpleGraph.triangleRemovalBound","SzemerediRegularity.bound","Zero.toOfNat0","instHDiv","instHMul","instHPow","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":10298,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Bool","Bool.false","CommGroupWithZero.toDivisionCommMonoid","CommRing.toRing","CommSemiring.toSemiring","DecidableEq","DecidableRel","Disjoint","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toDivInvMonoid","DivisionRing.toRatCast","DivisionRing.toRing","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Eq.casesOn","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Finpartition","Finpartition.IsEquipartition","Finpartition.disjoint","Finpartition.parts","Finset","Finset.card","Finset.instInsert","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.not_disjoint_iff","Finset.univ","Fintype","Fintype.card","FloorRing.toFloorSemiring","FloorSemiring.instCharZero","Function.onFun","GroupWithZero.toDivisionMonoid","HAdd.hAdd","HDiv.hDiv","HEq","HEq.refl","HMul.hMul","HPow.hPow","HSub.hSub","Iff.mpr","Insert.insert","Int","Int.mul","Int.negOfNat","Int.ofNat","Int.rawCast","Inv.inv","InvOneClass.toInv","IsOrderedAddMonoid.toAddLeftMono","IsOrderedRing.toMulPosMono","IsOrderedRing.toPosMulMono","IsOrderedRing.toZeroLEOneClass","IsStrictOrderedRing.toPosMulStrictMono","IsStrictOrderedRing.toZeroLEOneClass","LE.le","LE.le.trans","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toPartialOrder","Mathlib.Meta.NormNum.IsInt.of_raw","Mathlib.Meta.NormNum.IsInt.to_isNat","Mathlib.Meta.NormNum.IsInt.to_raw_eq","Mathlib.Meta.NormNum.IsNNRat.den_nz","Mathlib.Meta.NormNum.IsNNRat.of_raw","Mathlib.Meta.NormNum.IsNNRat.to_isNat","Mathlib.Meta.NormNum.IsNNRat.to_isRat","Mathlib.Meta.NormNum.IsNNRat.to_raw_eq","Mathlib.Meta.NormNum.IsNat.mk","Mathlib.Meta.NormNum.IsNat.of_raw","Mathlib.Meta.NormNum.IsNat.raw_refl","Mathlib.Meta.NormNum.IsNat.to_isInt","Mathlib.Meta.NormNum.IsNat.to_isNNRat","Mathlib.Meta.NormNum.IsNat.to_raw_eq","Mathlib.Meta.NormNum.IsNatPowT.bit1","Mathlib.Meta.NormNum.IsNatPowT.run","Mathlib.Meta.NormNum.IsRat.den_nz","Mathlib.Meta.NormNum.IsRat.of_raw","Mathlib.Meta.NormNum.IsRat.to_raw_eq","Mathlib.Meta.NormNum.instAddMonoidWithOne'","Mathlib.Meta.NormNum.instAtLeastTwo","Mathlib.Meta.NormNum.isInt_add","Mathlib.Meta.NormNum.isInt_mul","Mathlib.Meta.NormNum.isInt_neg","Mathlib.Meta.NormNum.isNNRat_div","Mathlib.Meta.NormNum.isNNRat_inv_pos","Mathlib.Meta.NormNum.isNNRat_mul","Mathlib.Meta.NormNum.isNNRat_pow","Mathlib.Meta.NormNum.isNat_add","Mathlib.Meta.NormNum.isNat_eq_true","Mathlib.Meta.NormNum.isNat_lt_true","Mathlib.Meta.NormNum.isNat_mul","Mathlib.Meta.NormNum.isNat_ofNat","Mathlib.Meta.NormNum.isRat_mul","Mathlib.Meta.NormNum.isRat_neg","Mathlib.Meta.NormNum.one_natPow","Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos","Mathlib.Meta.Positivity.pos_of_isNat","Mathlib.Tactic.CancelDenoms.div_subst","Mathlib.Tactic.CancelDenoms.mul_subst","Mathlib.Tactic.CancelDenoms.sub_subst","Mathlib.Tactic.Linarith.add_lt_of_neg_of_le","Mathlib.Tactic.Linarith.add_neg","Mathlib.Tactic.Linarith.lt_irrefl","Mathlib.Tactic.Linarith.mul_neg","Mathlib.Tactic.Linarith.mul_nonpos","Mathlib.Tactic.Linarith.sub_neg_of_lt","Mathlib.Tactic.Linarith.sub_nonpos_of_le","Mathlib.Tactic.Linarith.zero_lt_one","Mathlib.Tactic.Ring.Common.add_congr","Mathlib.Tactic.Ring.Common.add_mul","Mathlib.Tactic.Ring.Common.add_overlap_pf_zero","Mathlib.Tactic.Ring.Common.add_pf_add_gt","Mathlib.Tactic.Ring.Common.add_pf_add_lt","Mathlib.Tactic.Ring.Common.add_pf_add_overlap","Mathlib.Tactic.Ring.Common.add_pf_add_overlap_zero","Mathlib.Tactic.Ring.Common.add_pf_add_zero","Mathlib.Tactic.Ring.Common.add_pf_zero_add","Mathlib.Tactic.Ring.Common.atom_pf","Mathlib.Tactic.Ring.Common.div_congr","Mathlib.Tactic.Ring.Common.div_pf","Mathlib.Tactic.Ring.Common.inv_mul","Mathlib.Tactic.Ring.Common.inv_single","Mathlib.Tactic.Ring.Common.mul_add","Mathlib.Tactic.Ring.Common.mul_congr","Mathlib.Tactic.Ring.Common.mul_pf_left","Mathlib.Tactic.Ring.Common.mul_pf_right","Mathlib.Tactic.Ring.Common.mul_pow_mul","Mathlib.Tactic.Ring.Common.mul_pp_pf_overlap","Mathlib.Tactic.Ring.Common.mul_zero","Mathlib.Tactic.Ring.Common.neg_add","Mathlib.Tactic.Ring.Common.neg_congr","Mathlib.Tactic.Ring.Common.neg_mul","Mathlib.Tactic.Ring.Common.neg_zero","Mathlib.Tactic.Ring.Common.one_pow","Mathlib.Tactic.Ring.Common.pow_add","Mathlib.Tactic.Ring.Common.pow_congr","Mathlib.Tactic.Ring.Common.pow_zero","Mathlib.Tactic.Ring.Common.single_pow","Mathlib.Tactic.Ring.Common.sub_congr","Mathlib.Tactic.Ring.Common.sub_pf","Mathlib.Tactic.Ring.Common.zero_mul","Mathlib.Tactic.Ring.cast_pos","Mathlib.Tactic.Ring.cast_zero","Mathlib.Tactic.Ring.of_eq","Membership.mem","Monoid.toNPow","Mul","MulZeroClass.toMul","MulZeroClass.toZero","NNRat.rawCast","NPow.toPow","Nat","Nat.ble","Nat.cast","Nat.cast_nonneg'","Nat.cast_one","Nat.cast_pos'","Nat.cast_zero","Nat.ceil","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCommSemiring","Nat.instNeZeroSucc","Nat.mul","Nat.rawCast","Ne","NeZero.charZero_one","Neg.neg","NegZeroClass.toNeg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLE","Preorder.toLT","Rat","Rat.cast","Rat.cast_le_natCast._simp_1","Rat.instDivisionRing","Rat.instLE","Rat.instNatCast","Rat.instOfNat","Rat.rawCast","Real","Real.commRing","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instAddMonoid","Real.instCommSemiring","Real.instDivInvMonoid","Real.instDivisionRing","Real.instField","Real.instFloorRing","Real.instIsOrderedAddMonoid","Real.instIsOrderedRing","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instNontrivial","Real.instOne","Real.instPreorder","Real.instRatCast","Real.instRing","Real.instSub","Real.instZero","Real.instZeroLEOneClass","Real.linearOrder","Real.partialOrder","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toAddGroupWithOne","Ring.toSemiring","Semifield.toCommGroupWithZero","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Semiring","Semiring.toMonoid","Semiring.toMonoidWithZero","Semiring.toNonAssocSemiring","Set.PairwiseDisjoint.elim","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.IsUniform","SimpleGraph.cliqueFinset","SimpleGraph.edgeDensity","SimpleGraph.edgeDensity_le_one","SimpleGraph.is3Clique_iff","SimpleGraph.mem_cliqueFinset_iff","SimpleGraph.regularityReduced","SimpleGraph.regularityReduced.instDecidableRel_adj","SimpleGraph.triangleRemovalBound","SimpleGraph.triangleRemovalBound_le","SimpleGraph.triangle_counting","Singleton.singleton","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","SzemerediRegularity.bound","SzemerediRegularity.bound_pos","Trans.trans","Zero.toOfNat0","_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Removal.0.SimpleGraph.card_bound","cast","congrArg","div_pos","id","inferInstance","instAddNat","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulZeroClassOfSemiring","instNeZeroNatHAdd_1","instOfNatAtLeastTwo","instOfNatNat","instTransEq_1","instTransLE","le_of_lt","le_of_not_gt","mul_le_mul","mul_le_mul_of_nonneg_left","mul_le_mul_of_nonneg_right","mul_nonneg","mul_pos","neg_neg_of_pos","pow_nonneg","pow_pos","propext","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"],"value_dag_size":179,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₀₀.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₀₀","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Finset","Prod","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum3.in₀"],"value_dag_size":689,"value_refs":["Eq","Eq.ndrec","Eq.refl","False","False.elim","Finset","Finset.instSetLike","HEq","HEq.refl","Membership.mem","Prod","Prod.mk","SetLike.instMembership","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.Rel","SimpleGraph.TripartiteFromTriangles.Rel.casesOn","SimpleGraph.TripartiteFromTriangles.Rel.in₀₁","SimpleGraph.TripartiteFromTriangles.Rel.in₀₂","SimpleGraph.TripartiteFromTriangles.Rel.in₁₀","SimpleGraph.TripartiteFromTriangles.Rel.in₁₂","SimpleGraph.TripartiteFromTriangles.Rel.in₂₀","SimpleGraph.TripartiteFromTriangles.Rel.in₂₁","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum3.in₀","Sum3.in₁","Sum3.in₂","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₁₁.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₁₁","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Finset","Prod","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum3.in₁"],"value_dag_size":869,"value_refs":["Eq","Eq.ndrec","Eq.refl","False","False.elim","Finset","Finset.instSetLike","HEq","HEq.refl","Membership.mem","Prod","Prod.mk","SetLike.instMembership","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.Rel","SimpleGraph.TripartiteFromTriangles.Rel.casesOn","SimpleGraph.TripartiteFromTriangles.Rel.in₀₁","SimpleGraph.TripartiteFromTriangles.Rel.in₀₂","SimpleGraph.TripartiteFromTriangles.Rel.in₁₀","SimpleGraph.TripartiteFromTriangles.Rel.in₁₂","SimpleGraph.TripartiteFromTriangles.Rel.in₂₀","SimpleGraph.TripartiteFromTriangles.Rel.in₂₁","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum.ctorIdx","Sum.inl","Sum.inl.noConfusion","Sum.inr","Sum.inr.noConfusion","Sum3.in₀","Sum3.in₁","Sum3.in₂","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₂₂.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.Graph.not_in₂₂","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Finset","Prod","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum3.in₂"],"value_dag_size":868,"value_refs":["Eq","Eq.ndrec","Eq.refl","False","False.elim","Finset","Finset.instSetLike","HEq","HEq.refl","Membership.mem","Prod","Prod.mk","SetLike.instMembership","SimpleGraph.Adj","SimpleGraph.TripartiteFromTriangles.Rel","SimpleGraph.TripartiteFromTriangles.Rel.casesOn","SimpleGraph.TripartiteFromTriangles.Rel.in₀₁","SimpleGraph.TripartiteFromTriangles.Rel.in₀₂","SimpleGraph.TripartiteFromTriangles.Rel.in₁₀","SimpleGraph.TripartiteFromTriangles.Rel.in₁₂","SimpleGraph.TripartiteFromTriangles.Rel.in₂₀","SimpleGraph.TripartiteFromTriangles.Rel.in₂₁","SimpleGraph.TripartiteFromTriangles.graph","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.inr.noConfusion","Sum3.in₀","Sum3.in₁","Sum3.in₂","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.graph_triple._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.graph_triple","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.graph_triple._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.graph_triple","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","Sum","Sum.inl","Sum.inr"],"value_dag_size":41,"value_refs":["And","Sum","Sum.forall","Sum.inl","Sum.inr","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.rel_irrefl.match_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.rel_irrefl","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Finset","Prod","SimpleGraph.TripartiteFromTriangles.Rel","Sum"],"value_dag_size":706,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","Finset","Finset.instSetLike","HEq","HEq.refl","Membership.mem","Prod","Prod.mk","SetLike.instMembership","SimpleGraph.TripartiteFromTriangles.Rel","SimpleGraph.TripartiteFromTriangles.Rel.casesOn","SimpleGraph.TripartiteFromTriangles.Rel.in₀₁","SimpleGraph.TripartiteFromTriangles.Rel.in₀₂","SimpleGraph.TripartiteFromTriangles.Rel.in₁₀","SimpleGraph.TripartiteFromTriangles.Rel.in₁₂","SimpleGraph.TripartiteFromTriangles.Rel.in₂₀","SimpleGraph.TripartiteFromTriangles.Rel.in₂₁","Sum","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.inr.noConfusion","Sum3.in₀","Sum3.in₁","Sum3.in₂","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Sum","Sum.inl"],"value_dag_size":35,"value_refs":["Eq","Sum","Sum.inl","Sum.inl.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Sum","Sum.inr"],"value_dag_size":35,"value_refs":["Eq","Sum","Sum.inr","Sum.inr.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["And","Eq","Finset","Finset.Subset.antisymm_iff","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle._simp_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite","name":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle_is3Clique._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite.0.SimpleGraph.TripartiteFromTriangles.toTriangle_is3Clique","reducibility":null,"statement_dag_size":68,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","Singleton.singleton","instOfNatNat"],"value_dag_size":74,"value_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsNClique","SimpleGraph.is3Clique_triple_iff","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching","reducibility":null,"statement_dag_size":95,"type_refs":["And","Compl.compl","Exists","Finite","LE.le","Not","Set","Set.Elem","Set.instCompl","Set.instLE","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.IsClique","SimpleGraph.IsTutteViolator","SimpleGraph.Subgraph","SimpleGraph.Subgraph.IsMatching","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.verts","SimpleGraph.deleteUniversalVerts","SimpleGraph.universalVerts"],"value_dag_size":3417,"value_refs":["And","And.casesOn","And.intro","And.left","And.right","ChainCompletePartialOrder.instOfCompleteLattice","ChainCompletePartialOrder.toPartialOrder","Classical.choose","Classical.choose_spec","Classical.propDecidable","Compl.compl","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Disjoint","Disjoint.symm","Eq","Eq.mp","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Even","Exists","Exists.casesOn","Exists.intro","False","Finite","Finite.Set.finite_diff","Finite.Set.finite_image","HeytingAlgebra.toOrderBot","Iff.mpr","Iff.of_eq","LE.le","LinearOrder.toPartialOrder","Max.max","Membership.mem","Nat","Nat.instLinearOrder","Ne","Not","Or","Or.inr","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","Quot","Quot.out","SDiff.sdiff","Set","Set.Elem","Set.compl_eq_univ_sdiff","Set.compl_subset_comm","Set.disjoint_iUnion_right","Set.disjoint_image_of_injective","Set.disjoint_of_subset","Set.disjoint_sdiff_right","Set.iUnion","Set.image","Set.instCompl","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.instSDiff","Set.instUnion","Set.mem_image._simp_1","Set.mem_sdiff._simp_1","Set.mem_union._simp_1","Set.mem_union_left","Set.mem_univ._simp_1","Set.ncard","Set.ncard_image_of_injective","Set.sdiff_subset","Set.toFinite","Set.univ","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.Represents","SimpleGraph.ConnectedComponent.Represents.image_out","SimpleGraph.ConnectedComponent.Represents.ncard_eq","SimpleGraph.ConnectedComponent.eq._simp_1","SimpleGraph.ConnectedComponent.mem_supp_iff._simp_1","SimpleGraph.ConnectedComponent.supp","SimpleGraph.IsClique","SimpleGraph.IsClique.even_iff_exists_isMatching","SimpleGraph.IsClique.of_induce","SimpleGraph.IsClique.subset","SimpleGraph.IsTutteViolator","SimpleGraph.Reachable","SimpleGraph.Reachable.rfl._simp_1","SimpleGraph.Subgraph","SimpleGraph.Subgraph.IsMatching","SimpleGraph.Subgraph.IsMatching.exists_of_universalVerts","SimpleGraph.Subgraph.IsMatching.iSup","SimpleGraph.Subgraph.IsMatching.sup","SimpleGraph.Subgraph.IsMatching.support_eq_verts","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.deleteVerts","SimpleGraph.Subgraph.instMax","SimpleGraph.Subgraph.instSupSet","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.support","SimpleGraph.Subgraph.verts","SimpleGraph.Subgraph.verts_iSup","SimpleGraph.connectedComponentMk","SimpleGraph.deleteUniversalVerts","SimpleGraph.deleteUniversalVerts_verts","SimpleGraph.disjoint_image_val_universalVerts","SimpleGraph.even_ncard_image_val_supp_sdiff_image_val_rep_union","SimpleGraph.oddComponents","SimpleGraph.pairwise_disjoint_supp_connectedComponent","SimpleGraph.universalVerts","Subtype","Subtype.exists._simp_1","Subtype.finite","Subtype.mk","Subtype.val","Subtype.val_injective","Top.top","True","Union.union","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts._simp_1_3","and_true","congr","congrArg","congrFun'","dite","eq_false","exists_and_right._simp_1","exists_eq_right._simp_1","exists_false._simp_1","exists_prop._simp_1","exists_prop_congr","funext","iSup","id","instAddNat","instLENat","not_exists._simp_1","not_false_eq_true","not_or._simp_1","of_eq_true","or_self","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsMatching.exists_verts_compl_subset_universalVerts","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_supp._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_supp","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Finset.card","Fintype","Nat","Set","Set.Elem","Set.ncard","Set.toFinset"],"value_dag_size":34,"value_refs":["Eq.symm","Finset.card","Fintype","Nat","Set","Set.Elem","Set.ncard","Set.ncard_eq_toFinset_card'","Set.toFinset"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_supp._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_supp","reducibility":null,"statement_dag_size":43,"type_refs":["Compl.compl","Disjoint","Eq","GeneralizedHeytingAlgebra.toLattice","HeytingAlgebra","HeytingAlgebra.toCompl","HeytingAlgebra.toGeneralizedHeytingAlgebra","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","True"],"value_dag_size":44,"value_refs":["Compl.compl","Disjoint","GeneralizedHeytingAlgebra.toLattice","HeytingAlgebra","HeytingAlgebra.toCompl","HeytingAlgebra.toGeneralizedHeytingAlgebra","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","disjoint_compl_right","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator","reducibility":null,"statement_dag_size":262,"type_refs":["Eq","Membership.mem","Ne","Not","SDiff.sdiff","Set","Set.Elem","Set.instMembership","Set.instSDiff","Set.ofPred","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.IsUniversal","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.verts","SimpleGraph.deleteUniversalVerts","Subtype","Subtype.val","Top.top"],"value_dag_size":1305,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","HEq.trans","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_not","Membership.mem","Ne","Not","SDiff.sdiff","Set","Set.Elem","Set.instMembership","Set.instSDiff","Set.ofPred","SetLike.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.IsUniversal","SimpleGraph.Subgraph","SimpleGraph.Subgraph.coe","SimpleGraph.Subgraph.induce","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.verts","SimpleGraph.deleteUniversalVerts","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.val","Top.top","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap"],"value_dag_size":45,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.comap","SimpleGraph.comap_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Subtype","Subtype.val","True"],"value_dag_size":43,"value_refs":["Membership.mem","Set","Set.instMembership","Subtype","Subtype.coe_prop","Subtype.val","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.exists_isTutteViolator","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","Top.top"],"value_dag_size":40,"value_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.instTop","SimpleGraph.Subgraph.top_adj","Top.top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph","reducibility":null,"statement_dag_size":252,"type_refs":["And","Exists","LE.le","Max.max","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsAlternating","SimpleGraph.IsCycles","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.toSubgraph","SimpleGraph.edge","SimpleGraph.instLE","SimpleGraph.instMax"],"value_dag_size":1179,"value_refs":["And","And.intro","And.left","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists.intro","False","False.elim","Iff.mp","Iff.mpr","LE.le","Lattice.toSemilatticeSup","List","List.instMembership","Max.max","Membership.mem","Ne","Ne.symm","Not","Or","Or.inl","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.IsAlternating","SimpleGraph.IsAlternating.spanningCoe","SimpleGraph.IsAlternating.sup_edge","SimpleGraph.IsCycles","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.edgeSet","SimpleGraph.Subgraph.mem_edgeSet","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Walk","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.IsPath.isCycles_spanningCoe_toSubgraph_sup_edge","SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj","SimpleGraph.Walk.edges","SimpleGraph.Walk.mem_edges_toSubgraph","SimpleGraph.Walk.snd","SimpleGraph.Walk.toSubgraph","SimpleGraph.adj_congr_of_sym2","SimpleGraph.adj_edge","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.sup_adj._simp_1","Sym2","Sym2.mk","True","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles._simp_1_2","and_false","and_true","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","false_or","id","implies_congr_ctx","implies_true","not_and._simp_1","not_false_eq_true","not_true_eq_false","of_eq_true","propext","sup_le_iff","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph","reducibility":null,"statement_dag_size":137,"type_refs":["Exists","Finite","Max.max","Ne","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Subgraph","SimpleGraph.Subgraph.IsPerfectMatching","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":10533,"value_refs":["And","And.casesOn","And.intro","And.left","And.right","Classical.not_not._simp_2","Classical.propDecidable","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toCoframe","CompleteDistribLattice.toFrame","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","Disjoint","Disjoint.left_le_of_le_sup_right","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","ExistsUnique","False","False.elim","Finite","Finset","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert._simp_1","Finset.mem_singleton._simp_1","Fintype.ofFinite","GeneralizedCoheytingAlgebra.toLattice","GeneralizedCoheytingAlgebra.toSDiff","HeytingAlgebra.toOrderBot","Iff.mp","Iff.mpr","Insert.insert","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","List","List.instDecidableMemOfLawfulBEq","List.instMembership","Max.max","Membership.mem","Ne","Ne.symm","Not","Or","Or.casesOn","Or.resolve_left","Order.Coframe.toCoheytingAlgebra","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Set","Set.Elem","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff._simp_1","Set.mem_singleton_iff._simp_1","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.Adj.reachable","SimpleGraph.Adj.symm","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","SimpleGraph.ConnectedComponent.eq._simp_1","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.mem_supp_congr_adj","SimpleGraph.ConnectedComponent.mem_supp_iff._simp_1","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.IsAlternating","SimpleGraph.IsAlternating.mono","SimpleGraph.IsCycles","SimpleGraph.IsCycles.exists_cycle_toSubgraph_verts_eq_connectedComponentSupp","SimpleGraph.IsCycles.toSimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Reachable","SimpleGraph.Subgraph","SimpleGraph.Subgraph.Adj","SimpleGraph.Subgraph.Adj.adj_sub","SimpleGraph.Subgraph.Adj.symm","SimpleGraph.Subgraph.IsMatching","SimpleGraph.Subgraph.IsMatching.not_adj_left_of_ne","SimpleGraph.Subgraph.IsPerfectMatching","SimpleGraph.Subgraph.IsPerfectMatching.isAlternating_symmDiff_right","SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_isCycles","SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating","SimpleGraph.Subgraph.IsPerfectMatching.toSubgraph_iff","SimpleGraph.Subgraph.IsSpanning","SimpleGraph.Subgraph.adj_comm","SimpleGraph.Subgraph.spanningCoe","SimpleGraph.Subgraph.spanningCoe_adj","SimpleGraph.Subgraph.spanningCoe_le","SimpleGraph.Subgraph.spanningCoe_sup_edge_le","SimpleGraph.Subgraph.verts","SimpleGraph.Walk","SimpleGraph.Walk.IsCycle","SimpleGraph.Walk.IsCycle.adj_toSubgraph_iff_of_isCycles","SimpleGraph.Walk.IsCycle.exists_isCycle_snd_verts_eq","SimpleGraph.Walk.IsCycle.isPath_takeUntil","SimpleGraph.Walk.IsPath","SimpleGraph.Walk.Nil","SimpleGraph.Walk.exists_mem_support_forall_mem_support_imp_eq","SimpleGraph.Walk.mem_support_of_adj_toSubgraph","SimpleGraph.Walk.mem_verts_toSubgraph","SimpleGraph.Walk.nil_takeUntil","SimpleGraph.Walk.snd","SimpleGraph.Walk.snd_takeUntil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.toSubgraph","SimpleGraph.Walk.toSubgraph_adj_snd","SimpleGraph.adj_comm","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.connectedComponentMk","SimpleGraph.disjoint_edge","SimpleGraph.distribLattice","SimpleGraph.edge","SimpleGraph.instLE","SimpleGraph.instMax","SimpleGraph.instPartialOrder","SimpleGraph.neighborSet","SimpleGraph.sdiff","SimpleGraph.sdiff_adj._simp_1","SimpleGraph.sdiff_edge","SimpleGraph.spanningCoe","SimpleGraph.spanningCoe_induce_le","SimpleGraph.sup_adj._simp_1","SimpleGraph.toSubgraph","Singleton.singleton","Subtype.finite","True","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isAlternating_isCycles","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._proof_1_11","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_9","and_false","and_self","and_true","congr","congrArg","congrFun'","disjoint_sup_left._simp_1","dite","eq_false","eq_self","eq_true","false_and","funext","id","instBEqOfDecidableEq","instDecidableNot","instLawfulBEq","le_sup_of_le_right","le_trans","not_false_eq_true","not_true_eq_false","of_eq_true","or_false","or_self","or_true","propext","rfl","sdiff_le_iff'","sup_le_sup","symmDiff","symmDiff_le","symmDiff_le_sup","true_and","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":81,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Not","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton"],"value_dag_size":408,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_singleton","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","Singleton.singleton","True","True.intro","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Max.max","SimpleGraph","SimpleGraph.edge","SimpleGraph.instMax"],"value_dag_size":196,"value_refs":["Bool","Bool.true","Classical.byContradiction","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toLattice","Eq","Eq.refl","False","Lattice.toSemilatticeSup","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase_dup","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_unsat","Lean.RArray.branch","Lean.RArray.leaf","Max.max","Nat","Not","OfNat.ofNat","PLift","PLift.up","SimpleGraph","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.instMax","eagerReduce","id","instAssociativeMax_mathlib","instCommutativeMax_mathlib","instIdempotentOpMax_mathlib","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge"],"value_dag_size":52,"value_refs":["And","Eq","Ne","Or","SimpleGraph.Adj","SimpleGraph.edge","SimpleGraph.edge_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":53,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","Eq","HeytingAlgebra.toOrderBot","Not","Order.Frame.toHeytingAlgebra","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.edge","SimpleGraph.instPartialOrder"],"value_dag_size":57,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteDistribLattice.toFrame","Disjoint","HeytingAlgebra.toOrderBot","Not","Order.Frame.toHeytingAlgebra","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.disjoint_edge","SimpleGraph.edge","SimpleGraph.instPartialOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Membership.mem","Set","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.spanningCoe"],"value_dag_size":69,"value_refs":["And","Membership.mem","Set","Set.instMembership","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph","SimpleGraph.ConnectedComponent.instSetLike","SimpleGraph.ConnectedComponent.supp","SimpleGraph.ConnectedComponent.toSimpleGraph","SimpleGraph.spanningCoe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk"],"value_dag_size":47,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.mem_supp_iff","SimpleGraph.ConnectedComponent.supp","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk"],"value_dag_size":37,"value_refs":["Eq","SimpleGraph","SimpleGraph.ConnectedComponent","SimpleGraph.ConnectedComponent.eq","SimpleGraph.Reachable","SimpleGraph.connectedComponentMk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Tutte","name":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings._simp_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Tutte.0.SimpleGraph.tutte_exists_isPerfectMatching_of_near_matchings","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.UniversalVerts","name":"_private.Mathlib.Combinatorics.SimpleGraph.UniversalVerts.0.SimpleGraph.disjoint_image_val_universalVerts._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.UniversalVerts.0.SimpleGraph.disjoint_image_val_universalVerts","reducibility":null,"statement_dag_size":61,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instCompl","Set.instLE"],"value_dag_size":70,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Disjoint","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","LE.le","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.disjoint_compl_right_iff_subset","Set.instBooleanAlgebra","Set.instCompl","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.UniversalVerts","name":"_private.Mathlib.Combinatorics.SimpleGraph.UniversalVerts.0.SimpleGraph.even_ncard_image_val_supp_sdiff_image_val_rep_union._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.UniversalVerts.0.SimpleGraph.even_ncard_image_val_supp_sdiff_image_val_rep_union","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Inter.inter","SDiff.sdiff","Set","Set.instInter","Set.instSDiff","Set.instUnion","Union.union"],"value_dag_size":47,"value_refs":["Eq.symm","Inter.inter","SDiff.sdiff","Set","Set.instInter","Set.instSDiff","Set.instUnion","Set.sdiff_inter_sdiff","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum","reducibility":"abbrev","statement_dag_size":82,"type_refs":["DFunLike.coe","Function.Injective","Nonempty.intro","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.mk","SimpleGraph.Hom","SimpleGraph.IsContained"],"value_dag_size":144,"value_refs":["DFunLike.coe","Function.Injective","Nonempty.casesOn","Nonempty.intro","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Copy","SimpleGraph.Copy.casesOn","SimpleGraph.Copy.mk","SimpleGraph.Hom","SimpleGraph.IsContained"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.IsVertexCover.subset._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.IsVertexCover.subset","reducibility":null,"statement_dag_size":33,"type_refs":["LE.le","Set","Set.instLE","SimpleGraph","SimpleGraph.IsVertexCover"],"value_dag_size":377,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Set","Set.instLE","Set.instMembership","Set.subset_def","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsVertexCover","SimpleGraph.IsVertexCover.eq_1","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isIndepSet_compl_iff_isVertexCover._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isIndepSet_compl_iff_isVertexCover","reducibility":null,"statement_dag_size":39,"type_refs":["Compl.compl","Not","Set","Set.Pairwise","Set.instCompl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsVertexCover"],"value_dag_size":457,"value_refs":["Classical.byContradiction","Compl.compl","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Set","Set.Pairwise","Set.Pairwise.eq_1","Set.instCompl","Set.instMembership","Set.mem_compl_iff","SimpleGraph","SimpleGraph.Adj","SimpleGraph.IsVertexCover","SimpleGraph.IsVertexCover.eq_1","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_compl._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_compl","reducibility":null,"statement_dag_size":31,"type_refs":["Compl.compl","Eq","Set","Set.instCompl","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsVertexCover"],"value_dag_size":40,"value_refs":["Compl.compl","Eq.symm","Set","Set.instCompl","SimpleGraph","SimpleGraph.IsIndepSet","SimpleGraph.IsVertexCover","SimpleGraph.isIndepSet_compl_iff_isVertexCover","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_empty._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_empty","reducibility":null,"statement_dag_size":42,"type_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra"],"value_dag_size":44,"value_refs":["BooleanAlgebra.toBot","Bot.bot","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toBooleanAlgebra","Eq","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.completeAtomicBooleanAlgebra","SimpleGraph.eq_bot_iff_forall_not_adj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_preimage_iso._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_preimage_iso","reducibility":null,"statement_dag_size":80,"type_refs":["DFunLike.coe","Eq","RelIso","RelIso.instFunLike","RelIso.symm","Set","Set.image","Set.preimage"],"value_dag_size":88,"value_refs":["DFunLike.coe","Eq.symm","RelIso","RelIso.image_eq_preimage_symm","RelIso.instFunLike","RelIso.symm","Set","Set.image","Set.preimage"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_card_sub_one._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_card_sub_one","reducibility":null,"statement_dag_size":31,"type_refs":["SDiff.sdiff","Set","Set.instSDiff","Set.instSingletonSet","Set.univ","SimpleGraph","SimpleGraph.IsVertexCover","Singleton.singleton"],"value_dag_size":469,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","Set.mem_univ","Set.univ","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne'","SimpleGraph.IsVertexCover","SimpleGraph.IsVertexCover.eq_1","Singleton.singleton","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_card_sub_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_card_sub_one","reducibility":null,"statement_dag_size":63,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf"],"value_dag_size":68,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf","le_iInf_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet","reducibility":null,"statement_dag_size":111,"type_refs":["DFunLike.coe","LE.le","Membership.mem","Or","Prod","Prod.fst","Quot","Quot.out","RelEmbedding","Set","Set.image","Set.instLE","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2.Rel","instFunLikeOrderEmbedding"],"value_dag_size":808,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Prod","Prod.fst","Prod.mk","Quot","Quot.mk","Quot.out","RelEmbedding","Set","Set.image","Set.instLE","Set.instMembership","Set.mem_image","SetLike.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","SimpleGraph.mem_edgeSet","Sym2","Sym2.Rel","Sym2.instSetLike","Sym2.mem_iff","Sym2.mk","Sym2.out_fst_mem","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","instFunLikeOrderEmbedding","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet","reducibility":null,"statement_dag_size":141,"type_refs":["CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder.toCompletelyDistribLattice","CompleteSemilatticeSup.toPartialOrder","CompletelyDistribLattice.toCompleteLattice","DFunLike.coe","ENat","ENat.instNatCast","LE.le","Nat","Nat.cast","NatCast.natCast","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Quot","Quot.out","RelEmbedding","Set","Set.encard","Set.image","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Sym2","Sym2.Rel","instCompleteLinearOrderENat","instFunLikeOrderEmbedding","instLEENat"],"value_dag_size":285,"value_refs":["Classical.byContradiction","CompleteLattice.toCompleteSemilatticeSup","CompleteLinearOrder.toCompletelyDistribLattice","CompleteSemilatticeSup.toPartialOrder","CompletelyDistribLattice.toCompleteLattice","DFunLike.coe","ENat","ENat.instNatCast","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","LE.le","Lean.Grind.Order.le_eq_false_of_lt","Lean.Grind.Order.lt_le_trans","Lean.Grind.Order.lt_of_not_le","Nat","Nat.cast","NatCast.natCast","Not","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Quot","Quot.out","RelEmbedding","Set","Set.encard","Set.encard_image_le","Set.image","Set.instLE","SimpleGraph","SimpleGraph.edgeSet","SimpleGraph.edgeSetEmbedding","SimpleGraph.instLE","Std.IsLinearOrder.toIsLinearPreorder","Sym2","Sym2.Rel","True","True.intro","eq_true","id","instCompleteLinearOrderENat","instFunLikeOrderEmbedding","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instLinearOrderENat","instPreorderENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_encard_edgeSet","reducibility":null,"statement_dag_size":63,"type_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf"],"value_dag_size":68,"value_refs":["CompleteLattice","CompleteLattice.toCompleteSemilatticeInf","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeSup.toPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf","le_iInf_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_iff._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_le_iff","reducibility":null,"statement_dag_size":58,"type_refs":["CompleteSemilatticeInf","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeInf.toPartialOrder","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf"],"value_dag_size":63,"value_refs":["CompleteSemilatticeInf","CompleteSemilatticeInf.toInfSet","CompleteSemilatticeInf.toPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","iInf","iInf_le_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_top._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_top","reducibility":null,"statement_dag_size":59,"type_refs":["False","Membership.mem","Or","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.univ"],"value_dag_size":186,"value_refs":["And","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","Set.univ","True","True.intro","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.VertexCover","name":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_top._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.vertexCoverNum_top","reducibility":null,"statement_dag_size":62,"type_refs":["Add","Eq","HAdd.hAdd","HSub.hSub","LE.le","OrderedSub","Preorder","Preorder.toLE","Sub","True","instHAdd","instHSub"],"value_dag_size":67,"value_refs":["Add","HAdd.hAdd","HSub.hSub","LE.le","OrderedSub","Preorder","Preorder.toLE","Sub","eq_true","instHAdd","instHSub","le_tsub_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.Nil.eq.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.Nil.eq","reducibility":"abbrev","statement_dag_size":61,"type_refs":["SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.nil","SimpleGraph.Walk.nil","Unit"],"value_dag_size":289,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.casesOn","SimpleGraph.Walk.Nil.nil","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.adj_of_length_eq_one.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.adj_of_length_eq_one","reducibility":"abbrev","statement_dag_size":99,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":1122,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","Nat","Nat.Internal.elimOffset","Nat.ctorIdx","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.dart_fst_mem_support_of_mem_darts._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.dart_fst_mem_support_of_mem_darts","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.dart_fst_mem_support_of_mem_darts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.dart_fst_mem_support_of_mem_darts","reducibility":"abbrev","statement_dag_size":126,"type_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.darts"],"value_dag_size":987,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.casesOn","SimpleGraph.Dart.mk","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.darts","SimpleGraph.Walk.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.darts_nodup_of_support_nodup._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.darts_nodup_of_support_nodup","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.darts_ofDarts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.darts_ofDarts","reducibility":"abbrev","statement_dag_size":141,"type_refs":["List","List.IsChain","List.cons","List.nil","Ne","SimpleGraph","SimpleGraph.Dart","SimpleGraph.DartAdj"],"value_dag_size":282,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.IsChain","List.casesOn","List.cons","List.nil","Ne","SimpleGraph","SimpleGraph.Dart","SimpleGraph.DartAdj","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edge_getElem_darts._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edge_getElem_darts","reducibility":null,"statement_dag_size":59,"type_refs":["LT.lt","List.length","Nat","Prod","Quot","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.edges","Sym2.Rel","instLTNat"],"value_dag_size":502,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Quot","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_edges","Sym2","Sym2.Rel","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edges_injective.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edges_injective","reducibility":"abbrev","statement_dag_size":275,"type_refs":["Eq","List","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2"],"value_dag_size":1358,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edges_subset_edgeSet.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.edges_subset_edgeSet","reducibility":"abbrev","statement_dag_size":121,"type_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","Sym2"],"value_dag_size":761,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","Sym2","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.eq_of_length_eq_zero.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.eq_of_length_eq_zero","reducibility":"abbrev","statement_dag_size":79,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":521,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","Nat","Nat.ctorIdx","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","SimpleGraph.Walk.nil","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.eq_of_length_le_one._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.eq_of_length_le_one","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":2385,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HEq","HEq.refl","HEq.symm","HEq.trans","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.ne","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons.hcongr_7","SimpleGraph.Walk.length","SimpleGraph.Walk.length.hcongr_5","SimpleGraph.Walk.length_cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.nil.hcongr_3","True","True.intro","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_eq_cons_of_ne.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_eq_cons_of_ne","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":386,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_length_eq_one_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_length_eq_one_iff","reducibility":"abbrev","statement_dag_size":94,"type_refs":["Eq","Exists","Exists.intro","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":119,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_length_eq_zero_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_length_eq_zero_iff","reducibility":"abbrev","statement_dag_size":94,"type_refs":["Eq","Exists","Exists.intro","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":119,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_nil_iff.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.exists_nil_iff","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil"],"value_dag_size":99,"value_refs":["Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["LT.lt","List.dropLast","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":1162,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.dropLast","List.length","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":141,"value_refs":["Eq","Eq.rec","Eq.symm","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.support","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem","reducibility":null,"statement_dag_size":67,"type_refs":["LT.lt","List.length","List.map","Nat","Prod.fst","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"],"value_dag_size":360,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","List.map","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Prod.fst","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.map_fst_darts","SimpleGraph.Walk.support","True","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem","reducibility":null,"statement_dag_size":52,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"],"value_dag_size":402,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","List.length_map","List.map","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Prod.fst","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.map_fst_darts","SimpleGraph.Walk.support","True","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.dropLast","List.instGetElemNatLtLength","List.length","Nat","Prod.fst","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":812,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem_map","List.instGetElemNatLtLength","List.length","List.length_map","List.map","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.map_fst_darts","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1_3","cast","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.getElem_edges_eq_edge_getElem_darts._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.getElem_edges_eq_edge_getElem_darts","reducibility":null,"statement_dag_size":53,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.edges","Sym2","instLTNat"],"value_dag_size":498,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Quot","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_edges","Sym2","Sym2.Rel","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_adj_cons_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_adj_cons_support","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_adj_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_adj_support","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_dartAdj_darts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.isChain_dartAdj_darts","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts","reducibility":null,"statement_dag_size":44,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts","reducibility":null,"statement_dag_size":55,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":42,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofDarts","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","List","List.IsChain","List.getLast","List.head","List.length","List.nil","Nat","Ne","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.DartAdj","SimpleGraph.Walk.length","SimpleGraph.Walk.ofDarts"],"value_dag_size":309,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","List","List.IsChain","List.getLast","List.head","List.length","List.nil","Nat","Ne","Not","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.DartAdj","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_ofDarts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.ofDarts","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HSub.hSub","List","List.IsChain","List.getLast","List.head","List.length","List.nil","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk.length","SimpleGraph.Walk.ofSupport","instHSub","instOfNatNat","instSubNat"],"value_dag_size":942,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.getLast","List.head","List.length","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.ofSupport","SimpleGraph.Walk.support","SimpleGraph.Walk.support_ofSupport","Std.IsLinearOrder.toIsLinearPreorder","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.length_ofSupport._proof_1_2","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":46,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":420,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.length_nil","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","HSub.hSub","LT.lt","List.cons","List.length","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":203,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_6","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":399,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":38,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","instLTNat"],"value_dag_size":403,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_succ_lt_succ","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HSub.hSub","LT.lt","List.cons","List.length","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":150,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_13","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":167,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","Prod.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.mk","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat"],"value_dag_size":3712,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_cons","List.getElem_cons.match_1","List.getElem_cons_succ","List.getElem_cons_zero","List.getElem_dropLast","List.getElem_tail","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_cons","List.length_dropLast","List.length_nil","List.nil","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.add_lt_of_lt_sub","Nat.lt_of_lt_of_le","Nat.lt_of_succ_lt_succ","Nat.pred_le","Nat.sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.snd_darts_getElem","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_12","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_13","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_9","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1","cast","congrArg","congrFun'","dite","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_pos","heq_of_eq","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":52,"type_refs":["LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":52,"type_refs":["LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":79,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":744,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.dropLast","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":100,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.cons","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","List.tail","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":100,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.cons","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_22","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":163,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.cons","List.dropLast","List.length","List.length_dropLast","List.nil","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_20","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_23","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":84,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":109,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.cons","List.getElem_tail._proof_1","List.length","List.nil","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_21","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_24","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":85,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_25","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":249,"type_refs":["And","Eq","Exists","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","OfNat.ofNat","Option","Option.some","Prod.fst","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1887,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_cons","List.getElem_cons.match_1","List.getElem_dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_cons","List.length_dropLast","List.length_nil","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","Prod.fst","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_17","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_20","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_22","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_24","congr","congrArg","congrFun'","dite","dite_cond_eq_true","eagerReduce","eq_false","eq_self","eq_true","forall_congr","forall_prop_domain_congr","funext","getElem?_pos","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_26","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":705,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_17","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_24","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_27","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":50,"type_refs":["LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":202,"value_refs":["Eq","Eq.rec","False","False.elim","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.ctorIdx","Nat.sub_self","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_18","eq_false'","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_28","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":156,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_29","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":140,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":701,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_18","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_28","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_30","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":249,"type_refs":["And","Eq","Exists","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","OfNat.ofNat","Option","Option.some","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":2768,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_tail","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_cons","List.length_nil","List.nil","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.add_lt_of_lt_sub","Nat.ctorIdx","Nat.not_le_eq","Nat.sub_self","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.snd_darts_getElem","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_18","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_19","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_21","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_23","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_27","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_28","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_29","congr","congrArg","congrFun'","dite","dite_cond_eq_false","dite_cond_eq_true","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_self","eq_true","forall_congr","forall_prop_domain_congr","funext","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":79,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":745,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.length_nil","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","HSub.hSub","LT.lt","List.cons","List.length","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":148,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":91,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":141,"value_refs":["Eq","Eq.rec","Eq.symm","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.fst_darts_getElem._proof_1","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":83,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":"abbrev","statement_dag_size":384,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":493,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support","reducibility":"abbrev","statement_dag_size":288,"type_refs":["Eq","Exists","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","Prod.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.mk","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"],"value_dag_size":395,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","Prod.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Dart","SimpleGraph.Dart.mk","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.nil_of_subsingleton.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.nil_of_subsingleton","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.not_nil_cons.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.not_nil_cons","reducibility":"abbrev","statement_dag_size":59,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons"],"value_dag_size":317,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.casesOn","SimpleGraph.Walk.Nil.nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.ctorIdx","SimpleGraph.Walk.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["LT.lt","List.length","List.tail","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":1162,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","List.length_tail","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":83,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem","reducibility":null,"statement_dag_size":67,"type_refs":["LT.lt","List.length","List.map","Nat","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"],"value_dag_size":360,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.map","List.tail","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.map_snd_darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","True","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem","reducibility":null,"statement_dag_size":52,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat"],"value_dag_size":402,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_map","List.map","List.tail","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.map_snd_darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","True","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","List.tail","Nat","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":812,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_map","List.instGetElemNatLtLength","List.length","List.length_map","List.map","List.tail","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.map_snd_darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.snd_darts_getElem._proof_1_3","cast","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Basic","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.support_ofSupport.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.support_ofSupport","reducibility":"abbrev","statement_dag_size":118,"type_refs":["List","List.IsChain","List.cons","List.nil","Ne","SimpleGraph","SimpleGraph.Adj"],"value_dag_size":253,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.IsChain","List.casesOn","List.cons","List.nil","Ne","SimpleGraph","SimpleGraph.Adj","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Chord","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Adj.isChordless_toWalk._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Adj.isChordless_toWalk","reducibility":null,"statement_dag_size":36,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk.IsChordless","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":1258,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.edges_toWalk","SimpleGraph.Adj.ne","SimpleGraph.Adj.support_toWalk","SimpleGraph.Adj.toWalk","SimpleGraph.Walk.IsChordless","SimpleGraph.Walk.cons","SimpleGraph.Walk.edges","SimpleGraph.Walk.isChordless_iff_forall_mem_edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Chord","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.IsChord._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.IsChord","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"],"value_dag_size":382,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","Membership.mem","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","congr","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Chord","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges","reducibility":null,"statement_dag_size":154,"type_refs":["Iff","List","List.instMembership","Membership.mem","Not","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","Sym2.Rel"],"value_dag_size":1007,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","List","List.instMembership","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","Sym2.Rel","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Chord","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Sym2","Sym2.mk"],"value_dag_size":28,"value_refs":["Sym2","Sym2.forall","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Chord","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Chord.0.SimpleGraph.Walk.isChordless_iff_forall_mem_edges","reducibility":null,"statement_dag_size":84,"type_refs":["And","Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsChord","SimpleGraph.Walk.edges","SimpleGraph.Walk.support","Sym2","Sym2.mk"],"value_dag_size":91,"value_refs":["And","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.IsChord","SimpleGraph.Walk.edges","SimpleGraph.Walk.isChord_sym2Mk","SimpleGraph.Walk.support","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_add_one._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_add_one","reducibility":null,"statement_dag_size":137,"type_refs":["Eq","HAdd.hAdd","Iff","Membership.mem","Nat","OfNat.ofNat","Set","Set.iUnion","Set.image","Set.instMembership","Set.ofPred","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":4647,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HAdd.hAdd","HEq","HEq.refl","HEq.symm","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_false","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.iUnion","Set.image","Set.instMembership","Set.mem_iUnion","Set.mem_image","Set.mem_ofPred_eq","Set.mem_univ","Set.ofPred","Set.ofPred_true","Set.univ","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons.noConfusion","SimpleGraph.Walk.length","SimpleGraph.Walk.length.hcongr_5","SimpleGraph.Walk.length_cons","SimpleGraph.Walk.length_eq_zero_iff","True","True.casesOn","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","heq_eq_eq","heq_of_eq","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_add_one._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_add_one","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_zero._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_zero","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_zero._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.Walk.setOfPred_length_eq_zero","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.nil"],"value_dag_size":49,"value_refs":["Eq","Eq.symm","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.eq_nil_iff_nil","SimpleGraph.Walk.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLengthLT_eq._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLengthLT_eq","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength"],"value_dag_size":79,"value_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","SimpleGraph.mem_finsetWalkLength_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Nat","OfNat.ofNat","Set","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","instOfNatNat"],"value_dag_size":1655,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.instSingleton.hcongr_1","Finset.mem_coe","Finset.mem_singleton","Finset.notMem_empty","HEq.refl","HEq.symm","HEq.trans","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.heq_congr","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.ext","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.Nil.hcongr_5","SimpleGraph.Walk.eq_nil_iff_nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.nil","SimpleGraph.finsetWalkLength","SimpleGraph.finsetWalkLength.eq_1","Singleton.singleton","Singleton.singleton.hcongr_4","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_9","cast","cast_heq","congrArg","congrFun'","dite","dite_congr","eq_false","eq_of_heq","eq_true","forall_congr","funext","heq_of_eq","id","implies_congr","instOfNatNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":12,"type_refs":["Eq"],"value_dag_size":34,"value_refs":["Eq","Eq.substr","Iff","Iff.mpr","Lean.Grind.iff_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":32,"type_refs":["Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet"],"value_dag_size":229,"value_refs":["Eq","Eq.rec","Eq.refl","Eq.symm","HEq","HEq.refl","Iff.mpr","Iff.of_eq","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.neighborSet","eq_of_heq","iff_of_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":5,"type_refs":[],"value_dag_size":13,"value_refs":["Eq.refl","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_13"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":331,"type_refs":["DecidableEq","Eq","Eq.rec","Eq.refl","Eq.symm","Finset","Finset.instSetLike","HEq","HEq.refl","Iff.mpr","Iff.of_eq","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","SimpleGraph.neighborSet","Subtype.mk","Subtype.val","eq_of_heq","iff_of_eq"],"value_dag_size":409,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","HEq","HEq.refl","Iff.mpr","Iff.of_eq","Membership.mem","Nat","Not","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.Adj","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","SimpleGraph.neighborSet","Subtype.mk","Subtype.val","True","True.intro","eq_false","eq_of_heq","eq_true","id","iff_of_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":30,"value_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk"],"value_dag_size":31,"value_refs":["Eq","SimpleGraph","SimpleGraph.Walk","congrArg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk"],"value_dag_size":36,"value_refs":["Eq","Eq.symm","SimpleGraph","SimpleGraph.Walk","congrArg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":121,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","instOfNatNat"],"value_dag_size":279,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Iff","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.finsetWalkLength","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_4","eq_false","eq_true","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":127,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","instOfNatNat"],"value_dag_size":286,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Iff","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.finsetWalkLength","True","congrArg","eq_false","eq_true","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":127,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","instOfNatNat"],"value_dag_size":291,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Iff","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.finsetWalkLength","True","congrArg","eq_false","eq_true","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._simp_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._simp_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.finsetWalkLength.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.finsetWalkLength.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.finsetWalkLength.match_1","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph.finsetWalkLength.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.finsetWalkLength.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["SimpleGraph.finsetWalkLength.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLength._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLength","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength"],"value_dag_size":79,"value_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength","SimpleGraph.mem_finsetWalkLength_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLength._simp_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLength","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLengthLT._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.fintypeSetPathLengthLT","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","LT.lt","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLengthLT","instLTNat"],"value_dag_size":81,"value_refs":["DecidableEq","Finset","Finset.instSetLike","LT.lt","Membership.mem","Nat","SetLike.instMembership","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLengthLT","SimpleGraph.mem_finsetWalkLengthLT_iff","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Counting","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.set_walk_length_toFinset_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.set_walk_length_toFinset_eq","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Nat","Set","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.finsetWalkLength"],"value_dag_size":75,"value_refs":["DecidableEq","Eq","Eq.symm","Finset","Finset.instSetLike","Nat","Set","Set.ofPred","SetLike.coe","SimpleGraph","SimpleGraph.LocallyFinite","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.coe_finsetWalkLength_eq","SimpleGraph.finsetWalkLength"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":44,"value_refs":["Eq","Prod.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.count_edges_takeUntil_le_one","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel"],"value_dag_size":38,"value_refs":["Eq","Or","Prod","Prod.swap","Sym2.Rel","Sym2.rel_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":89,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":85,"value_refs":["DecidableEq","List","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":350,"type_refs":["DecidableEq","Eq","Eq.rec","Eq.symm","HSub.hSub","List","List.idxOf","List.instMembership","Membership.mem","Nat","Ne","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.drop","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_7","dite","instBEqOfDecidableEq","instHSub","instOfNatNat","instSubNat","rfl"],"value_dag_size":3965,"value_refs":["And","And.casesOn","BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf?","List.idxOf_cons","List.idxOf_eq_getD_idxOf?","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_cons","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option.getD","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.copy.hcongr_9","SimpleGraph.Walk.drop","SimpleGraph.Walk.drop.hcongr_6","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.support.hcongr_5","SimpleGraph.Walk.support_cons","SimpleGraph.Walk.takeUntil._proof_3","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_8","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_9","cond","congrArg","congrFun'","decide_eq_true_eq","dite","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":51,"value_refs":["Eq.symm","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropUntil._proof_1","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","Eq.symm","List","List.cons","List.instMembership","List.nil","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropUntil._proof_1","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","cast"],"value_dag_size":269,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.nil","Membership.mem","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropUntil._proof_1","SimpleGraph.Walk.mem_support_nil_iff","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.support.hcongr_5","SimpleGraph.Walk.support_nil","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_4","cast","cast_heq","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","Eq","List.idxOf","Nat","Ne","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","instBEqOfDecidableEq","instOfNatNat"],"value_dag_size":514,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.support_cons","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":95,"type_refs":["DecidableEq","Eq","HSub.hSub","List.idxOf","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq","instHSub","instOfNatNat","instSubNat"],"value_dag_size":117,"value_refs":["DecidableEq","Eq.symm","HSub.hSub","List.idxOf","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_7","instBEqOfDecidableEq","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.dropUntil_eq_drop","reducibility":null,"statement_dag_size":73,"type_refs":["List","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":105,"value_refs":["Eq","Eq.refl","Eq.trans","False","Lean.Grind.eq_congr'","List","List.instMembership","Membership.mem","Ne","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_3","eq_false","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_le_length_takeUntil_eq_iff._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_le_length_takeUntil_eq_iff","reducibility":null,"statement_dag_size":99,"type_refs":["DecidableEq","Eq","Iff","LE.le","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","instLENat"],"value_dag_size":954,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_length_takeUntil","SimpleGraph.Walk.getVert_lt_length_takeUntil_ne","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_length_takeUntil._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_length_takeUntil","reducibility":null,"statement_dag_size":112,"type_refs":["DecidableEq","Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil"],"value_dag_size":411,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.decLt","Nat.sub_self","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_append","SimpleGraph.Walk.getVert_zero","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_lt_length_takeUntil_ne._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.getVert_lt_length_takeUntil_ne","reducibility":null,"statement_dag_size":143,"type_refs":["DecidableEq","Eq","False","HAppend.hAppend","List","List.cons","List.count","List.dropLast","List.instAppend","List.instMembership","List.nil","Membership.mem","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","instBEqOfDecidableEq","instHAppendOfAppend","instOfNatNat"],"value_dag_size":741,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","Decidable.decide.congr_simp","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.beq_eq_decide_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.count","List.count_append","List.count_cons","List.dropLast","List.instAppend","List.instMembership","List.nil","List.not_mem_of_count_eq_zero","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_self","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instDecidableTrue","instHAdd","instHAppendOfAppend","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.length.match_1","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.length.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_dropUntil_lt_length._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_dropUntil_lt_length","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","LT.lt","List","List.instMembership","Membership.mem","Nat","Ne","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":1270,"value_refs":["BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf_cons","List.idxOf_lt_length_iff","List.instMembership","List.length","List.tail","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.cons_tail_support","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_dropUntil","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_takeUntil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_takeUntil","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.le_iff_lt_add_one","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_takeUntil._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.length_takeUntil","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HAdd.hAdd","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.symm","HAdd.hAdd","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","List","List.instMembership","Membership.mem","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support"],"value_dag_size":77,"value_refs":["List","List.instMembership","Membership.mem","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.mem_support_append_iff","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","True"],"value_dag_size":43,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.end_mem_support","SimpleGraph.Walk.support","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append._simp_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","True"],"value_dag_size":43,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.start_mem_support","SimpleGraph.Walk.support","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append._simp_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_append","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Or"],"value_dag_size":12,"value_refs":["Or","or_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_getVert.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_iff_exists_getVert","reducibility":"abbrev","statement_dag_size":147,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instLENat"],"value_dag_size":213,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_rotate_iff._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.mem_support_rotate_iff","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Iff","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.rotate","SimpleGraph.Walk.support"],"value_dag_size":603,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","Membership.mem","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.dropUntil","SimpleGraph.Walk.mem_support_append_iff","SimpleGraph.Walk.rotate","SimpleGraph.Walk.rotate.eq_1","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.take_spec","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.nil_rotate._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.nil_rotate","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq","Eq.symm","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset","reducibility":null,"statement_dag_size":105,"type_refs":["DecidableEq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil"],"value_dag_size":189,"value_refs":["DecidableEq","Eq","Eq.rec","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","SimpleGraph.Walk.support_takeUntil_subset_support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.takeUntil_takeUntil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset","reducibility":null,"statement_dag_size":208,"type_refs":["DecidableEq","Eq.ndrec","False","LT.lt","List","List.instMembership","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.support_takeUntil_subset_support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.takeUntil_takeUntil","instLTNat"],"value_dag_size":673,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.support_takeUntil_subset_support","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.takeUntil_takeUntil","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subset._proof_1_2","congrArg","eagerReduce","eq_of_heq","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.snd_takeUntil._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.snd_takeUntil","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1","reducibility":null,"statement_dag_size":157,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil.match_1"],"value_dag_size":154,"value_refs":["Eq.refl","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1","reducibility":null,"statement_dag_size":192,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil.match_1"],"value_dag_size":185,"value_refs":["Eq.refl","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil.match_1","reducibility":"abbrev","statement_dag_size":148,"type_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.takeUntil.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left","reducibility":null,"statement_dag_size":90,"type_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":80,"value_refs":["List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.support_subset_support_append_left"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":102,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left","reducibility":null,"statement_dag_size":91,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":135,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left","reducibility":null,"statement_dag_size":168,"type_refs":["DecidableEq","Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.support_subset_support_append_left","SimpleGraph.Walk.takeUntil"],"value_dag_size":870,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons_append","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.support_subset_support_append_left","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.takeUntil._proof_3","SimpleGraph.Walk.takeUntil.eq_2","SimpleGraph.Walk.takeUntil.hcongr_8","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_append_of_mem_left._proof_1_7","congrArg","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":75,"value_refs":["DecidableEq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support"],"value_dag_size":102,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":95,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":107,"value_refs":["DecidableEq","List","List.idxOf","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_10","congrArg","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":87,"value_refs":["DecidableEq","Eq","List","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_11"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":96,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":109,"value_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_13","congrArg","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":201,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.support","SimpleGraph.Walk.take","SimpleGraph.Walk.takeUntil","instBEqOfDecidableEq","rfl"],"value_dag_size":1587,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.forall_propagator","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","List","List.cons","List.idxOf","List.idxOf_cons","List.instMembership","List.nil","List.take","List.take_succ_cons","List.take_zero","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.copy.hcongr_9","SimpleGraph.Walk.copy_rfl_rfl","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_support_idxOf","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.support.eq_1","SimpleGraph.Walk.support.hcongr_5","SimpleGraph.Walk.support_cons","SimpleGraph.Walk.support_take","SimpleGraph.Walk.take","SimpleGraph.Walk.takeUntil","SimpleGraph.Walk.takeUntil._proof_3","SimpleGraph.Walk.takeUntil.eq_2","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_11","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_12","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_13","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_14","cast","cast_heq","cond","congrArg","congrFun'","decide_eq_true_eq","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLawfulBEq","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":50,"value_refs":["Eq.symm","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Decomp","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Eq.symm","List","List.cons","List.instMembership","List.nil","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.takeUntil._proof_1","cast"],"value_dag_size":266,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.nil","Membership.mem","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.mem_support_nil_iff","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","SimpleGraph.Walk.support.hcongr_5","SimpleGraph.Walk.support_nil","SimpleGraph.Walk.takeUntil._proof_1","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Decomp.0.SimpleGraph.Walk.takeUntil_eq_take._proof_1_4","cast","cast_heq","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_induce.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_induce","reducibility":"abbrev","statement_dag_size":175,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":605,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_induce_induceHomOfLE.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_induce_induceHomOfLE","reducibility":"abbrev","statement_dag_size":175,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":605,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_injective_of_injective._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_injective_of_injective","reducibility":null,"statement_dag_size":132,"type_refs":["And","DFunLike.coe","Eq","Function.Injective","HEq","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Walk","SimpleGraph.Walk.map"],"value_dag_size":268,"value_refs":["And","DFunLike.coe","Eq","Eq.symm","Eq.trans","Function.Injective","HEq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Nonempty","Nonempty.intro","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Walk","SimpleGraph.Walk.map","True","congrArg","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_injective_of_injective._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_injective_of_injective","reducibility":null,"statement_dag_size":207,"type_refs":["And","DFunLike.coe","Eq","Function.Injective","HEq","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.map"],"value_dag_size":878,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.Injective","HEq","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Nonempty","Nonempty.intro","Not","RelHom","RelHom.instFunLike","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Hom","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons.hcongr_7","SimpleGraph.Walk.map","SimpleGraph.Walk.map.hcongr_8","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.map_injective_of_injective._proof_1_1","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.reverse_transfer._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.reverse_transfer","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","List","List.instMembership","List.reverse","Membership.mem"],"value_dag_size":31,"value_refs":["List","List.instMembership","List.mem_reverse","List.reverse","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.support_induce.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.support_induce","reducibility":"abbrev","statement_dag_size":175,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support"],"value_dag_size":605,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","SimpleGraph.Walk.support","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.toDeleteEdges._simp_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.toDeleteEdges","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff"],"value_dag_size":46,"value_refs":["And","Membership.mem","Not","SDiff.sdiff","Set","Set.instMembership","Set.instSDiff","Set.mem_sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1","reducibility":null,"statement_dag_size":217,"type_refs":["Eq","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.transfer.match_1","SimpleGraph.edgeSet","Sym2"],"value_dag_size":214,"value_refs":["Eq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.transfer.match_1","SimpleGraph.edgeSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1","reducibility":null,"statement_dag_size":253,"type_refs":["Eq","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.transfer.match_1","SimpleGraph.edgeSet","Sym2"],"value_dag_size":246,"value_refs":["Eq.refl","List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.Walk.transfer.match_1","SimpleGraph.edgeSet","Sym2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Maps","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Maps.0.SimpleGraph.Walk.transfer.match_1","reducibility":"abbrev","statement_dag_size":205,"type_refs":["List","List.instMembership","Membership.mem","Set","Set.instMembership","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons'","SimpleGraph.Walk.edges","SimpleGraph.Walk.nil","SimpleGraph.edgeSet","Sym2"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.transfer.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil"],"value_dag_size":48,"value_refs":["Eq.symm","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","congrArg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil"],"value_dag_size":43,"value_refs":["SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","congrArg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.copy","SimpleGraph.Walk.nil","rfl"],"value_dag_size":426,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq.refl","HEq.symm","HEq.trans","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.Nil.eq","SimpleGraph.Walk.Nil.hcongr_5","SimpleGraph.Walk.copy","SimpleGraph.Walk.copy.hcongr_9","SimpleGraph.Walk.copy_rfl_rfl","SimpleGraph.Walk.eq_nil_iff_nil","SimpleGraph.Walk.nil","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.Nil.eq_copy_nil._proof_1_4","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.coe_support_append'._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.coe_support_append'","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","Multiset","Multiset.instAdd","Multiset.ofList","instHAdd","instHAppendOfAppend"],"value_dag_size":51,"value_refs":["Eq.symm","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","Multiset","Multiset.coe_add","Multiset.instAdd","Multiset.ofList","instHAdd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.coe_support_append'._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.coe_support_append'","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concatRecAux.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit"],"value_dag_size":77,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concatRecAux.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concatRecAux.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":99,"value_refs":["Eq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concatRecAux.match_1","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.concatRecAux.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.concatRecAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":108,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1","reducibility":null,"statement_dag_size":136,"type_refs":["Eq","False","HEq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":2999,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","SimpleGraph.Walk.rec","eq_of_heq","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":129,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop.match_1","SimpleGraph.Walk.nil","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop.match_1","reducibility":"abbrev","statement_dag_size":119,"type_refs":["Eq","False","HEq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":652,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.ctorIdx","SimpleGraph.Walk.nil","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.dropLast_concat._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.dropLast_concat","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq","Eq.symm","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.dropLast_support_concat.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.dropLast_support_concat","reducibility":"abbrev","statement_dag_size":263,"type_refs":["Eq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concat","SimpleGraph.Walk.cons"],"value_dag_size":426,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.concat","SimpleGraph.Walk.cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop_drop._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.drop_drop","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","List","List.drop","Min.min","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instMinNat","instSubNat"],"value_dag_size":4694,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List","List.drop","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","min_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.edgeSet_concat._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.edgeSet_concat","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.edges_nodup_of_support_nodup._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.edges_nodup_of_support_nodup","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.exists_concat_eq_cons.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.exists_concat_eq_cons","reducibility":"abbrev","statement_dag_size":95,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":391,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ext_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ext_support","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","Function.comp","List","List.map","List.unzip","Prod","Prod.fst","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support"],"value_dag_size":565,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","List","List.dropLast","List.map","List.map_map","List.tail","List.unzip","List.unzip_fst","List.unzip_snd","Not","Prod","Prod.fst","Prod.mk","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.map_fst_darts","SimpleGraph.Walk.map_snd_darts","SimpleGraph.Walk.support","True","True.intro","congr","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":50,"type_refs":["LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat"],"value_dag_size":109,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":46,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":285,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_1","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":73,"type_refs":["HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":128,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":101,"type_refs":["HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":165,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":113,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":540,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_3","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":137,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":696,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_dropLast","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_4","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List.dropLast","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":948,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_dropLast","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.support_dropLast","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_6","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":121,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":994,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","List.length_dropLast","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_dropLast","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.support_dropLast","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_6","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HSub.hSub","LT.lt","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2628,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem_dropLast","List.instGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.lt_add_one_of_le","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.dropLast","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_dropLast","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.penultimate","SimpleGraph.Walk.support","SimpleGraph.Walk.support_dropLast","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_6","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_dropLast._proof_1_8","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_mem_tail_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.getVert_mem_tail_support","reducibility":"abbrev","statement_dag_size":49,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","absurd","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.mem_support_append_iff._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.mem_support_append_iff","reducibility":null,"statement_dag_size":67,"type_refs":["Iff","List","List.instMembership","Membership.mem","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support"],"value_dag_size":704,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","List.tail","Membership.mem","Ne","Not","Or","Or.casesOn","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.end_mem_tail_support_of_ne","SimpleGraph.Walk.mem_support_iff","SimpleGraph.Walk.mem_tail_support_append_iff","SimpleGraph.Walk.support","True","True.intro","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.nodup_tail_support_reverse._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.nodup_tail_support_reverse","reducibility":null,"statement_dag_size":36,"type_refs":["LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat","instOfNatNat"],"value_dag_size":115,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.nodup_tail_support_reverse._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.nodup_tail_support_reverse","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":156,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_le","Nat.decLe","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ofDarts_darts.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ofDarts_darts","reducibility":"abbrev","statement_dag_size":171,"type_refs":["Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil"],"value_dag_size":909,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Not","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ofSupport_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.ofSupport_support","reducibility":"abbrev","statement_dag_size":105,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":701,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.reverse_dropLast.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.reverse_dropLast","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.reverse_tail.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.reverse_tail","reducibility":"abbrev","statement_dag_size":70,"type_refs":["SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit"],"value_dag_size":347,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.casesOn","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_add_heq._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_add_heq","reducibility":null,"statement_dag_size":186,"type_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","HAdd.hAdd","HEq","Nat","Nat.instAddCommSemigroup","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.drop","SimpleGraph.Walk.getVert","SimpleGraph.Walk.take","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":465,"value_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","HEq.refl","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.instAddCommSemigroup","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.cons","SimpleGraph.Walk.cons.hcongr_7","SimpleGraph.Walk.drop","SimpleGraph.Walk.drop_getVert","SimpleGraph.Walk.getVert","SimpleGraph.Walk.take","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","heq_of_eq","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_cons_eq._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_cons_eq","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","HSub.hSub","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","instHSub","instOfNatNat","instSubNat"],"value_dag_size":92,"value_refs":["Eq.symm","HSub.hSub","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Operations","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_cons_eq._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_cons_eq","reducibility":null,"statement_dag_size":132,"type_refs":["Eq","Eq.symm","HSub.hSub","List","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","SimpleGraph.Walk.support","SimpleGraph.Walk.take","instHSub","instOfNatNat","instSubNat","rfl"],"value_dag_size":1055,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.leaf","List","List.cons","List.take","List.take_succ_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.copy","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_cons","SimpleGraph.Walk.support","SimpleGraph.Walk.support_cons","SimpleGraph.Walk.support_copy","SimpleGraph.Walk.support_take","SimpleGraph.Walk.take","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Operations.0.SimpleGraph.Walk.take_cons_eq._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.copy._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.copy","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.support"],"value_dag_size":63,"value_refs":["List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.isSubwalk_iff_support_isInfix","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.darts_isInfix._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.darts_isInfix","reducibility":null,"statement_dag_size":55,"type_refs":["List.IsInfix","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.darts"],"value_dag_size":395,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","List","List.IsInfix","List.append_assoc","List.infix_append'","List.instAppend","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.eq_1","SimpleGraph.Walk.append","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_append","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.edges_isInfix._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.edges_isInfix","reducibility":null,"statement_dag_size":60,"type_refs":["List.IsInfix","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.edges","Sym2.Rel"],"value_dag_size":425,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","List","List.IsInfix","List.append_assoc","List.infix_append'","List.instAppend","Not","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.eq_1","SimpleGraph.Walk.append","SimpleGraph.Walk.edges","SimpleGraph.Walk.edges_append","Sym2","Sym2.Rel","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.map._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.map","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.support"],"value_dag_size":63,"value_refs":["List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.isSubwalk_iff_support_isInfix","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.map._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.IsSubwalk.map","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.IsInfix","List.map","True"],"value_dag_size":42,"value_refs":["List","List.IsInfix","List.IsInfix.map","List.map","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.infix_support_iff_mem_edges._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.infix_support_iff_mem_edges","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.support"],"value_dag_size":63,"value_refs":["List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.isSubwalk_iff_support_isInfix","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":97,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":189,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":54,"type_refs":["LT.lt","List.dropLast","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":63,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_12","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.dropLast","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":121,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_13","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":54,"type_refs":["LT.lt","List.length","List.tail","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":63,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_14","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","List.tail","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":121,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_15","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":186,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_12","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_16","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":141,"value_refs":["Eq","Eq.rec","Eq.symm","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_11","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_17","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":132,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_14","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_18","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":83,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_13","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_19","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":148,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","HAdd.hAdd","LE.le","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_20","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":91,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_21","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":210,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","Prod.fst","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":1681,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem_dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Option.some.inj","PartialOrder.toPreorder","Prod","Prod.fst","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_11","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_12","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_15","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_16","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_20","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","getElem?_pos","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_22","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":81,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":169,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_23","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":156,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1105,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_18","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_19","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_22","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_24","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":154,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1101,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_18","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_19","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_20","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_25","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":275,"type_refs":["And","Eq","Exists","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","Prod.snd","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":5115,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem_tail","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.add_lt_of_lt_sub","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.snd_darts_getElem","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_13","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_14","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_17","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_18","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_19","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_22","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_23","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","funext","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":822,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_27","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":87,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":103,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_28","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":184,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_29","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HSub.hSub","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":773,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_27","congrArg","congrFun'","eagerReduce","eq_false","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_30","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":65,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLENat","instLTNat","instOfNatNat"],"value_dag_size":58,"value_refs":["LE.le","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_31","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","instLTNat","instOfNatNat"],"value_dag_size":417,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.not_eq_of_eq_false","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_30","congrArg","eagerReduce","eq_false","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_32","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HSub.hSub","LT.lt","List.length","List.tail","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":99,"value_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_29","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_33","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":93,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":109,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_34","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":165,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1340,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_27","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_29","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_33","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_35","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":174,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":190,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_34","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_36","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","LT.lt","List.length","List.tail","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","LT.lt","Lean.Grind.nestedProof","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_31","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_37","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":149,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","instAddNat","instHAdd","instLTNat"],"value_dag_size":1116,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_30","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_31","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_38","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":102,"value_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_32","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_39","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":151,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Not","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat"],"value_dag_size":174,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_37","instAddNat","instHAdd","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_40","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","HAdd.hAdd","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":95,"value_refs":["Eq","LT.lt","Lean.Grind.nestedProof","List.getElem_tail._proof_1","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_36","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_41","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":173,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":202,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_35","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_42","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":157,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":186,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_39","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_43","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":227,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1946,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_30","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_31","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_37","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_44","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":93,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":109,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_45","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":241,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2305,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_27","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_29","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_33","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_34","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_44","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_46","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":248,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":268,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_45","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_47","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":234,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":254,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.snd_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_43","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_48","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":232,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":264,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_47","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_49","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":247,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":278,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_46","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":85,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_50","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":318,"type_refs":["And","Eq","Exists","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":4809,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_tail","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_tail","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.add_lt_of_lt_sub","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_eq_zero_iff","SimpleGraph.Walk.length_support","SimpleGraph.Walk.not_nil_iff_lt_length","SimpleGraph.Walk.snd_darts_getElem","SimpleGraph.Walk.snd_darts_getElem._proof_2","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_27","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_28","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_29","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_32","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_33","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_34","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_35","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_38","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_41","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","funext","getElem?_neg","getElem?_pos","heq_of_eq","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_51","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.dropLast","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":93,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_52","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":80,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":96,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_53","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":146,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":784,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_52","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_54","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":150,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":749,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_52","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_55","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":159,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":174,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_54","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_56","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":148,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":170,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem._proof_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_53","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_57","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":152,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_51","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_58","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":145,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":228,"value_refs":["Eq","Eq.rec","Eq.symm","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_56","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_59","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":288,"type_refs":["And","Eq","Exists","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Not","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":2599,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem_dropLast","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.lt_of_lt_of_le","Nat.not_le_eq","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.fst_darts_getElem","SimpleGraph.Walk.fst_darts_getElem._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_26","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_28","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_51","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_52","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_53","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_56","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_57","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_58","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","funext","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":82,"type_refs":["HAdd.hAdd","LE.le","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat"],"value_dag_size":707,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":90,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":82,"type_refs":["HAdd.hAdd","LE.le","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat"],"value_dag_size":714,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":null,"statement_dag_size":97,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":819,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":"abbrev","statement_dag_size":364,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":470,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","reducibility":"abbrev","statement_dag_size":385,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":493,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1323,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","Std.IsLinearOrder.toIsLinearPreorder","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support"],"value_dag_size":302,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.IsInfix","List.append_assoc","List.dropLast","List.infix_append'","List.instAppend","List.tail","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.append","SimpleGraph.Walk.support","SimpleGraph.Walk.support_append","SimpleGraph.Walk.support_append_eq_support_dropLast_append","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":95,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","List","List.instAppend","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instHAppendOfAppend","instLENat"],"value_dag_size":665,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.instAppend","List.length","List.length_append","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat"],"value_dag_size":317,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat"],"value_dag_size":368,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":142,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":"abbrev","statement_dag_size":149,"type_refs":["Eq","Exists","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append"],"value_dag_size":239,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.append"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_support_isInfix","reducibility":"abbrev","statement_dag_size":160,"type_refs":["Eq","Exists","Exists.intro","HAppend.hAppend","List","List.IsInfix","List.instAppend","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instHAppendOfAppend"],"value_dag_size":259,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.IsInfix","List.instAppend","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_darts._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_darts","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","List.IsInfix","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts"],"value_dag_size":77,"value_refs":["List.IsInfix","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.isSubwalk_iff_darts_isInfix","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_darts._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_darts","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.IsInfix","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":36,"value_refs":["List","List.IsInfix","List.cons","List.instMembership","List.nil","List.singleton_infix_iff","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_edges._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_edges","reducibility":null,"statement_dag_size":122,"type_refs":["And","Eq","Exists","List","List.instMembership","Membership.mem","Or","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Dart","SimpleGraph.Dart.edge","SimpleGraph.Dart.mk","SimpleGraph.Walk","SimpleGraph.Walk.darts","Sym2.Rel"],"value_dag_size":542,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.or_eq_of_eq_false_left","List","List.instMembership","Membership.mem","Not","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Adj.symm","SimpleGraph.Dart","SimpleGraph.Dart.edge","SimpleGraph.Dart.edge.eq_1","SimpleGraph.Dart.mk","SimpleGraph.Dart.toProd","SimpleGraph.Walk","SimpleGraph.Walk.darts","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","eq_true","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_edges.match_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_toWalk_iff_mem_edges","reducibility":"abbrev","statement_dag_size":194,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.edge","SimpleGraph.Walk","SimpleGraph.Walk.darts","Sym2","Sym2.mk"],"value_dag_size":279,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.edge","SimpleGraph.Walk","SimpleGraph.Walk.darts","Sym2","Sym2.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.length_le_of_isSubwalk._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.length_le_of_isSubwalk","reducibility":null,"statement_dag_size":55,"type_refs":["LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.length","instLENat"],"value_dag_size":602,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.IsSubwalk.eq_1","SimpleGraph.Walk.append","SimpleGraph.Walk.length","SimpleGraph.Walk.length_append","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.support"],"value_dag_size":63,"value_refs":["List.IsInfix","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.IsSubwalk","SimpleGraph.Walk.isSubwalk_iff_support_isInfix","SimpleGraph.Walk.support","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take._simp_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.IsInfix","List.IsPrefix","True"],"value_dag_size":28,"value_refs":["List","List.IsInfix","List.IsPrefix","List.IsPrefix.isInfix","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.one_lt_two","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":716,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","Nat.one_lt_two","NatCast.natCast","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","eagerReduce","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_11","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":140,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":1462,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_cons","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_7","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_8","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":52,"type_refs":["LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":44,"value_refs":["LE.le","List.cons","List.length","List.nil","Nat","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_3","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":52,"type_refs":["LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":44,"value_refs":["LE.le","List.cons","List.length","List.nil","Nat","OfNat.ofNat","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_3","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.one_lt_two","OfNat.ofNat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":687,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","Nat.one_lt_two","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","congrArg","eagerReduce","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":30,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":178,"value_refs":["Eq","Eq.rec","False","False.elim","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.ctorIdx","Nat.one_lt_two","Nat.sub_self","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","eq_false'","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":32,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":363,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_5","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_7","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":null,"statement_dag_size":28,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":44,"value_refs":["LT.lt","Lean.Grind.nestedProof","List.cons","List.length","List.nil","Nat","Nat.lt_of_succ_lt_succ","Nat.one_lt_two","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_of_infix_support","reducibility":"abbrev","statement_dag_size":384,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":493,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.nil","Nat","Option","Option.some","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_penultimate._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_penultimate","reducibility":null,"statement_dag_size":65,"type_refs":["HSub.hSub","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1346,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.adj_getVert_succ","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_length","SimpleGraph.Walk.length","SimpleGraph.Walk.length_eq_zero_iff","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_snd._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.adj_snd","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","instLTNat","instOfNatNat"],"value_dag_size":56,"value_refs":["LT.lt","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.not_nil_iff_lt_length","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.firstDart_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.firstDart_eq","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd"],"value_dag_size":42,"value_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.ext_iff","SimpleGraph.Dart.toProd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart","reducibility":null,"statement_dag_size":45,"type_refs":["List","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts"],"value_dag_size":74,"value_refs":["Eq","Iff.mp","Iff.not","List","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart","reducibility":null,"statement_dag_size":72,"type_refs":["HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":85,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.lastDart_eq._proof_2","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart","reducibility":null,"statement_dag_size":72,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":59,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","Iff.mp","Iff.not","List","List.getLast","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.lastDart"],"value_dag_size":687,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff","Iff.mp","Iff.not","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getLast","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.lastDart","SimpleGraph.Walk.lastDart_eq","SimpleGraph.Walk.lastDart_eq._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getLast_darts_eq_lastDart._proof_1_4","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","id","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":122,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1","reducibility":null,"statement_dag_size":146,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":141,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1.eq_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1","reducibility":null,"statement_dag_size":150,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":144,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.getVert.match_1","SimpleGraph.Walk.nil","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert.match_1","reducibility":"abbrev","statement_dag_size":113,"type_refs":["Nat","Nat.succ","OfNat.ofNat","SimpleGraph","SimpleGraph.Adj","SimpleGraph.Walk","SimpleGraph.Walk.cons","SimpleGraph.Walk.nil","instOfNatNat"],"value_dag_size":1,"value_refs":["SimpleGraph.Walk.getVert.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support","reducibility":null,"statement_dag_size":71,"type_refs":["Fin","Fin.val","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat"],"value_dag_size":140,"value_refs":["Eq","Eq.rec","Eq.symm","Fin","Fin.val","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support","reducibility":null,"statement_dag_size":48,"type_refs":["Fin","Fin.val","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":450,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Fin","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_1","eagerReduce","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Fin","Fin.val","Function.comp","List.get","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support"],"value_dag_size":848,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.isLt","Fin.val","Function.comp","Function.comp_apply","GetElem.getElem","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_eq_getD_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_eq_getD_support","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":85,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_eq_getD_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_eq_getD_support","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","LE.le","List.getD","Nat","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat"],"value_dag_size":750,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.getD","List.getD_eq_getElem?_getD","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Option.getD_none","Option.none","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_of_length_le","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","LE.le","LT.lt","List.idxOf","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instBEqOfDecidableEq","instLENat","instLTNat"],"value_dag_size":144,"value_refs":["DecidableEq","Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.idxOf","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","LT.lt","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instBEqOfDecidableEq","instLTNat"],"value_dag_size":472,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_1","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","List","List.idxOf","List.instMembership","Membership.mem","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instBEqOfDecidableEq"],"value_dag_size":711,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_idxOf","List.idxOf","List.idxOf_lt_length_iff","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_support_idxOf._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart","reducibility":null,"statement_dag_size":45,"type_refs":["List","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts"],"value_dag_size":74,"value_refs":["Eq","Iff.mp","Iff.not","List","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart","reducibility":null,"statement_dag_size":65,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLENat","instLTNat","instOfNatNat"],"value_dag_size":78,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart","reducibility":null,"statement_dag_size":61,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat","instOfNatNat"],"value_dag_size":80,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","Iff.mp","Iff.not","List","List.head","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.firstDart"],"value_dag_size":729,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HEq.trans","Iff.mp","Iff.mpr","Iff.not","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.head","List.head_eq_getElem","List.instGetElemNatLtLength","List.length","List.length_pos_iff","List.nil","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.firstDart","SimpleGraph.Walk.firstDart_eq","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.head_darts_eq_firstDart._proof_1_4","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq","reducibility":null,"statement_dag_size":76,"type_refs":["False","HSub.hSub","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":579,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","id","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq","reducibility":null,"statement_dag_size":62,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","instLENat","instLTNat","instOfNatNat"],"value_dag_size":309,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","List.length","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq","reducibility":null,"statement_dag_size":31,"type_refs":["LE.le","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","instLENat"],"value_dag_size":120,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq._simp_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.toProd"],"value_dag_size":42,"value_refs":["Eq","Prod","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Dart.ext_iff","SimpleGraph.Dart.toProd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","List","List.nil","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts"],"value_dag_size":67,"value_refs":["Eq","Iff.mpr","Iff.not","List","List.nil","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts","reducibility":null,"statement_dag_size":72,"type_refs":["HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":85,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.darts","SimpleGraph.Walk.lastDart_eq._proof_2","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts","reducibility":null,"statement_dag_size":65,"type_refs":["HSub.hSub","LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":60,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","Iff.mpr","Iff.not","List","List.getLast","List.nil","Not","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.lastDart"],"value_dag_size":695,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff","Iff.mpr","Iff.not","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getLast","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Dart","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.darts","SimpleGraph.Walk.darts_eq_nil","SimpleGraph.Walk.lastDart","SimpleGraph.Walk.lastDart_eq","SimpleGraph.Walk.lastDart_eq._proof_2","SimpleGraph.Walk.length","SimpleGraph.Walk.length_darts","SimpleGraph.Walk.not_nil_iff_lt_length","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_2","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_3","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.lastDart_eq_getLast_darts._proof_1_4","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","id","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists","reducibility":null,"statement_dag_size":82,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2.Rel","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":98,"value_refs":["HAdd.hAdd","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","Nat","OfNat.ofNat","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2.Rel","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists","reducibility":null,"statement_dag_size":123,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","Sym2.Rel","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1041,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_iff_getElem","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Prod","Prod.mk","Quot","Quot.mk","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.getElem_edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_edges","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_1","congrArg","congrFun'","eagerReduce","eq_true","exists_prop_congr","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","or_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","Sym2.Rel","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":343,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Prod","Quot","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.length","SimpleGraph.Walk.length_edges","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_1","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists","reducibility":null,"statement_dag_size":73,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2.Rel","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["LE.le","List.length","Nat","OfNat.ofNat","Prod","Quot","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","Sym2.Rel","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_1","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists","reducibility":null,"statement_dag_size":110,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","List","List.instMembership","Membership.mem","Nat","OfNat.ofNat","Prod","Prod.mk","Quot","Quot.mk","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","Sym2.Rel","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1020,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAdd.hAdd","Iff","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_iff_getElem","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod","Prod.mk","Quot","Quot.mk","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.edges","SimpleGraph.Walk.getElem_edges","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.length_edges","Sym2","Sym2.Rel","Sym2.mk","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.mk_mem_edges_iff_exists._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","exists_prop_congr","forall_congr","forall_not_of_not_exists","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":52,"type_refs":["HSub.hSub","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":47,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_10","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":82,"type_refs":["HSub.hSub","List","List.dropLast","List.instMembership","Membership.mem","Nat","Ne","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.penultimate","SimpleGraph.Walk.support","instHSub","instOfNatNat","instSubNat"],"value_dag_size":426,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","HSub.hSub","Iff","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getLast_support","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_mem_support","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.length","SimpleGraph.Walk.penultimate","SimpleGraph.Walk.support","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","instHSub","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","instHAppendOfAppend"],"value_dag_size":184,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","True","cast","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":76,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.isEmpty","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"],"value_dag_size":224,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","True","cast","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":91,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.isEmpty","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"],"value_dag_size":91,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.isEmpty","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":95,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":414,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":87,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.dropLast","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":99,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.dropLast","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_7","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.length","List.nil","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":566,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","True","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_8","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.nil","Ne","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"],"value_dag_size":163,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.ctorIdx","List.getLast","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_4","eq_false'","implies_congr","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support._proof_1_9","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.penultimate_mem_dropLast_support","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support"],"value_dag_size":122,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.getLast","List.nil","Not","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.head_support._proof_1","SimpleGraph.Walk.support","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem","reducibility":null,"statement_dag_size":67,"type_refs":["Fin","List.get","List.length","Membership.mem","Nat","Set","Set.instMembership","Set.range","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support"],"value_dag_size":313,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Iff","Lean.Grind.iff_eq","List","List.get","List.instMembership","List.length","Membership.mem","Nat","Not","Set","Set.instMembership","Set.mem_ofPred_eq","Set.mem_range","Set.ofPred","Set.range","Set.range_list_get","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_mem_support","SimpleGraph.Walk.support","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_4","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem","reducibility":null,"statement_dag_size":48,"type_refs":["Fin","Fin.val","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat"],"value_dag_size":41,"value_refs":["Fin","Fin.isLt","List.length","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_5","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem","reducibility":null,"statement_dag_size":71,"type_refs":["Fin","Fin.val","LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat"],"value_dag_size":140,"value_refs":["Eq","Eq.rec","Eq.symm","Fin","Fin.val","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_6","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Fin","Fin.val","List.get","List.length","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support"],"value_dag_size":732,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","GetElem.getElem","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_4","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem._proof_1_5","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem.match_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.range_getVert_eq_range_support_getElem","reducibility":"abbrev","statement_dag_size":127,"type_refs":["Eq","Exists.intro","Fin","List.get","List.length","Membership.mem","Set","Set.instMembership","Set.range","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"],"value_dag_size":158,"value_refs":["Eq","Exists.casesOn","Exists.intro","Fin","List.get","List.length","Membership.mem","Set","Set.instMembership","Set.range","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.snd_eq_support_getElem_one._proof_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.snd_eq_support_getElem_one","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List.length","Nat","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":450,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.Nil","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.not_nil_iff_lt_length","SimpleGraph.Walk.support","True","congrArg","eagerReduce","eq_false","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_eq_getVert._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_eq_getVert","reducibility":null,"statement_dag_size":50,"type_refs":["LE.le","LT.lt","List.length","Nat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat"],"value_dag_size":435,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate","reducibility":null,"statement_dag_size":73,"type_refs":["HSub.hSub","LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":128,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate","reducibility":null,"statement_dag_size":113,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":541,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1_1","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate","reducibility":null,"statement_dag_size":91,"type_refs":["Eq","GetElem.getElem","HSub.hSub","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.length","SimpleGraph.Walk.support","SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":754,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_length_sub_one_eq_penultimate._proof_1_1","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_1","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one","reducibility":null,"statement_dag_size":55,"type_refs":["LE.le","LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.support","instLENat","instLTNat","instOfNatNat"],"value_dag_size":107,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","LE.le","LT.lt","List.length","Nat","Nat.lt_add_one_of_le","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_2","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":386,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_1","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.SimpleGraph.Walk.Traversal","name":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_3","namespace":"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.support","instLTNat","instOfNatNat"],"value_dag_size":639,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.lt_add_one_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SimpleGraph","SimpleGraph.Walk","SimpleGraph.Walk.getVert","SimpleGraph.Walk.getVert_eq_support_getElem","SimpleGraph.Walk.length","SimpleGraph.Walk.length_support","SimpleGraph.Walk.support","True","True.intro","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_1","_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.support_getElem_one._proof_1_2","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext","reducibility":"abbrev","statement_dag_size":176,"type_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.mk","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","HasQuotient.Quotient","Membership.mem","MulAction","MulAction.stabilizer","QuotientGroup.instHasQuotientSubgroup","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"],"value_dag_size":265,"value_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.casesOn","DiscreteTiling.PlacedTile.mk","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","HasQuotient.Quotient","Membership.mem","MulAction","MulAction.stabilizer","QuotientGroup.instHasQuotientSubgroup","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext_iff_of_exists.match_1_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext_iff_of_exists","reducibility":"abbrev","statement_dag_size":821,"type_refs":["And","And.intro","DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.groupElts","DiscreteTiling.PlacedTile.index","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Eq","Exists","Exists.intro","Group","Group.toDivInvMonoid","Membership.mem","MulAction","MulAction.stabilizer","Quotient","Quotient.mk","QuotientGroup.leftRel","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"],"value_dag_size":1151,"value_refs":["And","And.casesOn","And.intro","DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.groupElts","DiscreteTiling.PlacedTile.index","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Eq","Exists","Exists.casesOn","Exists.intro","Group","Group.toDivInvMonoid","Membership.mem","MulAction","MulAction.stabilizer","Quotient","Quotient.mk","QuotientGroup.leftRel","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext_iff_of_preimage.match_1_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.ext_iff_of_preimage","reducibility":"abbrev","statement_dag_size":711,"type_refs":["And","And.intro","DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.groupElts","DiscreteTiling.PlacedTile.index","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Eq","Group","Group.toDivInvMonoid","HasQuotient.Quotient","Membership.mem","MulAction","MulAction.stabilizer","Quotient","Quotient.mk","QuotientGroup.instHasQuotientSubgroup","QuotientGroup.leftRel","Set","Set.instSingletonSet","Set.mulActionSet","Set.preimage","SetLike.instMembership","Singleton.singleton","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"],"value_dag_size":727,"value_refs":["And","And.casesOn","And.intro","DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.groupElts","DiscreteTiling.PlacedTile.index","DiscreteTiling.Protoset","DiscreteTiling.Protoset.tiles","DiscreteTiling.Prototile.carrier","DiscreteTiling.Prototile.symmetries","DivInvMonoid.toMonoid","Eq","Group","Group.toDivInvMonoid","HasQuotient.Quotient","Membership.mem","MulAction","MulAction.stabilizer","Quotient","Quotient.mk","QuotientGroup.instHasQuotientSubgroup","QuotientGroup.leftRel","Set","Set.instSingletonSet","Set.mulActionSet","Set.preimage","SetLike.instMembership","Singleton.singleton","Subgroup","Subgroup.instSetLike","Subgroup.map","Subgroup.subtype","Subgroup.toGroup","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.instSMul._simp_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.instSMul","reducibility":null,"statement_dag_size":95,"type_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","HasQuotient.Quotient","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","QuotientGroup.instHasQuotientSubgroup","QuotientGroup.mk","SetLike.instMembership","Subgroup","Subgroup.instSetLike","instHMul"],"value_dag_size":100,"value_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HMul.hMul","HasQuotient.Quotient","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","QuotientGroup.eq","QuotientGroup.instHasQuotientSubgroup","QuotientGroup.mk","SetLike.instMembership","Subgroup","Subgroup.instSetLike","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.instSMul._simp_2","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.instSMul","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem","reducibility":null,"statement_dag_size":86,"type_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.coeSet","DiscreteTiling.PlacedTile.instMembership","DiscreteTiling.Protoset","DivInvMonoid.toMonoid","Eq","Group","Group.toDivInvMonoid","Membership.mem","MulAction","Set","Set.instMembership"],"value_dag_size":100,"value_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.coeSet","DiscreteTiling.PlacedTile.instMembership","DiscreteTiling.PlacedTile.mem_coe","DiscreteTiling.Protoset","DivInvMonoid.toMonoid","Eq.symm","Group","Group.toDivInvMonoid","Membership.mem","MulAction","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem","reducibility":null,"statement_dag_size":101,"type_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HSMul.hSMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toSemigroup","MulAction","MulAction.toSemigroupAction","SemigroupAction.toSMul","Set","Set.instMembership","Set.smulSet","instHSMul"],"value_dag_size":108,"value_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HSMul.hSMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toSemigroup","MulAction","MulAction.toSemigroupAction","SemigroupAction.toSMul","Set","Set.instMembership","Set.mem_inv_smul_set_iff","Set.smulSet","instHSMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem","reducibility":null,"statement_dag_size":86,"type_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.coeSet","DiscreteTiling.PlacedTile.instMembership","DiscreteTiling.Protoset","DivInvMonoid.toMonoid","Eq","Group","Group.toDivInvMonoid","Membership.mem","MulAction","Set","Set.instMembership"],"value_dag_size":100,"value_refs":["DiscreteTiling.PlacedTile","DiscreteTiling.PlacedTile.coeSet","DiscreteTiling.PlacedTile.instMembership","DiscreteTiling.PlacedTile.mem_coe","DiscreteTiling.Protoset","DivInvMonoid.toMonoid","Eq.symm","Group","Group.toDivInvMonoid","Membership.mem","MulAction","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem","reducibility":null,"statement_dag_size":101,"type_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HSMul.hSMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toSemigroup","MulAction","MulAction.toSemigroupAction","SemigroupAction.toSMul","Set","Set.instMembership","Set.smulSet","instHSMul"],"value_dag_size":108,"value_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Group","Group.toDivInvMonoid","Group.toDivisionMonoid","HSMul.hSMul","Inv.inv","InvOneClass.toInv","Membership.mem","Monoid.toSemigroup","MulAction","MulAction.toSemigroupAction","SemigroupAction.toSMul","Set","Set.instMembership","Set.mem_smul_set_iff_inv_smul_mem","Set.smulSet","instHSMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.Protoset.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.Protoset.ext","reducibility":"abbrev","statement_dag_size":60,"type_refs":["DiscreteTiling.Protoset","DiscreteTiling.Protoset.mk","DiscreteTiling.Prototile","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","MulAction"],"value_dag_size":83,"value_refs":["DiscreteTiling.Protoset","DiscreteTiling.Protoset.casesOn","DiscreteTiling.Protoset.mk","DiscreteTiling.Prototile","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","MulAction"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Tiling.Tile","name":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.Prototile.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.Prototile.ext","reducibility":"abbrev","statement_dag_size":109,"type_refs":["DiscreteTiling.Prototile","DiscreteTiling.Prototile.mk","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","Membership.mem","MulAction","MulAction.stabilizer","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.toGroup","Subtype"],"value_dag_size":162,"value_refs":["DiscreteTiling.Prototile","DiscreteTiling.Prototile.casesOn","DiscreteTiling.Prototile.mk","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","Membership.mem","MulAction","MulAction.stabilizer","Set","Set.mulActionSet","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.toGroup","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1.eq_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.cons","List.nil","Nat","Unit","Unit.unit","YoungDiagram.cellsOfRowLens.match_1"],"value_dag_size":33,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Unit","YoungDiagram.cellsOfRowLens.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1.eq_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.cons","List.nil","Nat","Unit","YoungDiagram.cellsOfRowLens.match_1"],"value_dag_size":39,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Unit","YoungDiagram.cellsOfRowLens.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1.splitter","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.cellsOfRowLens.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":1,"value_refs":["YoungDiagram.cellsOfRowLens.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Prod","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.col","YoungDiagram.instSetLikeProdNat"],"value_dag_size":55,"value_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Prod","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.col","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_col_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.colLen","YoungDiagram.instSetLikeProdNat","instLTNat"],"value_dag_size":44,"value_refs":["LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.colLen","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_iff_lt_colLen","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.col_eq_prod","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ext.match_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ext","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Finset","Finset.instSetLike","IsLowerSet","Nat","Prod","Prod.instLE_mathlib","SetLike.coe","YoungDiagram","YoungDiagram.mk","instLENat"],"value_dag_size":49,"value_refs":["Finset","Finset.instSetLike","IsLowerSet","Nat","Prod","Prod.instLE_mathlib","SetLike.coe","YoungDiagram","YoungDiagram.casesOn","YoungDiagram.mk","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.instOrderBot._simp_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.instOrderBot","reducibility":null,"statement_dag_size":26,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":28,"value_refs":["EmptyCollection.emptyCollection","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.instOrderBot._simp_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.instOrderBot","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens._proof_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens","reducibility":null,"statement_dag_size":46,"type_refs":["False","LE.le","LT.lt","List","List.length","Nat","Not","Prod.fst","Prod.mk","instLENat","instLTNat"],"value_dag_size":494,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","GetElem.getElem","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_fst_mk","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List","List.cons","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Prod.fst","Prod.mk","id","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.ofRowLens","instLTNat"],"value_dag_size":81,"value_refs":["Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_ofRowLens","YoungDiagram.ofRowLens","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.colLen","YoungDiagram.instSetLikeProdNat","instLTNat"],"value_dag_size":50,"value_refs":["Eq.symm","LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.colLen","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_iff_lt_colLen","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.rowLen","instLTNat"],"value_dag_size":44,"value_refs":["LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_iff_lt_rowLen","YoungDiagram.rowLen","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens._proof_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens","reducibility":null,"statement_dag_size":26,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":351,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Not","instLTNat"],"value_dag_size":52,"value_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Nat.find_eq_iff","Not","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLen_ofRowLens","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.ofRowLens","instLTNat"],"value_dag_size":81,"value_refs":["Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_ofRowLens","YoungDiagram.ofRowLens","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Not","instLTNat"],"value_dag_size":52,"value_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Nat.find_eq_iff","Not","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.ofRowLens","instLTNat"],"value_dag_size":81,"value_refs":["Exists","GetElem.getElem","LT.lt","List","List.SortedGE","List.instGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.instPreorder","Prod","Prod.fst","Prod.snd","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_ofRowLens","YoungDiagram.ofRowLens","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists","False","IsEmpty"],"value_dag_size":25,"value_refs":["Exists","False","IsEmpty","IsEmpty.exists_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.rowLens_length_ofRowLens","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_3","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_4","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Prod","Prod.fst","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.row"],"value_dag_size":55,"value_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Prod","Prod.fst","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_row_iff","YoungDiagram.row","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_5","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.rowLen","instLTNat"],"value_dag_size":44,"value_refs":["LT.lt","Membership.mem","Nat","Prod","Prod.mk","SetLike.instMembership","YoungDiagram","YoungDiagram.instSetLikeProdNat","YoungDiagram.mem_iff_lt_rowLen","YoungDiagram.rowLen","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_6","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod._simp_1_7","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.row_eq_prod","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.transpose._simp_1","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.transpose","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Combinatorics.Young.YoungDiagram","name":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.transpose._simp_2","namespace":"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.transpose","reducibility":null,"statement_dag_size":82,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.instSetLike","Finset.map","Membership.mem","SetLike.instMembership"],"value_dag_size":87,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.instSetLike","Finset.map","Finset.mem_map_equiv","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1.eq_1","namespace":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.Partrec.Code.pappAck.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.pappAck.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1.eq_2","namespace":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.Partrec.Code.pappAck.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.pappAck.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1.splitter","namespace":"_private.Mathlib.Computability.Ackermann.0.Nat.Partrec.Code.pappAck.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.pappAck.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Computability.Ackermann.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack.match_1._arg_pusher","namespace":"_private.Mathlib.Computability.Ackermann.0.ack.match_1","reducibility":null,"statement_dag_size":141,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"],"value_dag_size":467,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Computability.Ackermann.0.ack.match_1.splitter","ack.match_1","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack.match_1.eq_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack.match_1.eq_2","namespace":"_private.Mathlib.Computability.Ackermann.0.ack.match_1","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"],"value_dag_size":48,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack.match_1.eq_3","namespace":"_private.Mathlib.Computability.Ackermann.0.ack.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","ack.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack.match_1.splitter","namespace":"_private.Mathlib.Computability.Ackermann.0.ack.match_1","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["ack.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_four._proof_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_four","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":115,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.instPreorder","Nat.not_le_eq","Not","OfNat.ofNat","Preorder.toLE","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_three._proof_1_3","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_three","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":163,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.decLe","Nat.instPreorder","Nat.not_le_eq","Not","OfNat.ofNat","Preorder.toLE","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_three.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_add_one_sq_lt_ack_add_three","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_pos.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_pos","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_strictMono_right.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_strictMono_right","reducibility":"abbrev","statement_dag_size":91,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.instPreorder","Nat.succ","OfNat.ofNat","Preorder.toLT","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":304,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LT.lt","Nat","Nat.casesOn","Nat.ctorIdx","Nat.instPreorder","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","Preorder.toLT","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'","namespace":"_private.Mathlib.Computability.Ackermann.0","reducibility":null,"statement_dag_size":21,"type_refs":["LT.lt","Nat","ack","instLTNat"],"value_dag_size":22,"value_refs":["Nat","PSigma","PSigma.mk","_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'._unary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'._proof_1_3","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'","reducibility":null,"statement_dag_size":38,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":166,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'._unary","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'","reducibility":null,"statement_dag_size":31,"type_refs":["LT.lt","Nat","PSigma","ack","instLTNat"],"value_dag_size":1180,"value_refs":["AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","Bool","Bool.true","Decidable.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","False.elim","HAdd.hAdd","HSub.hSub","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_nonneg_of_le","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsRightCancelAdd.addRightStrictMono_of_addRightMono","LE.le","LT.lt","LT.lt.trans","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","Lean.opaqueId","List.cons","List.nil","Nat","Nat.cast","Nat.decLt","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instLinearOrder","Nat.instPartialOrder","Nat.instPreorder","Nat.instTransLe","Nat.instTransLeLt","Nat.le_of_not_lt","Nat.not_lt_zero","Nat.succ","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","PSigma","PSigma.casesOn","PSigma.mk","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.Lex","Prod.Lex.left","Prod.Lex.right","Prod.instWellFoundedRelation","Prod.mk","Trans.trans","WellFounded","WellFounded.fix","_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'._proof_1_3","_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'.match_1_1","ack","ack_strictMono_right","ack_succ_succ","ack_succ_zero","ack_zero","addRightReflectLE_of_addLeftReflectLE","add_add_one_le_ack","add_le_add","add_lt_ack","add_lt_add_iff_right","congr","congrArg","contravariant_lt_of_covariant_le","contravariant_swap_add_of_contravariant_add","covariant_swap_add_of_covariant_add","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instIsRightCancelAddOfAddRightReflectLE","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSizeOfNat","invImage","le_of_le_of_eq","le_refl","of_decide_eq_true","one_lt_ack_succ_right","sizeOfWFRel","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_strict_mono_left'","reducibility":"abbrev","statement_dag_size":61,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":110,"value_refs":["Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_succ_right_le_ack_succ_left._proof_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_succ_right_le_ack_succ_left","reducibility":null,"statement_dag_size":40,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":170,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.instPreorder","Nat.not_le_eq","Not","OfNat.ofNat","Preorder.toLE","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_three._proof_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_three","reducibility":null,"statement_dag_size":36,"type_refs":["LE.le","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","Nat","Nat.instMonoidWithZero","Nat.instPreorder","OfNat.ofNat","One.toOfNat1","Preorder.toLE","instOfNatNat"],"value_dag_size":103,"value_refs":["Bool","Bool.false","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","Nat","Nat.decLe","Nat.instMonoidWithZero","Nat.instPreorder","Nat.not_le_eq","Not","OfNat.ofNat","One.toOfNat1","Preorder.toLE","eq_false_of_decide","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.ack_three._proof_1_2","namespace":"_private.Mathlib.Computability.Ackermann.0.ack_three","reducibility":null,"statement_dag_size":27,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":90,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_le_gt","Nat.decLt","Nat.not_le_eq","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.add_lt_ack._proof_1_3","namespace":"_private.Mathlib.Computability.Ackermann.0.add_lt_ack","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":163,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.add_lt_ack.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.add_lt_ack","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec._proof_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec","reducibility":null,"statement_dag_size":45,"type_refs":["HAdd.hAdd","LT.lt","LinearOrder.toMax","Max.max","Nat","Nat.instLinearOrder","Nat.instMax","Nat.instPreorder","OfNat.ofNat","Preorder.toLT","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":185,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","LinearOrder.toMax","Max.max","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.instLinearOrder","Nat.instMax","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLT","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec._proof_1_2","namespace":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec","reducibility":null,"statement_dag_size":29,"type_refs":["False","LE.le","Max.max","Nat","Nat.instMax","Nat.instPreorder","Not","Preorder.toLE"],"value_dag_size":693,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMax","Int.instNegInt","Int.instSub","Int.max_def","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_max","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.coordinate_eval_6","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Max.max","Nat","Nat.cast","Nat.instMax","Nat.instPreorder","Nat.lt_of_not_le","Nat.pair","Nat.rec","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","Preorder.toLE","ack","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec._proof_1_3","namespace":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec","reducibility":null,"statement_dag_size":32,"type_refs":["False","LE.le","Nat","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","instOfNatNat"],"value_dag_size":232,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.mk","Lean.Omega.tidy_sat","List.cons","List.nil","Max.max","Nat","Nat.cast","Nat.instMax","Nat.instPreorder","Nat.lt_of_not_le","Nat.pair","Nat.rec","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Preorder.toLE","ack","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec._proof_1_4","namespace":"_private.Mathlib.Computability.Ackermann.0.exists_lt_ack_of_nat_primrec","reducibility":null,"statement_dag_size":40,"type_refs":["False","HAdd.hAdd","LE.le","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":472,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Max.max","Nat","Nat.cast","Nat.instMax","Nat.lt_of_not_le","Nat.pair","Nat.rec","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","ack","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.one_lt_ack_succ_left.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.one_lt_ack_succ_left","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.one_lt_ack_succ_right.match_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.one_lt_ack_succ_right","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":42,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three","namespace":"_private.Mathlib.Computability.Ackermann.0","reducibility":null,"statement_dag_size":66,"type_refs":["HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHPow","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":318,"value_refs":["AddMonoid.toAddZeroClass","Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.casesAuxOn","Nat.decLe","Nat.instAddMonoid","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instMonoid","Nat.instMonoidWithZero","Nat.instNeZeroSucc","Nat.instPreorder","Nat.recAux","Nat.sub_eq_zero_of_le","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","Std.le_refl._simp_1","True","Zero.toOfNat0","_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three._proof_1_1","_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three._proof_1_2","congr","congrArg","congrFun'","eq_true_of_decide","instAddNat","instHAdd","instHPow","instHSub","instLENat","instOfNatNat","instReflLe","instSubNat","not_false_eq_true","of_eq_true","pow_one","zero_add","zero_pow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three._proof_1_1","namespace":"_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three","reducibility":null,"statement_dag_size":70,"type_refs":["HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHPow","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":132,"value_refs":["Bool","Bool.false","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Monoid.toNPow","NPow.toPow","Nat","Nat.decLe","Nat.instMonoid","Nat.not_le_eq","Nat.one_pow","Not","OfNat.ofNat","congrArg","eq_false_of_decide","instAddNat","instHAdd","instHPow","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Ackermann","name":"_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three._proof_1_2","namespace":"_private.Mathlib.Computability.Ackermann.0.sq_le_two_pow_add_one_minus_three","reducibility":null,"statement_dag_size":83,"type_refs":["HAdd.hAdd","HPow.hPow","HSub.hSub","LE.le","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instHPow","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":2650,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_def'_norm","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Nonneg.natCast","Int.Nonneg.pow","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNatPow","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_pow","Lean.Grind.Semiring.npow","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.mulR","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.instMonoid","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_10","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":74,"type_refs":["GE.ge","GT.gt","HMul.hMul","Inv.inv","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instInv","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instZero","Zero.toOfNat0","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":533,"value_refs":["Bool","Bool.true","Classical.byContradiction","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","Eq","Eq.mp","Eq.refl","Eq.trans","False","Field.toGrindField","Field.toSemifield","GE.ge","GT.gt","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HMul.hMul","Iff","Int","Int.instNegInt","Inv.inv","InvOneClass.toInv","IsStrictOrderedRing.toPosMulStrictMono","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.le_norm","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_norm","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.toRing","Lean.Grind.Field.toCommRing","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Ring.toIntModule","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","Not","OfNat.ofNat","One.one","PartialOrder.toPreorder","PosMulReflectLE.toPosMulReflectLT","PosMulStrictMono.toPosMulReflectLE","Preorder.toLT","Real","Real.instAddCommMonoid","Real.instField","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","True","Zero.toOfNat0","eagerReduce","eq_true","id","instHMul","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instMulZeroClassOfSemiring","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing","inv_pos","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_11","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":82,"type_refs":["AkraBazziRecurrence","AkraBazziRecurrence.n₀","Fintype","LE.le","Nat","Nat.instPreorder","Nonempty","Preorder.toLE","Real","instLENat"],"value_dag_size":447,"value_refs":["AkraBazziRecurrence","AkraBazziRecurrence.n₀","Bool","Bool.true","Classical.byContradiction","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","HAdd.hAdd","Int","Int.instAdd","Int.instConditionallyCompleteLinearOrder","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Nonempty","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_12","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":59,"type_refs":["Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","SetLike.instMembership","instLENat","instLTNat"],"value_dag_size":243,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.iff_eq","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","forall_congr","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_13","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":135,"type_refs":["AkraBazziRecurrence.p","AkraBazziRecurrence.smoothingFn","Fintype","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Nat","Nat.cast","NatCast.natCast","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPow","Real.instPreorder","Real.instSub","instHMul","instHPow","instHSub"],"value_dag_size":226,"value_refs":["AkraBazziRecurrence.p","AkraBazziRecurrence.smoothingFn","Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fintype","HMul.hMul","HPow.hPow","HSub.hSub","LE.le","Nat","Nat.cast","NatCast.natCast","Not","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instLE","Real.instMul","Real.instNatCast","Real.instOne","Real.instPow","Real.instPreorder","Real.instSub","True","True.intro","eq_false","eq_true","id","instHMul","instHPow","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":122,"type_refs":["AkraBazziRecurrence.min_bi","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Field.toSemifield","Finite.of_fintype","Fintype","GroupWithZero.toMonoidWithZero","HDiv.hDiv","LT.lt","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instDivInvMonoid","Real.instField","Real.instLT","Real.instNatCast","Real.instZero","Real.partialOrder","Semifield.toDivisionSemiring","Zero.toOfNat0","instHDiv","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":254,"value_refs":["AkraBazziRecurrence.min_bi","Classical.byContradiction","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq.mp","Eq.symm","Eq.trans","False","Field.toGrindField","Field.toSemifield","Finite","Finite.of_fintype","Fintype","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","Inv.inv","LT.lt","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nonempty","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLT","Real.instMul","Real.instNatCast","Real.instZero","Real.partialOrder","Semifield.toDivisionSemiring","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","id","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":120,"type_refs":["AkraBazziRecurrence.min_bi","DivInvMonoid.toDiv","Finite.of_fintype","Fintype","HDiv.hDiv","HMul.hMul","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Nonempty","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":334,"value_refs":["AkraBazziRecurrence.min_bi","Classical.byContradiction","DivInvMonoid.toDiv","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Finite","Finite.of_fintype","Fintype","HDiv.hDiv","HMul.hMul","Inv.inv","LE.le","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Nonempty","Not","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLE","Real.instMul","Real.instNatCast","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","id","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_5","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":28,"type_refs":["LE.le","LT.lt","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":37,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_6","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","Real","Real.instLT","Real.instZero","Zero.toOfNat0","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":93,"value_refs":["Eq.mpr_prop","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","Real","Real.instLT","Real.instZero","Zero.toOfNat0","forall_congr","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_7","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":108,"value_refs":["Eq.mpr_prop","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","forall_congr","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_8","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":123,"type_refs":["Asymptotics.IsLittleO","DivInvMonoid.toDiv","Filter.atTop","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NatCast.natCast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.log","Real.norm","instHDiv","instHMul","instHPow","instHSub","instOfNatNat"],"value_dag_size":194,"value_refs":["Asymptotics.IsLittleO","DivInvMonoid.toDiv","Eq.mpr_prop","Field.toGrindField","Filter.atTop","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NatCast.natCast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.log","Real.norm","congrArg","forall_congr","funext","instHDiv","instHMul","instHPow","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_9","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound","reducibility":null,"statement_dag_size":76,"type_refs":["AkraBazziRecurrence","AkraBazziRecurrence.n₀","Fintype","LE.le","LT.lt","Nat","Nat.instPreorder","Nonempty","Preorder.toLE","Real","instLTNat"],"value_dag_size":1464,"value_refs":["AkraBazziRecurrence","AkraBazziRecurrence.GrowsPolynomially","AkraBazziRecurrence.casesOn","AkraBazziRecurrence.mk","AkraBazziRecurrence.n₀","Asymptotics.IsLittleO","Bool","Bool.false","Bool.true","Classical.byContradiction","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Filter.atTop","Finset.sum","Finset.univ","Fintype","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instAdd","Int.instConditionallyCompleteLinearOrder","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.intro_with_eq'","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Nonempty","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.instZero","Real.log","Real.norm","True","True.intro","Zero.toOfNat0","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_5","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_6","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_7","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound._proof_1_8","congrArg","eagerReduce","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_AkraBazzi___macroRules__private_Mathlib_Computability_AkraBazzi_AkraBazzi_0_AkraBazziRecurrence_termε_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":191,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_AkraBazzi___unexpand_AkraBazziRecurrence_smoothingFn_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":181,"value_refs":["Applicative.toPure","Bind.bind","Bool.false","Bool.or","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instMonadExceptOfMonadExceptOf","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HPow.hPow","Inv.inv","Neg.neg","OfNat.ofNat","One.toOfNat1","Real","Real.instInv","Real.instNeg","Real.instOne","Real.instPow","instHPow"],"value_dag_size":41,"value_refs":["Eq.symm","HPow.hPow","Inv.inv","Neg.neg","OfNat.ofNat","One.toOfNat1","Real","Real.instInv","Real.instNeg","Real.instOne","Real.instPow","Real.rpow_neg_one","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn","reducibility":null,"statement_dag_size":70,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","Asymptotics.IsLittleO","Eq","Filter","Neg.neg","NegZeroClass.toNeg","Norm","SeminormedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid"],"value_dag_size":78,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","Asymptotics.IsLittleO","Asymptotics.isLittleO_neg_left","Filter","Neg.neg","NegZeroClass.toNeg","Norm","SeminormedAddCommGroup","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toNorm","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_ge._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_ge","reducibility":null,"statement_dag_size":55,"type_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul"],"value_dag_size":62,"value_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq.symm","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul","mul_div_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_le._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_le","reducibility":null,"statement_dag_size":55,"type_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul"],"value_dag_size":62,"value_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq.symm","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul","mul_div_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_10","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":69,"type_refs":["GE.ge","GT.gt","HMul.hMul","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","Real","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instZero","Zero.toOfNat0","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":411,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","Field.toGrindField","GE.ge","GT.gt","HMul.hMul","Int","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.le_norm","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_norm","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.toRing","Lean.Grind.Field.toCommRing","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Ring.toIntModule","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","Not","OfNat.ofNat","One.one","Real","Real.instAddCommMonoid","Real.instField","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Zero.toOfNat0","eagerReduce","id","instHMul","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_11","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":137,"type_refs":["AkraBazziRecurrence","AkraBazziRecurrence.n₀","Eq","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.instPreorder","NatCast.natCast","Nonempty","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","instHAdd","instHMul","instLENat","instLTNat"],"value_dag_size":1697,"value_refs":["AkraBazziRecurrence","AkraBazziRecurrence.GrowsPolynomially","AkraBazziRecurrence.casesOn","AkraBazziRecurrence.min_bi","AkraBazziRecurrence.mk","AkraBazziRecurrence.n₀","Asymptotics.IsLittleO","Bool","Bool.true","Classical.byContradiction","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Filter.atTop","Finite","Finite.of_fintype","Finset.sum","Finset.univ","Fintype","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instAdd","Int.instConditionallyCompleteLinearOrder","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.diseq_to_eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq'","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.instPreorder","NatCast.natCast","Neg.neg","Nonempty","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSub","Real.instZero","Real.log","Real.norm","Real.partialOrder","Real.semiring","True","Zero.toOfNat0","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_5","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_6","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_7","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_8","congrArg","eagerReduce","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLawfulOrderLT_mathlib","instNatCastInt","instOfNat","instOfNatNat","instOrderedRingOfIsStrictOrderedRing","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_12","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":109,"type_refs":["CommRing.toNonUnitalCommRing","Distrib.toMul","Eq","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","Nat","NatCast.natCast","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","instHAdd","instHMul"],"value_dag_size":586,"value_refs":["Bool","Bool.true","Classical.byContradiction","CommRing.toNonUnitalCommRing","Distrib.toMul","Eq","Eq.mp","Eq.refl","Eq.trans","Exists","Exists.casesOn","False","Field.toGrindField","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instNegInt","Inv.inv","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.diseq_to_eq","Lean.Grind.CommRing.toRing","Lean.Grind.Field.toCommRing","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","NatCast.natCast","Neg.neg","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","Or","Or.casesOn","Real","Real.commRing","Real.instAdd","Real.instAddCommMonoid","Real.instField","Real.instInv","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instPreorder","Real.instSub","Real.partialOrder","Real.semiring","congrArg","eagerReduce","eq_false","funext","id","instHAdd","instHMul","instHSub","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatNat","instOrderedRingOfIsStrictOrderedRing","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_13","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":59,"type_refs":["Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","SetLike.instMembership","instLENat","instLTNat"],"value_dag_size":243,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.iff_eq","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","forall_congr","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_14","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":137,"type_refs":["AkraBazziRecurrence.asympBound","AkraBazziRecurrence.p","AkraBazziRecurrence.smoothingFn","Eq","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Nat","NatCast.natCast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instAddCommMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPow","Real.instSub","instHAdd","instHMul","instHPow","instHSub"],"value_dag_size":714,"value_refs":["AkraBazziRecurrence.asympBound","AkraBazziRecurrence.p","AkraBazziRecurrence.smoothingFn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","Exists","Exists.casesOn","False","Field.toGrindField","Finset.sum","Finset.univ","Fintype","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instNegInt","Inv.inv","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.diseq_to_eq","Lean.Grind.CommRing.toRing","Lean.Grind.Field.toCommRing","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","One.toOfNat1","Or","Or.casesOn","Real","Real.instAdd","Real.instAddCommMonoid","Real.instField","Real.instInv","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instOne","Real.instPow","Real.instPreorder","Real.instSub","Real.partialOrder","Real.semiring","congrArg","eagerReduce","eq_false","funext","id","instHAdd","instHMul","instHPow","instHSub","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatNat","instOrderedRingOfIsStrictOrderedRing","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_15","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":93,"type_refs":["AkraBazziRecurrence.smoothingFn","DivInvMonoid.toDiv","HAdd.hAdd","HDiv.hDiv","HSub.hSub","LT.lt","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","OfNat.ofNat","One.toOfNat1","Real","Real.instAdd","Real.instDivInvMonoid","Real.instLT","Real.instNatCast","Real.instOne","Real.instSub","instHAdd","instHDiv","instHSub","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":551,"value_refs":["AkraBazziRecurrence.smoothingFn","Bool","Bool.true","Classical.byContradiction","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.refl","Eq.trans","False","Field.toGrindField","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","Int","Int.instNegInt","Inv.inv","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.inv_int_eq'","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.lt_cancel_var","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_mul","Lean.Grind.CommRing.lt_norm","Lean.Grind.CommRing.not_lt_norm","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Linarith.zero_lt_one","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toIntModule","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.one_mul","Lean.Grind.Semiring.toMul","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","One.one","One.toOfNat1","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSub","Real.linearOrder","Real.partialOrder","Real.semiring","congrArg","congrFun'","eagerReduce","id","instHAdd","instHDiv","instHMul","instHSub","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":122,"type_refs":["AkraBazziRecurrence.min_bi","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Field.toSemifield","Finite.of_fintype","Fintype","GroupWithZero.toMonoidWithZero","HDiv.hDiv","LT.lt","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instDivInvMonoid","Real.instField","Real.instLT","Real.instNatCast","Real.instZero","Real.partialOrder","Semifield.toDivisionSemiring","Zero.toOfNat0","instHDiv","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":254,"value_refs":["AkraBazziRecurrence.min_bi","Classical.byContradiction","DivInvMonoid.toDiv","DivisionSemiring.toGroupWithZero","Eq.mp","Eq.symm","Eq.trans","False","Field.toGrindField","Field.toSemifield","Finite","Finite.of_fintype","Fintype","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","Inv.inv","LT.lt","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nonempty","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLT","Real.instMul","Real.instNatCast","Real.instZero","Real.partialOrder","Semifield.toDivisionSemiring","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","id","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":120,"type_refs":["AkraBazziRecurrence.min_bi","DivInvMonoid.toDiv","Finite.of_fintype","Fintype","HDiv.hDiv","HMul.hMul","LE.le","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Nonempty","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instLE","Real.instMul","Real.instNatCast","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":334,"value_refs":["AkraBazziRecurrence.min_bi","Classical.byContradiction","DivInvMonoid.toDiv","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Finite","Finite.of_fintype","Fintype","HDiv.hDiv","HMul.hMul","Inv.inv","LE.le","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Nonempty","Not","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLE","Real.instMul","Real.instNatCast","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","id","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_5","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":28,"type_refs":["LE.le","LT.lt","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":37,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_6","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","Real","Real.instLT","Real.instZero","Zero.toOfNat0","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":93,"value_refs":["Eq.mpr_prop","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","Real","Real.instLT","Real.instZero","Zero.toOfNat0","forall_congr","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_7","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":108,"value_refs":["Eq.mpr_prop","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","forall_congr","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_8","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":123,"type_refs":["Asymptotics.IsLittleO","DivInvMonoid.toDiv","Filter.atTop","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NatCast.natCast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.log","Real.norm","instHDiv","instHMul","instHPow","instHSub","instOfNatNat"],"value_dag_size":194,"value_refs":["Asymptotics.IsLittleO","DivInvMonoid.toDiv","Eq.mpr_prop","Field.toGrindField","Filter.atTop","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Inv.inv","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Monoid.toNPow","NPow.toPow","Nat","Nat.instPreorder","NatCast.natCast","OfNat.ofNat","Real","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instSub","Real.log","Real.norm","congrArg","forall_congr","funext","instHDiv","instHMul","instHPow","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_9","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T","reducibility":null,"statement_dag_size":76,"type_refs":["AkraBazziRecurrence","AkraBazziRecurrence.n₀","Fintype","LE.le","LT.lt","Nat","Nat.instPreorder","Nonempty","Preorder.toLE","Real","instLTNat"],"value_dag_size":1464,"value_refs":["AkraBazziRecurrence","AkraBazziRecurrence.GrowsPolynomially","AkraBazziRecurrence.casesOn","AkraBazziRecurrence.mk","AkraBazziRecurrence.n₀","Asymptotics.IsLittleO","Bool","Bool.false","Bool.true","Classical.byContradiction","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Filter.atTop","Finset.sum","Finset.univ","Fintype","GE.ge","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instAdd","Int.instConditionallyCompleteLinearOrder","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.toMul","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.intro_with_eq'","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Nonempty","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instInv","Real.instLE","Real.instLT","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instSub","Real.instZero","Real.log","Real.norm","True","True.intro","Zero.toOfNat0","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_5","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_6","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_7","_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T._proof_1_8","congrArg","eagerReduce","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.AkraBazzi","name":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence.termε","namespace":"_private.Mathlib.Computability.AkraBazzi.AkraBazzi.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":44,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.add_isLittleO._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.add_isLittleO","reducibility":null,"statement_dag_size":95,"type_refs":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","DistribLattice.toLattice","Eq","IsOrderedAddMonoid","LE.le","Lattice.toSemilatticeInf","LinearOrder","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","instDistribLatticeOfLinearOrder"],"value_dag_size":100,"value_refs":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommGroup.toDivisionAddCommMonoid","DistribLattice.toLattice","Eq","IsOrderedAddMonoid","LE.le","Lattice.toSemilatticeInf","LinearOrder","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","abs_eq_self","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.add_isLittleO.match_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.add_isLittleO","reducibility":"abbrev","statement_dag_size":76,"type_refs":["And.intro","HMul.hMul","LE.le","Membership.mem","Preorder.toLE","Real","Real.instMul","Real.instPreorder","Set","Set.Icc","Set.instMembership","instHMul"],"value_dag_size":95,"value_refs":["And.casesOn","And.intro","HMul.hMul","LE.le","Membership.mem","Preorder.toLE","Real","Real.instMul","Real.instPreorder","Set","Set.Icc","Set.instMembership","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos._proof_1_4","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos._proof_1_5","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":null,"statement_dag_size":129,"type_refs":["DivInvMonoid.toDiv","Eq","HDiv.hDiv","HMul.hMul","LE.le","Max.max","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instDivInvMonoid","Real.instMax","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Set","Set.Icc","Set.Ico","Set.instMembership","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":3787,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff","Int","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.eq_int_module","Lean.Grind.CommRing.eq_norm","Lean.Grind.CommRing.inv_int_eq'","Lean.Grind.CommRing.le_norm0","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_cancel_var","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_mul","Lean.Grind.CommRing.lt_norm","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_of_eq","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Linarith.zero_lt_one","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_trans_k","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toIntModule","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.one_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","One.one","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.decidableLE","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIntCast","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMax","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Set","Set.Icc","Set.Ico","Set.instMembership","Set.mem_Icc","Set.mem_Ico","Std.IsLinearOrder.toIsLinearPreorder","True","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instHAdd","instHDiv","instHMul","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing","ite","ite_cond_eq_false","ite_cond_eq_true","max_def","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos._proof_1_6","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":null,"statement_dag_size":188,"type_refs":["DivInvMonoid.toDiv","Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Max.max","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instDivInvMonoid","Real.instLE","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Set","Set.Icc","Set.Ico","Set.instMembership","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":5323,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toGrindField","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff","Int","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.inv","Lean.Grind.CommRing.eq_int_module","Lean.Grind.CommRing.eq_norm","Lean.Grind.CommRing.inv_int_eq'","Lean.Grind.CommRing.le_cancel_var","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.le_mul","Lean.Grind.CommRing.le_norm","Lean.Grind.CommRing.le_norm0","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_cancel_var","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_mul","Lean.Grind.CommRing.lt_norm","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.not_lt_norm","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_le_combine","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.le_of_eq","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Linarith.zero_lt_one","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toIntModule","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.npow","Lean.Grind.Semiring.one_mul","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.Semiring.pow_one","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","One.one","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.decidableLE","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIntCast","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instSemigroup","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Semigroup.toMul","Set","Set.Icc","Set.Ico","Set.instMembership","Set.mem_Icc","Set.mem_Ico","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing","ite","ite_cond_eq_false","ite_cond_eq_true","max_def","mul_assoc","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos._proof_1_7","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":null,"statement_dag_size":183,"type_refs":["DivInvMonoid.toDiv","Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","LE.le","Max.max","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","Preorder.toLE","Real","Real.instDivInvMonoid","Real.instLE","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Set","Set.Icc","Set.Ico","Set.instMembership","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":2324,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DivInvMonoid.toDiv","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Field.toGrindField","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HPow.hPow","Iff","Int","Int.instNegInt","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.eq_int_module","Lean.Grind.CommRing.eq_norm","Lean.Grind.CommRing.inv_int_eq'","Lean.Grind.CommRing.le_cancel_var","Lean.Grind.CommRing.le_int_module","Lean.Grind.CommRing.le_mul","Lean.Grind.CommRing.le_norm","Lean.Grind.CommRing.le_norm0","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_cancel_var","Lean.Grind.CommRing.lt_int_module","Lean.Grind.CommRing.lt_mul","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.not_le_norm","Lean.Grind.CommRing.not_lt_norm","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Linarith.Expr","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.intMul","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.Expr.zero","Lean.Grind.Linarith.Poly","Lean.Grind.Linarith.Poly.add","Lean.Grind.Linarith.Poly.nil","Lean.Grind.Linarith.le_le_combine","Lean.Grind.Linarith.le_lt_combine","Lean.Grind.Linarith.le_norm","Lean.Grind.Linarith.le_of_eq","Lean.Grind.Linarith.lt_lt_combine","Lean.Grind.Linarith.lt_norm","Lean.Grind.Linarith.lt_unsat","Lean.Grind.Linarith.zero_lt_one","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_false_of_lt_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.OrderedRing.instIsCharPOfNatNatOfLawfulOrderLT","Lean.Grind.Ring.toIntModule","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.one_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","One.one","One.toOfNat1","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.decidableLE","Real.instAdd","Real.instAddCommMonoid","Real.instDivInvMonoid","Real.instField","Real.instIntCast","Real.instInv","Real.instIsOrderedCancelAddMonoid","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMax","Real.instMonoid","Real.instMul","Real.instNatCast","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.partialOrder","Real.semiring","Set","Set.Icc","Set.Ico","Set.instMembership","Set.mem_Icc","Set.mem_Ico","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHDiv","instHMul","instHPow","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedAddOfIsOrderedCancelAddMonoid","instOrderedRingOfIsStrictOrderedRing","ite","ite_cond_eq_false","ite_cond_eq_true","max_def","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos.match_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos","reducibility":"abbrev","statement_dag_size":99,"type_refs":["Eq","LT.lt","LinearOrder.toPartialOrder","Or","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder.toLT","Real","Real.linearOrder"],"value_dag_size":141,"value_refs":["Eq","LT.lt","LinearOrder.toPartialOrder","Or","Or.casesOn","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder.toLT","Real","Real.linearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["And","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","lt_iff_le_and_ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero._proof_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero._proof_1_4","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero","reducibility":null,"statement_dag_size":38,"type_refs":["HSub.hSub","Int","Int.instLEInt","Int.instNegInt","Int.instSub","LE.le","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instHSub","instNatCastInt","instOfNat"],"value_dag_size":123,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.le_eq_false","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero._simp_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero","reducibility":null,"statement_dag_size":57,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","Neg.neg","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":63,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","HAdd.hAdd","HSub.hSub","Neg.neg","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","instHAdd","instHSub","sub_eq_add_neg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.inv._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.inv","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.neg._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.neg","reducibility":null,"statement_dag_size":76,"type_refs":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","Eq","IsOrderedAddMonoid","Membership.mem","Neg.neg","NegZeroClass.toNeg","PartialOrder","PartialOrder.toPreorder","Set","Set.Icc","Set.instMembership","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid"],"value_dag_size":83,"value_refs":["AddCommGroup","AddCommGroup.toAddCommMonoid","AddCommGroup.toDivisionAddCommMonoid","IsOrderedAddMonoid","Membership.mem","Neg.neg","NegZeroClass.toNeg","PartialOrder","PartialOrder.toPreorder","Set","Set.Icc","Set.instMembership","Set.neg_mem_Icc_iff","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.pow._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.pow","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Real","Real.instMonoid","Real.instNatCast","Real.instPow","instHPow"],"value_dag_size":45,"value_refs":["Eq.symm","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Real","Real.instMonoid","Real.instNatCast","Real.instPow","Real.rpow_natCast","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.rpow._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.rpow","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.rpow.match_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.rpow","reducibility":"abbrev","statement_dag_size":159,"type_refs":["Eq","Filter.Eventually","Filter.atTop","LT.lt","OfNat.ofNat","Or","Or.inl","Or.inr","Real","Real.instLT","Real.instPreorder","Real.instZero","Zero.toOfNat0"],"value_dag_size":214,"value_refs":["Eq","Filter.Eventually","Filter.atTop","LT.lt","OfNat.ofNat","Or","Or.casesOn","Or.inl","Or.inr","Real","Real.instLT","Real.instPreorder","Real.instZero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.zpow._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.GrowsPolynomially.zpow","reducibility":null,"statement_dag_size":41,"type_refs":["DivInvMonoid.toZPow","Eq","HPow.hPow","Int","Int.cast","Real","Real.instDivInvMonoid","Real.instIntCast","Real.instPow","ZPow.toPow","instHPow"],"value_dag_size":45,"value_refs":["DivInvMonoid.toZPow","Eq.symm","HPow.hPow","Int","Int.cast","Real","Real.instDivInvMonoid","Real.instIntCast","Real.instPow","Real.rpow_intCast","ZPow.toPow","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_id._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_id","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.Icc","Set.instMembership"],"value_dag_size":51,"value_refs":["And","LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.Icc","Set.instMembership","Set.mem_Icc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_log._proof_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_log","reducibility":null,"statement_dag_size":21,"type_refs":["HAdd.hAdd","Nat","Nat.AtLeastTwo","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":17,"value_refs":["Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.GrowsPolynomially","name":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_log._proof_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.GrowsPolynomially.0.AkraBazziRecurrence.growsPolynomially_log","reducibility":null,"statement_dag_size":174,"type_refs":["Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toSemiring","Field.toSemifield","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","Lattice.toSemilatticeInf","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.instAdd","Real.instDivInvMonoid","Real.instField","Real.instLE","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.linearOrder","Real.log","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Set","Set.Icc","Set.instMembership","id","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":816,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Distrib.toMul","DistribLattice.toLattice","DivInvMonoid.toDiv","DivisionSemiring.toSemiring","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Field.toGrindField","Field.toSemifield","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Iff","Int","IntCast.intCast","Inv.inv","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm0","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Field.div_eq_mul_inv","Lean.Grind.Field.toCommRing","Lean.Grind.Field.toDiv","Lean.Grind.Field.toInv","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_false_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.one_mul","Lean.Grind.Semiring.toMul","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Real","Real.instAdd","Real.instDivInvMonoid","Real.instField","Real.instIntCast","Real.instInv","Real.instIsStrictOrderedRing","Real.instLE","Real.instLT","Real.instMul","Real.instNatCast","Real.instNeg","Real.instOne","Real.instPreorder","Real.instZero","Real.linearOrder","Real.log","Real.partialOrder","Real.semiring","Semifield.toDivisionSemiring","SemilatticeInf.toPartialOrder","Set","Set.Icc","Set.instMembership","Set.mem_Icc","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","eq_true","forall_congr","id","id.eq_1","implies_congr","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHAdd","instHDiv","instHMul","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instOrderedRingOfIsStrictOrderedRing","of_eq_false","of_eq_true"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_SumTransform___macroRules__private_Mathlib_Computability_AkraBazzi_SumTransform_0_AkraBazziRecurrence_termε_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":192,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence._aux_Mathlib_Computability_AkraBazzi_SumTransform___unexpand_AkraBazziRecurrence_smoothingFn_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":182,"value_refs":["Applicative.toPure","Bind.bind","Bool.false","Bool.or","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instMonadExceptOfMonadExceptOf","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_ge._proof_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_ge","reducibility":null,"statement_dag_size":38,"type_refs":["And","LE.le","LT.lt","Nat","Nat.instPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":286,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_ge._proof_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_ge","reducibility":null,"statement_dag_size":40,"type_refs":["And","LE.le","LT.lt","Nat","Nat.instPreorder","Preorder.toLE","Preorder.toLT","instLENat"],"value_dag_size":286,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._proof_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le","reducibility":null,"statement_dag_size":38,"type_refs":["And","LE.le","LT.lt","Nat","Nat.instPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":286,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._proof_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le","reducibility":null,"statement_dag_size":40,"type_refs":["And","LE.le","LT.lt","Nat","Nat.instPreorder","Preorder.toLE","Preorder.toLT","instLENat"],"value_dag_size":286,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","Preorder.toLT","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._simp_1_3","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le","reducibility":null,"statement_dag_size":60,"type_refs":["Add","Eq","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub"],"value_dag_size":68,"value_refs":["Add","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub","propext","tsub_le_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._simp_1_4","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le","reducibility":null,"statement_dag_size":74,"type_refs":["AddLeftMono","AddLeftReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":81,"value_refs":["AddLeftMono","AddLeftReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd","le_add_iff_nonneg_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._simp_1_5","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le","reducibility":null,"statement_dag_size":67,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","IsOrderedRing","LE.le","MulZeroClass.toZero","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","True","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dag_size":70,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","IsOrderedRing","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_nonneg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","eq_true","instMulZeroClassOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_r_ge._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_r_ge","reducibility":null,"statement_dag_size":78,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DistribLattice.toLattice","Eq","FloorSemiring","LE.le","Lattice.toSemilatticeInf","LinearOrder","Nat.cast","Nat.ceil","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring","Semiring.toNonAssocSemiring","True","instDistribLatticeOfLinearOrder"],"value_dag_size":81,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DistribLattice.toLattice","FloorSemiring","LE.le","Lattice.toSemilatticeInf","LinearOrder","Nat.cast","Nat.ceil","Nat.le_ceil","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Semiring","Semiring.toNonAssocSemiring","eq_true","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.isLittleO_deriv_smoothingFn._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.isLittleO_deriv_smoothingFn","reducibility":null,"statement_dag_size":60,"type_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq","HMul.hMul","Inv.inv","InvOneClass.toInv","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"],"value_dag_size":66,"value_refs":["DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","Eq.symm","HMul.hMul","Inv.inv","InvOneClass.toInv","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul","mul_inv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.isTheta_smoothingFn_sub_self._simp_1_1","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.isTheta_smoothingFn_sub_self","reducibility":null,"statement_dag_size":55,"type_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul"],"value_dag_size":62,"value_refs":["DivInvMonoid","DivInvMonoid.toDiv","DivInvMonoid.toMonoid","Eq.symm","HDiv.hDiv","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHDiv","instHMul","mul_div_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.one_add_smoothingFn_le_two._simp_1_2","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.one_add_smoothingFn_le_two","reducibility":null,"statement_dag_size":68,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":72,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat","one_add_one_eq_two"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.termε","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":45,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.AkraBazzi.SumTransform","name":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.wrapped._proof_1._@.Mathlib.Computability.AkraBazzi.SumTransform.2571614175._hygCtx._hyg.54","namespace":"_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.wrapped._proof_1._@.Mathlib.Computability.AkraBazzi.SumTransform.2571614175._hygCtx._hyg","reducibility":null,"statement_dag_size":18,"type_refs":["AkraBazziRecurrence.definition._@.Mathlib.Computability.AkraBazzi.SumTransform.2571614175._hygCtx._hyg.54","Eq","Fintype","Real"],"value_dag_size":17,"value_refs":["AkraBazziRecurrence.definition._@.Mathlib.Computability.AkraBazzi.SumTransform.2571614175._hygCtx._hyg.54","Fintype","Real","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.Produces.append_left.match_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.Produces.append_left","reducibility":"abbrev","statement_dag_size":139,"type_refs":["And","And.intro","ContextFreeGrammar","ContextFreeGrammar.NT","ContextFreeGrammar.Produces","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.Rewrites","Exists.intro","Finset","Finset.instSetLike","List","Membership.mem","SetLike.instMembership","Symbol"],"value_dag_size":223,"value_refs":["And","And.casesOn","And.intro","ContextFreeGrammar","ContextFreeGrammar.NT","ContextFreeGrammar.Produces","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.Rewrites","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","List","Membership.mem","SetLike.instMembership","Symbol"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.Produces.append_right.match_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.Produces.append_right","reducibility":"abbrev","statement_dag_size":139,"type_refs":["And","And.intro","ContextFreeGrammar","ContextFreeGrammar.NT","ContextFreeGrammar.Produces","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.Rewrites","Exists.intro","Finset","Finset.instSetLike","List","Membership.mem","SetLike.instMembership","Symbol"],"value_dag_size":223,"value_refs":["And","And.casesOn","And.intro","ContextFreeGrammar","ContextFreeGrammar.NT","ContextFreeGrammar.Produces","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.Rewrites","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","List","Membership.mem","SetLike.instMembership","Symbol"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.derives_nonterminal._simp_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.derives_nonterminal","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.language_eq_zero_of_forall_input_ne_initial._simp_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeGrammar.language_eq_zero_of_forall_input_ne_initial","reducibility":null,"statement_dag_size":100,"type_refs":["ContextFreeGrammar","ContextFreeGrammar.Derives","ContextFreeGrammar.NT","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.input","Eq","False","Finset","Finset.instSetLike","List","List.cons","List.nil","Membership.mem","Ne","SetLike.instMembership","Symbol","Symbol.nonterminal"],"value_dag_size":104,"value_refs":["ContextFreeGrammar","ContextFreeGrammar.Derives","ContextFreeGrammar.NT","ContextFreeGrammar.derives_nonterminal","ContextFreeGrammar.rules","ContextFreeRule","ContextFreeRule.input","Finset","Finset.instSetLike","List","List.cons","List.nil","Membership.mem","Ne","SetLike.instMembership","Symbol","Symbol.nonterminal","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.nonterminal_input_mem._simp_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.nonterminal_input_mem","reducibility":null,"statement_dag_size":102,"type_refs":["And","ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.input","ContextFreeRule.output","Eq","Exists","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Symbol","Symbol.nonterminal","instHAppendOfAppend"],"value_dag_size":107,"value_refs":["And","ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.input","ContextFreeRule.output","ContextFreeRule.rewrites_iff","Eq","Exists","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Symbol","Symbol.nonterminal","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.reverse.match_1_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.reverse","reducibility":"abbrev","statement_dag_size":134,"type_refs":["ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.Rewrites.cons","ContextFreeRule.Rewrites.head","ContextFreeRule.input","ContextFreeRule.output","HAppend.hAppend","List","List.cons","List.instAppend","Symbol","Symbol.nonterminal","instHAppendOfAppend"],"value_dag_size":585,"value_refs":["ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.Rewrites.casesOn","ContextFreeRule.Rewrites.cons","ContextFreeRule.Rewrites.head","ContextFreeRule.input","ContextFreeRule.output","Eq","Eq.ndrec","Eq.refl","Eq.symm","HAppend.hAppend","HEq","HEq.refl","List","List.cons","List.instAppend","Symbol","Symbol.nonterminal","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.reverse.match_1_7","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.Rewrites.reverse","reducibility":"abbrev","statement_dag_size":274,"type_refs":["ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.Rewrites.below","ContextFreeRule.Rewrites.below.cons","ContextFreeRule.Rewrites.below.head","ContextFreeRule.Rewrites.cons","ContextFreeRule.Rewrites.head","ContextFreeRule.input","ContextFreeRule.output","HAppend.hAppend","List","List.cons","List.instAppend","Symbol","Symbol.nonterminal","instHAppendOfAppend"],"value_dag_size":1264,"value_refs":["ContextFreeRule","ContextFreeRule.Rewrites","ContextFreeRule.Rewrites.below","ContextFreeRule.Rewrites.below.casesOn","ContextFreeRule.Rewrites.below.cons","ContextFreeRule.Rewrites.below.head","ContextFreeRule.Rewrites.cons","ContextFreeRule.Rewrites.head","ContextFreeRule.input","ContextFreeRule.output","Eq","Eq.ndrec","Eq.refl","Eq.symm","HAppend.hAppend","HEq","HEq.refl","List","List.cons","List.instAppend","Symbol","Symbol.nonterminal","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.ContextFreeGrammar","name":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.ext.match_1","namespace":"_private.Mathlib.Computability.ContextFreeGrammar.0.ContextFreeRule.ext","reducibility":"abbrev","statement_dag_size":34,"type_refs":["ContextFreeRule","ContextFreeRule.mk","List","Symbol"],"value_dag_size":50,"value_refs":["ContextFreeRule","ContextFreeRule.casesOn","ContextFreeRule.mk","List","Symbol"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.DFA.acceptsFrom_inter._simp_1_2","namespace":"_private.Mathlib.Computability.DFA.0.DFA.acceptsFrom_inter","reducibility":null,"statement_dag_size":58,"type_refs":["And","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toLattice","Eq","Language","Language.instMembershipList","Lattice.toSemilatticeInf","List","Membership.mem","Min.min","SemilatticeInf.toMin","instCompleteAtomicBooleanAlgebraLanguage"],"value_dag_size":62,"value_refs":["And","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toLattice","Language","Language.instMembershipList","Language.mem_inf","Lattice.toSemilatticeInf","List","Membership.mem","Min.min","SemilatticeInf.toMin","instCompleteAtomicBooleanAlgebraLanguage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.DFA.accepts_comap._simp_1_1","namespace":"_private.Mathlib.Computability.DFA.0.DFA.accepts_comap","reducibility":null,"statement_dag_size":54,"type_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","Eq","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership"],"value_dag_size":58,"value_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","DFA.mem_accepts","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.DFA.accepts_reindex._simp_1_1","namespace":"_private.Mathlib.Computability.DFA.0.DFA.accepts_reindex","reducibility":null,"statement_dag_size":54,"type_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","Eq","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership"],"value_dag_size":58,"value_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","DFA.mem_accepts","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.DFA.evalFrom_split._proof_1_1","namespace":"_private.Mathlib.Computability.DFA.0.DFA.evalFrom_split","reducibility":null,"statement_dag_size":108,"type_refs":["False","Fin","Fin.val","Fintype","Fintype.card","HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Min.min","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":1892,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","Fintype","Fintype.card","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMin","Int.instNegInt","Int.instSub","Int.min_def","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_min","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.coordinate_eval_6","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Min.min","Nat","Nat.cast","Nat.lt_of_not_le","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.DFA.evalFrom_split._proof_1_2","namespace":"_private.Mathlib.Computability.DFA.0.DFA.evalFrom_split","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","False","Fin","Fin.val","Fintype","Fintype.card","HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Min.min","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":1763,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","Fin.val_add_one_le_of_lt","Fintype","Fintype.card","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMin","Int.instNegInt","Int.instSub","Int.min_def","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Fin.lt_or_gt_of_ne","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_min","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Min.min","Nat","Nat.cast","Ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTFin","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.add.match_1_1","namespace":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.add","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language","Language.IsRegular"],"value_dag_size":214,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language","Language.IsRegular"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.compl.match_1_1","namespace":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.compl","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language","Language.IsRegular"],"value_dag_size":214,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language","Language.IsRegular"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.inf.match_1_1","namespace":"_private.Mathlib.Computability.DFA.0.Language.IsRegular.inf","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language","Language.IsRegular"],"value_dag_size":214,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language","Language.IsRegular"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper","namespace":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff","reducibility":null,"statement_dag_size":65,"type_refs":["DFA","DFA.accepts","Eq","Exists","Fintype","Language"],"value_dag_size":273,"value_refs":["Countable.toSmall","DFA","DFA.accepts","DFA.accepts_reindex","DFA.reindex","DFunLike.coe","Eq","Eq.rec","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.intro","Finite.of_fintype","Finite.to_countable","Fintype","Fintype.ofEquiv","Language","Nonempty","Small.equiv_small","_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper.match_1_1","_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper.match_1_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper.match_1_1","namespace":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Equiv","Exists","Exists.intro","Nonempty","Nonempty.intro"],"value_dag_size":81,"value_refs":["Equiv","Exists","Exists.casesOn","Exists.intro","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.DFA","name":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper.match_1_3","namespace":"_private.Mathlib.Computability.DFA.0.Language.isRegular_iff.helper","reducibility":"abbrev","statement_dag_size":133,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language"],"value_dag_size":242,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.eq_1","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Bool","Bool.false","Bool.true","Computability.decodePosNum.match_1","Eq","List","List.cons"],"value_dag_size":40,"value_refs":["Bool","Bool.false","Bool.true","Computability.decodePosNum.match_1","Eq.refl","List","List.cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.eq_2","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Bool","Bool.false","Bool.true","Computability.decodePosNum.match_1","Eq","List","List.cons"],"value_dag_size":40,"value_refs":["Bool","Bool.false","Bool.true","Computability.decodePosNum.match_1","Eq.refl","List","List.cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.eq_3","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1","reducibility":null,"statement_dag_size":55,"type_refs":["Bool","Bool.false","Bool.true","Computability.decodePosNum.match_1","Eq","False","List","List.cons"],"value_dag_size":408,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.rec","Bool.true","Computability.decodePosNum._sparseCasesOn_1","Computability.decodePosNum._sparseCasesOn_1.else_eq","Computability.decodePosNum.match_1","Eq","Eq.mpr","Eq.refl","False","False.elim","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.splitter._sparseCasesOn_3","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.splitter","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1","reducibility":"abbrev","statement_dag_size":44,"type_refs":["Bool","Bool.false","Bool.true","Eq","False","List","List.cons"],"value_dag_size":150,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","List","List.cons","List.ctorIdx","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.decodePosNum.match_1.splitter","reducibility":"abbrev","statement_dag_size":33,"type_refs":["List","List.cons","List.ctorIdx","Nat.hasNotBit"],"value_dag_size":105,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1.eq_1","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Computability.encodePosNum.match_1","Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Computability.encodePosNum.match_1","Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1.eq_2","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Computability.encodePosNum.match_1","Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":36,"value_refs":["Computability.encodePosNum.match_1","Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1.eq_3","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Computability.encodePosNum.match_1","Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":36,"value_refs":["Computability.encodePosNum.match_1","Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Encoding","name":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1.splitter","namespace":"_private.Mathlib.Computability.Encoding.0.Computability.encodePosNum.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":1,"value_refs":["Computability.encodePosNum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match._simp_1_3","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match._simp_1_4","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match._simp_1_5","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.NFA.toεNFA_evalFrom_match","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.isPath_append.match_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.isPath_append","reducibility":"abbrev","statement_dag_size":115,"type_refs":["And","And.intro","Exists","Exists.intro","List","Option","εNFA","εNFA.IsPath"],"value_dag_size":175,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","Option","εNFA","εNFA.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.isPath_nil._simp_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.isPath_nil","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_accepts_iff_exists_path.match_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_accepts_iff_exists_path","reducibility":"abbrev","statement_dag_size":129,"type_refs":["And","And.intro","Exists.intro","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","εNFA","εNFA.accept","εNFA.accepts","εNFA.eval"],"value_dag_size":200,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","εNFA","εNFA.accept","εNFA.accepts","εNFA.eval"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_accepts_iff_exists_path.match_1_4","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_accepts_iff_exists_path","reducibility":"abbrev","statement_dag_size":344,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List","List.reduceOption","Membership.mem","Option","Set","Set.instMembership","εNFA","εNFA.IsPath","εNFA.accept","εNFA.start"],"value_dag_size":778,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","List","List.reduceOption","Membership.mem","Option","Set","Set.instMembership","εNFA","εNFA.IsPath","εNFA.accept","εNFA.start"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path._simp_1_10","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":null,"statement_dag_size":84,"type_refs":["And","Eq","Exists","HAppend.hAppend","List","List.concat","List.cons","List.instAppend","List.nil","List.reduceOption","Option","Option.some","instHAppendOfAppend"],"value_dag_size":88,"value_refs":["And","Eq","Exists","HAppend.hAppend","List","List.concat","List.cons","List.instAppend","List.nil","List.reduceOption","List.reduceOption_eq_concat_iff","Option","Option.some","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path._simp_1_3","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Exists","List","List.nil","List.reduceOption","List.replicate","Nat","Option","Option.none"],"value_dag_size":43,"value_refs":["Eq","Exists","List","List.nil","List.reduceOption","List.reduceOption_eq_nil_iff","List.replicate","Nat","Option","Option.none","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path._simp_1_8","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Exists","List.replicate","Membership.mem","Nat","Option","Option.none","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","εNFA","εNFA.IsPath","εNFA.εClosure"],"value_dag_size":68,"value_refs":["Exists","List.replicate","Membership.mem","Nat","Option","Option.none","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","propext","εNFA","εNFA.IsPath","εNFA.mem_εClosure_iff_exists_path","εNFA.εClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path._simp_1_9","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HAppend.hAppend","List","List.concat","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":41,"value_refs":["Eq.symm","HAppend.hAppend","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.nil","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path.match_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Exists","Exists.intro","List.replicate","Nat","Option","Option.none","εNFA","εNFA.IsPath"],"value_dag_size":114,"value_refs":["Exists","Exists.casesOn","Exists.intro","List.replicate","Nat","Option","Option.none","εNFA","εNFA.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path.match_1_11","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":"abbrev","statement_dag_size":427,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.reduceOption","List.replicate","Nat","Option","Option.none","Option.some","instHAppendOfAppend","εNFA","εNFA.IsPath"],"value_dag_size":2064,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.cons","List.instAppend","List.reduceOption","List.replicate","Nat","Option","Option.none","Option.some","eq_of_heq","instHAppendOfAppend","εNFA","εNFA.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path.match_1_4","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":"abbrev","statement_dag_size":160,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","List","List.replicate","Nat","Option","Option.none","εNFA","εNFA.IsPath"],"value_dag_size":530,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.replicate","Nat","Option","Option.none","eq_of_heq","εNFA","εNFA.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path.match_1_6","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path","reducibility":"abbrev","statement_dag_size":226,"type_refs":["And","And.intro","Exists","Exists.intro","List","Membership.mem","Option.some","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","εNFA","εNFA.evalFrom","εNFA.step","εNFA.εClosure"],"value_dag_size":321,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","Membership.mem","Option.some","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","εNFA","εNFA.evalFrom","εNFA.step","εNFA.εClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_stepSet_iff._simp_1_2","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_stepSet_iff","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":68,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion₂","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_stepSet_iff._simp_1_3","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_stepSet_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists.match_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists","reducibility":"abbrev","statement_dag_size":158,"type_refs":["And","And.intro","Exists","Exists.intro","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","εNFA","εNFA.εClosure"],"value_dag_size":228,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","εNFA","εNFA.εClosure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists_path._simp_1_3","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists_path","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","Exists","HAppend.hAppend","List","List.instAppend","Option","instHAppendOfAppend","εNFA","εNFA.IsPath"],"value_dag_size":75,"value_refs":["And","Exists","HAppend.hAppend","List","List.instAppend","Option","instHAppendOfAppend","propext","εNFA","εNFA.IsPath","εNFA.isPath_append"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists_path.match_1_1","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_εClosure_iff_exists_path","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Exists","Exists.intro","List.replicate","Nat","Option","Option.none","εNFA","εNFA.IsPath"],"value_dag_size":114,"value_refs":["Exists","Exists.casesOn","Exists.intro","List.replicate","Nat","Option","Option.none","εNFA","εNFA.IsPath"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.EpsilonNFA","name":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.stepSet_empty._simp_1_2","namespace":"_private.Mathlib.Computability.EpsilonNFA.0.εNFA.stepSet_empty","reducibility":null,"statement_dag_size":26,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":28,"value_refs":["EmptyCollection.emptyCollection","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Halting","name":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂._simp_1_6","namespace":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂","reducibility":null,"statement_dag_size":26,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership"],"value_dag_size":28,"value_refs":["EmptyCollection.emptyCollection","False","Membership.mem","Set","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Halting","name":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂.match_1_1","namespace":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂","reducibility":"abbrev","statement_dag_size":82,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Set","Set.image","Set.instMembership"],"value_dag_size":131,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Halting","name":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂.match_1_3","namespace":"_private.Mathlib.Computability.Halting.0.ComputablePred.rice₂","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Exists.intro","Membership.mem","Nat.Partrec.Code","Set","Set.Nonempty","Set.instMembership"],"value_dag_size":54,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Nat.Partrec.Code","Set","Set.Nonempty","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow._proof_1_4","namespace":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow","reducibility":null,"statement_dag_size":97,"type_refs":["And","Eq","Exists","Iff","Language","Language.instMembershipList","List","List.flatten","List.instMembership","List.length","Membership.mem","Nat"],"value_dag_size":1139,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Language","Language.instMembershipList","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","List","List.flatten","List.instMembership","List.length","Membership.mem","Nat","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow","reducibility":null,"statement_dag_size":70,"type_refs":["And","Eq","Exists","KStar.kstar","Language","Language.instKStar","Language.instMembershipList","List","List.flatten","List.instMembership","Membership.mem"],"value_dag_size":73,"value_refs":["And","Eq","Exists","KStar.kstar","Language","Language.instKStar","Language.instMembershipList","Language.mem_kstar","List","List.flatten","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow._simp_1_2","namespace":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow","reducibility":null,"statement_dag_size":64,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","iSup","instCompleteAtomicBooleanAlgebraLanguage"],"value_dag_size":68,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toCompleteSemilatticeSup","CompleteSemilatticeSup.toSupSet","Exists","Language","Language.instMembershipList","Language.mem_iSup","List","Membership.mem","iSup","instCompleteAtomicBooleanAlgebraLanguage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow._simp_1_3","namespace":"_private.Mathlib.Computability.Language.0.Language.kstar_eq_iSup_pow","reducibility":null,"statement_dag_size":97,"type_refs":["And","Eq","Exists","HPow.hPow","Language","Language.instMembershipList","Language.instSemiring","List","List.flatten","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Semiring.toMonoid","instHPow"],"value_dag_size":102,"value_refs":["And","Eq","Exists","HPow.hPow","Language","Language.instMembershipList","Language.instSemiring","Language.mem_pow","List","List.flatten","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Semiring.toMonoid","instHPow","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.map_kstar._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.map_kstar","reducibility":null,"statement_dag_size":98,"type_refs":["DFunLike.coe","Eq","FunLike","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MonoidHomClass","MulOneClass.toMulOne","NPow.toPow","Nat","instHPow"],"value_dag_size":110,"value_refs":["DFunLike.coe","Eq.symm","FunLike","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MonoidHomClass","MulOneClass.toMulOne","NPow.toPow","Nat","instHPow","map_pow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty","reducibility":null,"statement_dag_size":41,"type_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","List.mem_filter","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty._simp_1_2","namespace":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty","reducibility":null,"statement_dag_size":18,"type_refs":["Bool","Bool.not","Eq"],"value_dag_size":21,"value_refs":["Bool","Bool.not","Bool.not_eq_eq_eq_not","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty._simp_1_3","namespace":"_private.Mathlib.Computability.Language.0.Language.mem_kstar_iff_exists_nonempty","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Eq","List","List.isEmpty","List.nil","Ne"],"value_dag_size":30,"value_refs":["Bool","Bool.false","Eq","List","List.isEmpty","List.isEmpty_eq_false_iff","List.nil","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mem_pow._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.mem_pow","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Exists","HAppend.hAppend","HMul.hMul","Language","Language.instMembershipList","Language.instMul","List","List.instAppend","Membership.mem","instHAppendOfAppend","instHMul"],"value_dag_size":91,"value_refs":["And","Eq","Exists","HAppend.hAppend","HMul.hMul","Language","Language.instMembershipList","Language.instMul","Language.mem_mul","List","List.instAppend","Membership.mem","instHAppendOfAppend","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mul_self_kstar_comm._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.mul_self_kstar_comm","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat","pow_succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.mul_self_kstar_comm._simp_1_2","namespace":"_private.Mathlib.Computability.Language.0.Language.mul_self_kstar_comm","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat","pow_succ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.one_add_self_mul_kstar_eq_kstar._simp_1_1","namespace":"_private.Mathlib.Computability.Language.0.Language.one_add_self_mul_kstar_eq_kstar","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instOfNatNat","pow_succ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.Language.reverse_one._simp_1_2","namespace":"_private.Mathlib.Computability.Language.0.Language.reverse_one","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Language","Language.instOne","List","List.nil","OfNat.ofNat","One.toOfNat1","Set","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":35,"value_refs":["Eq.symm","Language","Language.instOne","Language.one_def","List","List.nil","OfNat.ofNat","One.toOfNat1","Set","Set.instSingletonSet","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Language","name":"_private.Mathlib.Computability.Language.0.instReprSymbol.repr.match_1","namespace":"_private.Mathlib.Computability.Language.0.instReprSymbol.repr","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Symbol","Symbol.nonterminal","Symbol.terminal"],"value_dag_size":48,"value_refs":["Symbol","Symbol.casesOn","Symbol.nonterminal","Symbol.terminal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.MyhillNerode","name":"_private.Mathlib.Computability.MyhillNerode.0.Language.IsRegular.finite_range_leftQuotient.match_1_1","namespace":"_private.Mathlib.Computability.MyhillNerode.0.Language.IsRegular.finite_range_leftQuotient","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language","Language.IsRegular"],"value_dag_size":214,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language","Language.IsRegular"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.MyhillNerode","name":"_private.Mathlib.Computability.MyhillNerode.0.Language.leftQuotient_accepts_apply._simp_1_1","namespace":"_private.Mathlib.Computability.MyhillNerode.0.Language.leftQuotient_accepts_apply","reducibility":null,"statement_dag_size":54,"type_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","Eq","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership"],"value_dag_size":58,"value_refs":["DFA","DFA.accept","DFA.accepts","DFA.eval","DFA.mem_accepts","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.MyhillNerode","name":"_private.Mathlib.Computability.MyhillNerode.0.Language.leftQuotient_accepts_apply._simp_1_2","namespace":"_private.Mathlib.Computability.MyhillNerode.0.Language.leftQuotient_accepts_apply","reducibility":null,"statement_dag_size":58,"type_refs":["DFA","DFA.accept","DFA.acceptsFrom","DFA.evalFrom","Eq","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership"],"value_dag_size":63,"value_refs":["DFA","DFA.accept","DFA.acceptsFrom","DFA.evalFrom","DFA.mem_acceptsFrom","Language","Language.instMembershipList","List","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.Language.IsRegular.reverse.match_1_1","namespace":"_private.Mathlib.Computability.NFA.0.Language.IsRegular.reverse","reducibility":"abbrev","statement_dag_size":104,"type_refs":["DFA","DFA.accepts","Eq","Exists","Exists.intro","Fintype","Language","Language.IsRegular"],"value_dag_size":214,"value_refs":["DFA","DFA.accepts","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","Language","Language.IsRegular"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1.eq_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1","reducibility":null,"statement_dag_size":131,"type_refs":["Eq","List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.Path.supp.match_1","NFA.step","Set","Set.instMembership"],"value_dag_size":129,"value_refs":["Eq.refl","List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.Path.supp.match_1","NFA.step","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1.eq_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1","reducibility":null,"statement_dag_size":177,"type_refs":["Eq","List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.Path.supp.match_1","NFA.step","Set","Set.instMembership"],"value_dag_size":169,"value_refs":["Eq.refl","List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.Path.supp.match_1","NFA.step","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1.splitter","namespace":"_private.Mathlib.Computability.NFA.0.NFA.Path.supp.match_1","reducibility":"abbrev","statement_dag_size":121,"type_refs":["List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.step","Set","Set.instMembership"],"value_dag_size":1,"value_refs":["NFA.Path.supp.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_iUnion._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_iUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_union._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_union","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","Set","Set.instMembership"],"value_dag_size":74,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","NFA.mem_acceptsFrom","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_union._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.acceptsFrom_union","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Union.union"],"value_dag_size":44,"value_refs":["Membership.mem","Or","Set","Set.instMembership","Set.instUnion","Set.mem_union","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.accepts_iff_exists_path._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.accepts_iff_exists_path","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","List","Membership.mem","NFA","NFA.Path","NFA.evalFrom","Nonempty","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":68,"value_refs":["Eq.symm","List","Membership.mem","NFA","NFA.Path","NFA.evalFrom","NFA.mem_evalFrom_iff_nonempty_path","Nonempty","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.accepts_iff_exists_path._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.accepts_iff_exists_path","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.accepts","NFA.evalFrom","NFA.start","Set","Set.instMembership"],"value_dag_size":73,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.accepts","NFA.evalFrom","NFA.mem_accepts","NFA.start","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.append_mem_acceptsFrom._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.append_mem_acceptsFrom","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","Set","Set.instMembership"],"value_dag_size":74,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","NFA.mem_acceptsFrom","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.cons_mem_acceptsFrom._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.cons_mem_acceptsFrom","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","Set","Set.instMembership"],"value_dag_size":74,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","NFA.mem_acceptsFrom","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.disjoint_stepSet_reverse._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.disjoint_stepSet_reverse","reducibility":null,"statement_dag_size":66,"type_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Exists","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":69,"value_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Exists","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","Set.not_disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.disjoint_stepSet_reverse._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.disjoint_stepSet_reverse","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Exists","Membership.mem","NFA","NFA.step","NFA.stepSet","Set","Set.instMembership"],"value_dag_size":68,"value_refs":["And","Exists","Membership.mem","NFA","NFA.mem_stepSet","NFA.step","NFA.stepSet","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.evalFrom_eq_biUnion_singleton._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.evalFrom_eq_biUnion_singleton","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","List","NFA","NFA.evalFrom","Set","Set.iUnion"],"value_dag_size":72,"value_refs":["Eq.symm","List","NFA","NFA.evalFrom","NFA.evalFrom_iUnion₂","Set","Set.iUnion"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact","namespace":"_private.Mathlib.Computability.NFA.0.NFA","reducibility":null,"statement_dag_size":62,"type_refs":["And","Iff","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.acceptsFrom","Set","Set.instMembership","Set.ofPred"],"value_dag_size":1105,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.mpr","Eq.trans","Exists","Exists.casesOn","Exists.intro","Iff","Iff.intro","Language","Language.instMembershipList","List","List.cons","List.nil","List.rec","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.cons_mem_acceptsFrom._simp_1","NFA.nil_mem_acceptsFrom._simp_1","NFA.step","NFA.stepSet","Set","Set.ext","Set.iUnion","Set.instMembership","Set.ofPred","True","_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact._simp_1_2","_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact._simp_1_3","congr","congrArg","congrFun'","funext","id","iff_self","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact._simp_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.acceptsFrom","Set","Set.instMembership","Set.ofPred"],"value_dag_size":70,"value_refs":["And","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.acceptsFrom","Set","Set.instMembership","Set.ofPred","_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact._simp_1_3","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_acceptsFrom_sep_fact","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.accepts","NFA.evalFrom","NFA.start","Set","Set.instMembership"],"value_dag_size":73,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.accepts","NFA.evalFrom","NFA.mem_accepts","NFA.start","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse","reducibility":null,"statement_dag_size":66,"type_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Exists","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":75,"value_refs":["And","BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq.symm","Exists","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","Set.not_disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse._simp_1_3","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_accepts_reverse","reducibility":null,"statement_dag_size":84,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Disjoint","Eq","HeytingAlgebra.toOrderBot","List","List.reverse","NFA","NFA.evalFrom","NFA.reverse","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra"],"value_dag_size":90,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Disjoint","HeytingAlgebra.toOrderBot","List","List.reverse","NFA","NFA.disjoint_evalFrom_reverse_iff","NFA.evalFrom","NFA.reverse","Order.Frame.toHeytingAlgebra","Set","Set.instCompleteAtomicBooleanAlgebra","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path.match_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path","reducibility":"abbrev","statement_dag_size":61,"type_refs":["List","NFA","NFA.Path","Nonempty","Nonempty.intro"],"value_dag_size":70,"value_refs":["List","NFA","NFA.Path","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path.match_1_3","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path","reducibility":"abbrev","statement_dag_size":194,"type_refs":["And","And.intro","Exists","Exists.intro","List","Membership.mem","NFA","NFA.evalFrom","NFA.step","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":278,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","Membership.mem","NFA","NFA.evalFrom","NFA.step","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path.match_1_5","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path","reducibility":"abbrev","statement_dag_size":128,"type_refs":["List","List.cons","List.nil","Membership.mem","NFA","NFA.evalFrom","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":186,"value_refs":["List","List.casesOn","List.cons","List.nil","Membership.mem","NFA","NFA.evalFrom","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path.match_1_7","namespace":"_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path","reducibility":"abbrev","statement_dag_size":141,"type_refs":["List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.cons","NFA.Path.nil","NFA.step","Nonempty","Nonempty.intro","Set","Set.instMembership"],"value_dag_size":696,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.cons","List.nil","Membership.mem","NFA","NFA.Path","NFA.Path.casesOn","NFA.Path.cons","NFA.Path.nil","NFA.step","Nonempty","Nonempty.casesOn","Nonempty.intro","Set","Set.instMembership","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.nil_mem_acceptsFrom._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.nil_mem_acceptsFrom","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","Set","Set.instMembership"],"value_dag_size":74,"value_refs":["And","Exists","Language","Language.instMembershipList","List","Membership.mem","NFA","NFA.accept","NFA.acceptsFrom","NFA.evalFrom","NFA.mem_acceptsFrom","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union._simp_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Exists","Membership.mem","NFA","NFA.step","NFA.stepSet","Set","Set.instMembership"],"value_dag_size":68,"value_refs":["And","Exists","Membership.mem","NFA","NFA.mem_stepSet","NFA.step","NFA.stepSet","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union._simp_1_2","namespace":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union._simp_1_3","namespace":"_private.Mathlib.Computability.NFA.0.NFA.stepSet_union","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.toDFA_correct.match_1_1","namespace":"_private.Mathlib.Computability.NFA.0.NFA.toDFA_correct","reducibility":"abbrev","statement_dag_size":150,"type_refs":["And","And.intro","DFA.accept","DFA.eval","Exists.intro","List","Membership.mem","NFA","NFA.accept","NFA.toDFA","Set","Set.instMembership"],"value_dag_size":227,"value_refs":["And","And.casesOn","And.intro","DFA.accept","DFA.eval","Exists.casesOn","Exists.intro","List","Membership.mem","NFA","NFA.accept","NFA.toDFA","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.NFA","name":"_private.Mathlib.Computability.NFA.0.NFA.toDFA_correct.match_1_3","namespace":"_private.Mathlib.Computability.NFA.0.NFA.toDFA_correct","reducibility":"abbrev","statement_dag_size":167,"type_refs":["And","And.intro","Exists","Exists.intro","List","Membership.mem","NFA","NFA.accept","NFA.evalFrom","NFA.start","Set","Set.instMembership"],"value_dag_size":233,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","Membership.mem","NFA","NFA.accept","NFA.evalFrom","NFA.start","Set","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Computable.list_ofFn.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Computable.list_ofFn","reducibility":"abbrev","statement_dag_size":113,"type_refs":["Computable","Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","Primcodable","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":152,"value_refs":["Computable","Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Primcodable","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Computable.to₂.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Computable.to₂","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":42,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.none.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.none","reducibility":"abbrev","statement_dag_size":131,"type_refs":["Applicative.toFunctor","Bool","Decidable.decide","Eq","Exists.intro","Functor.map","Membership.mem","Monad.toApplicative","Nat","Nat.pair","Nat.rfind","OfNat.ofNat","PFun.lift","Part","Part.Dom","Part.get","Part.instMembership","Part.instMonad","instDecidableEqNat","instOfNatNat"],"value_dag_size":150,"value_refs":["Applicative.toFunctor","Bool","Decidable.decide","Eq","Exists.casesOn","Exists.intro","Functor.map","Membership.mem","Monad.toApplicative","Nat","Nat.pair","Nat.rfind","OfNat.ofNat","PFun.lift","Part","Part.Dom","Part.get","Part.instMembership","Part.instMonad","instDecidableEqNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.of_primrec._simp_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.of_primrec","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.bind","Part.instMembership"],"value_dag_size":66,"value_refs":["And","Exists","Membership.mem","Part","Part.bind","Part.instMembership","Part.mem_bind_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.of_primrec._simp_1_2","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.of_primrec","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.mem_some_iff","Part.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.ppred._proof_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.Partrec.ppred","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","LT.lt","Nat","Not","instLTNat"],"value_dag_size":225,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":3,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.lbp","namespace":"_private.Mathlib.Computability.Partrec.0.Nat","reducibility":"regular","statement_dag_size":9,"type_refs":["Bool","Nat","PFun"],"value_dag_size":56,"value_refs":["And","Bool","Bool.false","Eq","HAdd.hAdd","LE.le","Membership.mem","Nat","OfNat.ofNat","PFun","Part","Part.instMembership","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.mem_rfind.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.mem_rfind","reducibility":"abbrev","statement_dag_size":84,"type_refs":["And","And.intro","Bool","Bool.false","Bool.true","LT.lt","Membership.mem","Nat","PFun","Part","Part.instMembership","instLTNat"],"value_dag_size":100,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.false","Bool.true","LT.lt","Membership.mem","Nat","PFun","Part","Part.instMembership","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.mem_rfind.match_1_3","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.mem_rfind","reducibility":"abbrev","statement_dag_size":53,"type_refs":["Bool","Exists","Exists.intro","Membership.mem","Nat","Nat.rfind","PFun","Part","Part.instMembership"],"value_dag_size":70,"value_refs":["Bool","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.rfind","PFun","Part","Part.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_mono._simp_1_3","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_mono","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Membership.mem","Part","Part.Dom","Part.get","Part.instMembership","True"],"value_dag_size":32,"value_refs":["Membership.mem","Part","Part.Dom","Part.get","Part.get_mem","Part.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_mono.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_mono","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Exists","Exists.intro","Membership.mem","Nat","Option","Option.instMembership"],"value_dag_size":91,"value_refs":["Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_spec.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.rfindOpt_spec","reducibility":"abbrev","statement_dag_size":164,"type_refs":["And","And.intro","Bool","Exists","Exists.intro","Membership.mem","Nat","Nat.rfind","Option","Option.isSome","Option.some","Part","Part.instMembership","Part.ofOption"],"value_dag_size":237,"value_refs":["And","And.casesOn","And.intro","Bool","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.rfind","Option","Option.isSome","Option.some","Part","Part.instMembership","Part.ofOption"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.rfind_min'.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.rfind_min'","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Bool","Exists","Exists.intro","Membership.mem","Nat","Nat.rfind","PFun.lift","Part","Part.instMembership"],"value_dag_size":76,"value_refs":["Bool","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.rfind","PFun.lift","Part","Part.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.rfind_zero_none.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.rfind_zero_none","reducibility":"abbrev","statement_dag_size":105,"type_refs":["And","And.intro","Bool","Bool.true","Exists","Exists.intro","LE.le","Membership.mem","Nat","PFun","Part","Part.Dom","Part.instMembership","instLENat"],"value_dag_size":159,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.true","Exists","Exists.casesOn","Exists.intro","LE.le","Membership.mem","Nat","PFun","Part","Part.Dom","Part.instMembership","instLENat"]}
+{"definition_height":4,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp","namespace":"_private.Mathlib.Computability.Partrec.0.Nat","reducibility":"regular","statement_dag_size":46,"type_refs":["And","Bool","Bool.true","Exists","LT.lt","Membership.mem","Nat","PFun","Part","Part.Dom","Part.instMembership","WellFounded","_private.Mathlib.Computability.Partrec.0.Nat.lbp","instLTNat"],"value_dag_size":327,"value_refs":["Acc","Acc.intro","And","And.casesOn","And.left","Bool","Bool.ctorIdx","Bool.false","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Exists","False.elim","HAdd.hAdd","LE.le","LT.lt","Membership.mem","Nat","Nat.add_right_comm","Nat.le_add_left","Nat.recAux","OfNat.ofNat","PFun","Part","Part.Dom","Part.instMembership","Part.mem_unique","WellFounded.intro","_private.Mathlib.Computability.Partrec.0.Nat.lbp","_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp.match_1","congrArg","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp.match_1","namespace":"_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp","reducibility":"abbrev","statement_dag_size":88,"type_refs":["And","Bool","Bool.true","Exists","Exists.intro","LT.lt","Membership.mem","Nat","PFun","Part","Part.Dom","Part.instMembership","instLTNat"],"value_dag_size":110,"value_refs":["And","Bool","Bool.true","Exists","Exists.casesOn","Exists.intro","LT.lt","Membership.mem","Nat","PFun","Part","Part.Dom","Part.instMembership","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Partrec.fix_aux._proof_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Partrec.fix_aux","reducibility":null,"statement_dag_size":298,"type_refs":["And","Exists","HAdd.hAdd","Membership.mem","Nat","Nat.rec","OfNat.ofNat","Or","PFun","PFun.fix","Part","Part.bind","Part.instMembership","Part.some","Sum","Sum.casesOn","Sum.inl","Sum.inr","Sum.rec","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1286,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.casesOn","False.elim","HAdd.hAdd","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.exists_const","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Nat","Nat.rec","Not","OfNat.ofNat","Or","Or.casesOn","PFun","PFun.fix","PFun.mem_fix_iff","Part","Part.bind","Part.instMembership","Part.mem_unique","Part.some","Sum","Sum.casesOn","Sum.ctorIdx","Sum.inl","Sum.inr","Sum.inr.inj","Sum.rec","True","True.intro","congrArg","eq_false","eq_false'","eq_self","eq_true","funext","id","implies_congr","instAddNat","instHAdd","instInhabitedNat","instNonemptyOfInhabited","instOfNatNat","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Partrec.fix_aux._proof_1_2","namespace":"_private.Mathlib.Computability.Partrec.0.Partrec.fix_aux","reducibility":null,"statement_dag_size":149,"type_refs":["And","Exists","LE.le","LT.lt","Membership.mem","Nat","Nat.succ","PFun","Part","Part.instMembership","Sum","Sum.inl","Sum.inr","instLENat","instLTNat"],"value_dag_size":933,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HEq","HEq.refl","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PFun","Part","Part.instMembership","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","Sum","Sum.inl","Sum.inr","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Partrec.to₂.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Partrec.to₂","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":42,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Partrec","name":"_private.Mathlib.Computability.Partrec.0.Partrec.vector_mOfFn.match_1_1","namespace":"_private.Mathlib.Computability.Partrec.0.Partrec.vector_mOfFn","reducibility":"abbrev","statement_dag_size":118,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","PFun","Partrec","Primcodable","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":158,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","PFun","Partrec","Primcodable","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecBasis","name":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt._simp_1_2","namespace":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HSub.hSub","LE.le","Nat","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":40,"value_refs":["Eq","HSub.hSub","LE.le","Nat","Nat.sub_eq_zero_iff_le","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecBasis","name":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt._simp_1_3","namespace":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.bind","Part.instMembership"],"value_dag_size":66,"value_refs":["And","Exists","Membership.mem","Part","Part.bind","Part.instMembership","Part.mem_bind_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecBasis","name":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt._simp_1_4","namespace":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.mem_some_iff","Part.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecBasis","name":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt._simp_1_5","namespace":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecBasis","name":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt._simp_1_6","namespace":"_private.Mathlib.Computability.PartrecBasis.0.Nat.Partrec'.rfindOpt","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Part","Part.instMembership","Part.ofOption"],"value_dag_size":37,"value_refs":["Membership.mem","Option","Option.instMembership","Part","Part.instMembership","Part.mem_coe","Part.ofOption","propext"]}
+{"definition_height":15,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":"regular","statement_dag_size":8,"type_refs":["List","Nat","Option"],"value_dag_size":214,"value_refs":["Bind.bind","Denumerable.nat","Denumerable.ofNat","Denumerable.prod","HAdd.hAdd","List","List.length","List.map","List.range","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.Partrec.Code.recOn","Nat.casesOn","Nat.pair","Nat.succ","Nat.unpair","OfNat.ofNat","Option","Option.none","Option.some","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","instAddNat","instHAdd","instMonadOption","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G","reducibility":null,"statement_dag_size":221,"type_refs":["Bind.bind","Denumerable.nat","Denumerable.ofNat","Denumerable.prod","Eq","HAdd.hAdd","List","List.length","List.map","List.range","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.Partrec.Code.recOn","Nat.casesOn","Nat.pair","Nat.succ","Nat.unpair","OfNat.ofNat","Option","Option.none","Option.some","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","instAddNat","instHAdd","instMonadOption","instOfNatNat"],"value_dag_size":14,"value_refs":["Eq.refl","List","Nat","Option","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.Partrec.Code.const.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.const.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1.eq_2","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.Partrec.Code.const.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.const.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1.splitter","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.const.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const_inj.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.const_inj","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.Partrec.Code","Nat.Partrec.Code.const","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":246,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.const","Nat.Partrec.Code.ctorIdx","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit","Unit.unit"],"value_dag_size":71,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_2","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit","Unit.unit"],"value_dag_size":71,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_3","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit","Unit.unit"],"value_dag_size":71,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_4","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit","Unit.unit"],"value_dag_size":71,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_5","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"],"value_dag_size":77,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_6","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"],"value_dag_size":77,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_7","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"],"value_dag_size":77,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.eq_8","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"],"value_dag_size":74,"value_refs":["Eq.refl","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1.splitter","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encodeCode.match_1","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Unit"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.encodeCode.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_lt_rfind'._proof_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_lt_rfind'","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","HMul.hMul","LT.lt","Nat","Nat.Partrec.Code","Nat.Partrec.Code.encodeCode","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":195,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Partrec.Code","Nat.Partrec.Code.encodeCode","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_ofNatCode","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","Nat","Nat.Partrec.Code.encodeCode","Nat.Partrec.Code.ofNatCode"],"value_dag_size":1237,"value_refs":["AddMonoid.toAddZeroClass","Bool","Bool.casesOn","Bool.false","Bool.toNat","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HDiv.hDiv","HMul.hMul","InvImage","LT.lt","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.encodeCode","Nat.Partrec.Code.encodeCode.eq_1","Nat.Partrec.Code.encodeCode.eq_2","Nat.Partrec.Code.encodeCode.eq_3","Nat.Partrec.Code.encodeCode.eq_4","Nat.Partrec.Code.left","Nat.Partrec.Code.ofNatCode","Nat.Partrec.Code.ofNatCode.eq_1","Nat.Partrec.Code.ofNatCode.eq_2","Nat.Partrec.Code.ofNatCode.eq_3","Nat.Partrec.Code.ofNatCode.eq_4","Nat.Partrec.Code.ofNatCode.eq_5","Nat.Partrec.Code.ofNatCode.match_1","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.add_left_cancel_iff._simp_1","Nat.bit","Nat.bit_bodd_div2","Nat.bit_val","Nat.bodd","Nat.div2","Nat.div_le_self","Nat.instAddMonoid","Nat.instDiv","Nat.instPreorder","Nat.le_add_right","Nat.pair","Nat.pair_unpair","Nat.succ","Nat.succ_le_succ","Nat.unpair","Nat.unpair_left_le","Nat.unpair_right_le","OfNat.ofNat","Prod.fst","Prod.snd","True","Unit","WellFounded.Nat.fix","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_ofNatCode.match_1_1","add_zero","congr","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat","le_trans","lt_of_le_of_lt","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_ofNatCode.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.encode_ofNatCode","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":87,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.eval_const.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.eval_const","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":42,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1._arg_pusher","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":299,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1322,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":106,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_2","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":107,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_3","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":107,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_4","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":107,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_5","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":107,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_6","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":117,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":113,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_7","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":117,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":113,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_8","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":117,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":113,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_9","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":null,"statement_dag_size":113,"type_refs":["Eq","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":110,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.evaln.match_1","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.splitter","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1","reducibility":"abbrev","statement_dag_size":91,"type_refs":["Nat","Nat.Partrec.Code","Nat.Partrec.Code.comp","Nat.Partrec.Code.left","Nat.Partrec.Code.pair","Nat.Partrec.Code.prec","Nat.Partrec.Code.rfind'","Nat.Partrec.Code.right","Nat.Partrec.Code.succ","Nat.Partrec.Code.zero","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.evaln.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_bound._simp_1_12","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_bound","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Option","Option.bind","Option.some"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Option","Option.bind","Option.bind_eq_some_iff","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_bound.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_bound","reducibility":"abbrev","statement_dag_size":98,"type_refs":["HAdd.hAdd","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.succ","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":135,"value_refs":["HAdd.hAdd","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete._simp_1_22","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Option","Option.bind","Option.some"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Option","Option.bind","Option.bind_eq_some_iff","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete._simp_1_23","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete._simp_1_24","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":null,"statement_dag_size":28,"type_refs":["Decidable","Eq","Option","Option.some","Unit","guard","instAlternativeOption"],"value_dag_size":33,"value_refs":["Decidable","Eq","Option","Option.guard_eq_some'","Option.some","Unit","guard","instAlternativeOption","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete._simp_1_25","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete._simp_1_26","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Exists","Nonempty"],"value_dag_size":23,"value_refs":["Exists","Nonempty","exists_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_complete","reducibility":"abbrev","statement_dag_size":60,"type_refs":["Exists","Exists.intro","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Option","Option.instMembership"],"value_dag_size":77,"value_refs":["Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_map","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.range","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Option","Option.bind","instLTNat"],"value_dag_size":334,"value_refs":["Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","GetElem?.getElem?","LE.le","LT.lt","LinearOrder.toPartialOrder","List","List.getElem?_eq_none","List.getElem?_range","List.instGetElem?NatLtLength","List.length","List.length_range","List.range","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.Partrec.Code.evaln_bound","Nat.decLt","Nat.instLinearOrder","Not","Not.elim","Option","Option.bind","Option.bind_congr'","Option.casesOn","Option.instMembership","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLE","True","congrArg","congrFun'","dite","eq_self","id","instLENat","instLTNat","not_lt._simp_1","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_12","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_13","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Option","Option.bind","Option.some"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Option","Option.bind","Option.bind_eq_some_iff","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_14","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":28,"type_refs":["Decidable","Eq","Option","Option.some","Unit","guard","instAlternativeOption"],"value_dag_size":33,"value_refs":["Decidable","Eq","Option","Option.guard_eq_some'","Option.some","Unit","guard","instAlternativeOption","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_15","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_16","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Exists","Nonempty"],"value_dag_size":23,"value_refs":["Exists","Nonempty","exists_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono._simp_1_17","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_mono","reducibility":"abbrev","statement_dag_size":129,"type_refs":["HAdd.hAdd","LE.le","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.succ","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":294,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LE.le","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instLENat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound._simp_1_21","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Option","Option.bind","Option.some"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Option","Option.bind","Option.bind_eq_some_iff","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound._simp_1_23","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln_sound","reducibility":"abbrev","statement_dag_size":98,"type_refs":["HAdd.hAdd","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.succ","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":135,"value_refs":["HAdd.hAdd","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.evaln","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Option","Option.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point","reducibility":"abbrev","statement_dag_size":101,"type_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.instDenumerable","PFun","PFun.lift","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.toEncodable"],"value_dag_size":122,"value_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.casesOn","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.instDenumerable","PFun","PFun.lift","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.toEncodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point.match_1_3","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point","reducibility":"abbrev","statement_dag_size":123,"type_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Part","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Prod","Prod.fst","Prod.snd"],"value_dag_size":146,"value_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.casesOn","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Part","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Prod","Prod.fst","Prod.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point₂.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.fixed_point₂","reducibility":"abbrev","statement_dag_size":123,"type_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.instDenumerable","PFun","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Prod","Prod.fst","Prod.snd"],"value_dag_size":146,"value_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Eq","Exists","Exists.casesOn","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.instDenumerable","PFun","Part.bind","Part.map","Part.ofOption","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Prod","Prod.fst","Prod.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.hG","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":null,"statement_dag_size":28,"type_refs":["Denumerable.nat","List","Nat","Option","Primcodable.list","Primcodable.ofDenumerable","Primcodable.option","Primrec","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.G"],"value_dag_size":2356,"value_refs":["Bind.bind","Denumerable.nat","Denumerable.ofNat","Denumerable.prod","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Function.comp","HAdd.hAdd","List","List.length","List.map","List.range","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.Partrec.Code.primrec_recOn","Nat.Partrec.Code.recOn","Nat.casesOn","Nat.pair","Nat.succ","Nat.unpair","OfNat.ofNat","Option","Option.bind","Option.bind_eq_bind","Option.map","Option.map_eq_bind","Option.none","Option.some","Primcodable","Primcodable.list","Primcodable.ofDenumerable","Primcodable.option","Primcodable.prod","Primrec","Primrec.comp","Primrec.const","Primrec.fst","Primrec.list_length","Primrec.list_map","Primrec.list_range","Primrec.nat_casesOn","Primrec.ofNat","Primrec.option_bind","Primrec.option_map","Primrec.option_some","Primrec.pair","Primrec.snd","Primrec.succ","Primrec.unpair","Primrec₂","Primrec₂.comp","Primrec₂.natPair","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.hlup","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","congrArg","funext","id","instAddNat","instHAdd","instMonadOption","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.hlup","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":null,"statement_dag_size":68,"type_refs":["Denumerable.nat","List","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Option","Primcodable.list","Primcodable.ofDenumerable","Primcodable.option","Primcodable.prod","Primrec","Prod","Prod.fst","Prod.snd","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup"],"value_dag_size":287,"value_refs":["Bind.bind","Denumerable.nat","Encodable.Prod.encodable","Encodable.encode","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.encodable","Option","Primcodable.list","Primcodable.ofDenumerable","Primcodable.option","Primcodable.prod","Primcodable.toEncodable","Primrec.comp","Primrec.encode","Primrec.fst","Primrec.list_getElem?","Primrec.option_bind","Primrec.snd","Primrec₂.comp","Prod","Prod.fst","Prod.snd","instLTNat","instMonadOption"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.instCountableSubtypePFunPartrec.match_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.instCountableSubtypePFunPartrec","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Denumerable.nat","Nat","PFun","Partrec","Primcodable.ofDenumerable","Subtype","Subtype.mk"],"value_dag_size":47,"value_refs":["Denumerable.nat","Nat","PFun","Partrec","Primcodable.ofDenumerable","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":14,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code","reducibility":"regular","statement_dag_size":13,"type_refs":["List","Nat","Nat.Partrec.Code","Option","Prod"],"value_dag_size":84,"value_refs":["Bind.bind","Encodable.Prod.encodable","Encodable.encode","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.encodable","Option","Primcodable.ofDenumerable","Primcodable.toEncodable","Prod","instLTNat","instMonadOption"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","reducibility":null,"statement_dag_size":92,"type_refs":["Bind.bind","Encodable.Prod.encodable","Encodable.encode","Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Monad.toBind","Nat","Nat.Partrec.Code","Nat.Partrec.Code.instDenumerable","Nat.encodable","Option","Primcodable.ofDenumerable","Primcodable.toEncodable","Prod","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup","instLTNat","instMonadOption"],"value_dag_size":23,"value_refs":["Eq.refl","List","Nat","Nat.Partrec.Code","Option","Prod","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.lup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat.Partrec.Code.ofNatCode.match_1","Unit","Unit.unit"],"value_dag_size":42,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat.Partrec.Code.ofNatCode.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1.eq_2","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat.Partrec.Code.ofNatCode.match_1","Unit","Unit.unit"],"value_dag_size":42,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat.Partrec.Code.ofNatCode.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1.eq_3","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1","reducibility":null,"statement_dag_size":44,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat.Partrec.Code.ofNatCode.match_1","Unit","Unit.unit"],"value_dag_size":41,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat.Partrec.Code.ofNatCode.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1.eq_4","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1","reducibility":null,"statement_dag_size":43,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat.Partrec.Code.ofNatCode.match_1","Unit","Unit.unit"],"value_dag_size":40,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat.Partrec.Code.ofNatCode.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1.splitter","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_1","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.ofNatCode.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3._arg_pusher","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":166,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":448,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.eq_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.eq_2","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.eq_3","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.eq_4","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.eq_5","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.refl","Nat","Nat.Partrec.Code.ofNatCode.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3.splitter","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.ofNatCode.match_3","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.Partrec.Code.ofNatCode.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln._simp_1_14","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","List","List.instMembership","List.range","Membership.mem","Nat","instLTNat"],"value_dag_size":30,"value_refs":["LT.lt","List","List.instMembership","List.mem_range","List.range","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln._simp_1_15","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln._simp_1_4","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Option","Option.some"],"value_dag_size":28,"value_refs":["Eq","Option","Option.some","Option.some_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln.match_1_1","namespace":"_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.primrec_evaln","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Nat","Nat.Partrec.Code","Prod","Prod.mk"],"value_dag_size":55,"value_refs":["Nat","Nat.Partrec.Code","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.PartrecCode","name":"_private.Mathlib.Computability.PartrecCode.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Computability.PartrecCode.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.eq_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Bool","Bool.false","Encodable.decodeSum.match_1","Eq","Nat"],"value_dag_size":33,"value_refs":["Bool","Bool.false","Encodable.decodeSum.match_1","Eq.refl","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.eq_2","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Bool","Bool.false","Encodable.decodeSum.match_1","Eq","False","Nat"],"value_dag_size":231,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.rec","Bool.true","Encodable.decodeSum._sparseCasesOn_1","Encodable.decodeSum._sparseCasesOn_1.else_eq","Encodable.decodeSum.match_1","Eq","Eq.mpr","Eq.refl","False","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.splitter._sparseCasesOn_2","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.splitter","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Bool","Bool.false","Eq","False","Nat"],"value_dag_size":107,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.splitter._sparseCasesOn_2","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.splitter._sparseCasesOn_2","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Encodable.decodeSum.match_1.splitter","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Bool","Bool.ctorIdx","Bool.false","Nat.hasNotBit"],"value_dag_size":63,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.rec","Bool.true","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Nat.Primrec.const.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Nat.Primrec.const","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.dom_bool₂.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.dom_bool₂","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Bool","Prod","Prod.mk"],"value_dag_size":33,"value_refs":["Bool","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.dom_finite.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.dom_finite","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists","Exists.intro","List","List.Nodup","List.instMembership","Membership.mem"],"value_dag_size":160,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","List.Nodup","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.eq._simp_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.eq","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.list_findIdx₁.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.list_findIdx₁","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.list_getElem?₁.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.list_getElem?₁","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div._simp_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div._simp_1_2","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","propext","zero_lt_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.of_equiv_symm._simp_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.of_equiv_symm","reducibility":null,"statement_dag_size":30,"type_refs":["Denumerable.nat","Encodable.encode","Eq","Nat","Primcodable","Primcodable.ofDenumerable","Primcodable.toEncodable","Primrec","True"],"value_dag_size":30,"value_refs":["Denumerable.nat","Encodable.encode","Nat","Primcodable","Primcodable.ofDenumerable","Primcodable.toEncodable","Primrec","Primrec.encode","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.option_getD.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.option_getD","reducibility":"abbrev","statement_dag_size":31,"type_refs":["Option","Prod","Prod.mk"],"value_dag_size":45,"value_refs":["Option","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.option_orElse.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec.option_orElse","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Option","Prod","Prod.mk"],"value_dag_size":45,"value_refs":["Option","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.and.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.and","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":155,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.comp.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.comp","reducibility":"abbrev","statement_dag_size":97,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":124,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.not.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.not","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":91,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.or.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.or","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":155,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.Basic","name":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec₂.uncurry.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.Basic.0.Primrec₂.uncurry","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":42,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1.eq_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","List.cons","List.lookup.match_1","List.nil","Prod","Prod.mk"],"value_dag_size":69,"value_refs":["Eq.refl","List","List.cons","List.lookup.match_1","List.nil","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1.eq_2","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","List","List.cons","List.lookup.match_1","List.nil","Prod","Prod.mk"],"value_dag_size":84,"value_refs":["Eq.refl","List","List.cons","List.lookup.match_1","List.nil","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1.splitter","namespace":"_private.Mathlib.Computability.Primrec.List.0.List.lookup.match_1","reducibility":"abbrev","statement_dag_size":60,"type_refs":["List","List.cons","List.nil","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["List.lookup.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.const.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.const","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.encode.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.encode","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Eq","List","List.Vector","List.cons","List.length","Nat","Nat.succ","Subtype.mk"],"value_dag_size":161,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Vector","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.ctorIdx","Nat.succ","Subtype.casesOn","Subtype.mk","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.encode.match_1_3","namespace":"_private.Mathlib.Computability.Primrec.List.0.Nat.Primrec'.encode","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.fin_app.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.fin_app","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Fin","Nat","Prod","Prod.mk"],"value_dag_size":54,"value_refs":["Fin","Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_modify'.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_modify'","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Nat","Prod","Prod.mk"],"value_dag_size":38,"value_refs":["Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_ofFn.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_ofFn","reducibility":"abbrev","statement_dag_size":113,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","Primcodable","Primrec","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":152,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Primcodable","Primrec","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_set.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_set","reducibility":"abbrev","statement_dag_size":26,"type_refs":["Nat","Prod","Prod.mk"],"value_dag_size":38,"value_refs":["Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_take.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.list_take","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","Nat","Prod","Prod.mk"],"value_dag_size":43,"value_refs":["List","Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.nat_omega_rec'._proof_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.nat_omega_rec'","reducibility":null,"statement_dag_size":140,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.flatMap","List.instMembership","List.nil","Membership.mem","Nat","Nat.rec","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2996,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.flatMap","List.instMembership","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","Nat.rec","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.vector_head.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.vector_head","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Eq","List","List.Vector","List.cons","List.length","Nat","Nat.succ","Subtype.mk"],"value_dag_size":197,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Vector","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.ctorIdx","Nat.succ","Subtype.casesOn","Subtype.mk","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.Primrec.vector_tail.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.Primrec.vector_tail","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Eq","List","List.Vector","List.length","Nat","Subtype.mk"],"value_dag_size":64,"value_refs":["Eq","List","List.Vector","List.length","Nat","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.exists_mem_list.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.exists_mem_list","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":91,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.forall_mem_list.match_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.forall_mem_list","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":91,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.listFilter_listRange._simp_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.PrimrecPred.listFilter_listRange","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Eq","List","List.filter","List.filterMap","Option.guard"],"value_dag_size":32,"value_refs":["Bool","Eq.symm","List","List.filter","List.filterMap","List.filterMap_eq_filter","Option.guard"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.PrimrecRel.listFilter._simp_1_1","namespace":"_private.Mathlib.Computability.Primrec.List.0.PrimrecRel.listFilter","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Eq","List","List.filter","List.filterMap","Option.guard"],"value_dag_size":32,"value_refs":["Bool","Eq.symm","List","List.filter","List.filterMap","List.filterMap_eq_filter","Option.guard"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.list_casesOn'","namespace":"_private.Mathlib.Computability.Primrec.List.0","reducibility":null,"statement_dag_size":132,"type_refs":["Encodable.decode","Encodable.encode","List","List.casesOn","List.encodable","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.prod","Primcodable.toEncodable","Primrec","Primrec₂","Prod","Prod.mk","_private.Mathlib.Computability.Primrec.List.0.prim"],"value_dag_size":901,"value_refs":["Denumerable.nat","Encodable.Prod.encodable","Encodable.decode","Encodable.decode_prod_val","Encodable.encode","Encodable.encodek","Eq","Eq.trans","Iff.mp","Iff.mpr","List","List.casesOn","List.cons","List.encodable","Membership.mem","Nat","Nat.Primrec","Nat.pair","Nat.unpair","Nat.unpair_pair","Option","Option.bind","Option.bind_congr'","Option.casesOn","Option.encodable","Option.instMembership","Option.map","Option.rec","Option.some","Primcodable","Primcodable.ofDenumerable","Primcodable.option","Primcodable.prod","Primcodable.toEncodable","Primrec","Primrec.comp","Primrec.comp₂","Primrec.encode_iff","Primrec.fst","Primrec.id","Primrec.map_decode_iff","Primrec.of_eq","Primrec.option_casesOn","Primrec.option_some_iff","Primrec.snd","Primrec.to₂","Primrec₂","Primrec₂.comp","Primrec₂.comp₂","Primrec₂.left","Primrec₂.right","Prod","Prod.fst","Prod.mk","Prod.snd","True","_private.Mathlib.Computability.Primrec.List.0.prim","congrArg","congrFun'","eq_self","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.list_cons'","namespace":"_private.Mathlib.Computability.Primrec.List.0","reducibility":null,"statement_dag_size":48,"type_refs":["Encodable.decode","Encodable.encode","List","List.cons","List.encodable","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.toEncodable","Primrec₂","_private.Mathlib.Computability.Primrec.List.0.prim"],"value_dag_size":178,"value_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Encodable.encodeList","Iff.mp","Iff.mpr","List","List.cons","List.encodable","Nat","Nat.Primrec","Nat.pair","Nat.succ","Option","Option.encodable","Primcodable","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Primrec","Primrec.comp","Primrec.encode_iff","Primrec.fst","Primrec.snd","Primrec.succ","Primrec₂.comp","Primrec₂.natPair","Prod","Prod.fst","Prod.snd","_private.Mathlib.Computability.Primrec.List.0.prim"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.list_foldl'","namespace":"_private.Mathlib.Computability.Primrec.List.0","reducibility":null,"statement_dag_size":124,"type_refs":["Encodable.decode","Encodable.encode","List","List.encodable","List.foldl","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.prod","Primcodable.toEncodable","Primrec","Primrec₂","Prod","Prod.mk","_private.Mathlib.Computability.Primrec.List.0.prim"],"value_dag_size":1179,"value_refs":["Denumerable.nat","Encodable.decode","Encodable.encode","Encodable.length_le_encode","Eq","Eq.mpr","Eq.refl","Eq.trans","HAdd.hAdd","Iff.mpr","List","List.casesOn","List.cons","List.drop","List.drop_nil","List.drop_succ_cons","List.encodable","List.foldl","List.nil","List.take","List.take_nil","List.take_of_length_le","Nat","Nat.Primrec","Nat.iterate","Nat.recAux","OfNat.ofNat","Option","Option.encodable","Primcodable","Primcodable.ofDenumerable","Primcodable.prod","Primcodable.toEncodable","Primrec","Primrec.comp","Primrec.encode_iff","Primrec.fst","Primrec.nat_iterate","Primrec.of_eq","Primrec.pair","Primrec.snd","Primrec.to₂","Primrec₂","Primrec₂.comp","Prod","Prod.fst","Prod.mk","Prod.snd","True","_private.Mathlib.Computability.Primrec.List.0.list_casesOn'","_private.Mathlib.Computability.Primrec.List.0.prim","congr","congrArg","eq_self","id","instAddNat","instHAdd","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.list_reverse'","namespace":"_private.Mathlib.Computability.Primrec.List.0","reducibility":null,"statement_dag_size":46,"type_refs":["Encodable.decode","Encodable.encode","List","List.encodable","List.reverse","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.toEncodable","Primrec","_private.Mathlib.Computability.Primrec.List.0.prim"],"value_dag_size":426,"value_refs":["Encodable.decode","Encodable.encode","Eq","Eq.trans","HAppend.hAppend","List","List.cons","List.encodable","List.foldl","List.instAppend","List.nil","List.rec","List.reverse","List.reverseAux","List.reverseAux_eq","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.prod","Primcodable.toEncodable","Primrec.comp","Primrec.const","Primrec.fst","Primrec.id","Primrec.of_eq","Primrec.snd","Primrec.to₂","Primrec₂.comp","Prod","Prod.fst","Prod.mk","Prod.snd","True","_private.Mathlib.Computability.Primrec.List.0.list_cons'","_private.Mathlib.Computability.Primrec.List.0.list_foldl'","_private.Mathlib.Computability.Primrec.List.0.prim","congr","congrArg","eq_self","forall_congr","id","implies_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Primrec.List","name":"_private.Mathlib.Computability.Primrec.List.0.prim","namespace":"_private.Mathlib.Computability.Primrec.List.0","reducibility":"regular","statement_dag_size":35,"type_refs":["Encodable.decode","Encodable.encode","List","List.encodable","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.toEncodable"],"value_dag_size":38,"value_refs":["Encodable.decode","Encodable.encode","List","List.encodable","Nat","Nat.Primrec","Option","Option.encodable","Primcodable","Primcodable.mk","Primcodable.toEncodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Computable.find._simp_1_1","namespace":"_private.Mathlib.Computability.RE.0.Computable.find","reducibility":null,"statement_dag_size":27,"type_refs":["DecidablePred","Eq","Exists","Nat","Nat.find","True"],"value_dag_size":29,"value_refs":["DecidablePred","Exists","Nat","Nat.find","Nat.find_spec","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Computable","ComputablePred","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool"],"value_dag_size":91,"value_refs":["Bool","Computable","ComputablePred","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_3","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map","Part.mem_map_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_4","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Membership.mem","Part","Part.assert","Part.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Part","Part.assert","Part.instMembership","Part.mem_assert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_5","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.mem_some_iff","Part.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_6","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_7","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Exists","Nonempty"],"value_dag_size":23,"value_refs":["Exists","Nonempty","exists_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_8","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":19,"type_refs":["Bool","Bool.true","Decidable","Decidable.decide","Eq"],"value_dag_size":23,"value_refs":["Bool","Bool.true","Decidable","Decidable.decide","Eq","propext","true_eq_decide_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re._simp_1_9","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":null,"statement_dag_size":21,"type_refs":["Bool","Bool.false","Decidable","Decidable.decide","Eq","Not"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Decidable","Decidable.decide","Eq","Not","false_eq_decide_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.computable_iff_re_compl_re","reducibility":"abbrev","statement_dag_size":65,"type_refs":["And","And.intro","Not","Primcodable","REPred"],"value_dag_size":79,"value_refs":["And","And.casesOn","And.intro","Not","Primcodable","REPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.ComputablePred.not.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.ComputablePred.not","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Computable","ComputablePred","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool"],"value_dag_size":91,"value_refs":["Bool","Computable","ComputablePred","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'._simp_1_1","namespace":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Membership.mem","Part","Part.Dom","Part.instMembership"],"value_dag_size":31,"value_refs":["Exists","Membership.mem","Part","Part.Dom","Part.dom_iff_mem","Part.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'._simp_1_2","namespace":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.evaln","Option","Option.instMembership","Part","Part.instMembership"],"value_dag_size":46,"value_refs":["Exists","Membership.mem","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","Nat.Partrec.Code.evaln","Nat.Partrec.Code.evaln_complete","Option","Option.instMembership","Part","Part.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'._simp_1_3","namespace":"_private.Mathlib.Computability.RE.0.Nat.Partrec.merge'","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.cond.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.Partrec.cond","reducibility":"abbrev","statement_dag_size":154,"type_refs":["Encodable.decode","Encodable.encode","Eq","Exists","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Part.bind","Part.map","Part.ofOption","Primcodable","Primcodable.toEncodable"],"value_dag_size":190,"value_refs":["Encodable.decode","Encodable.encode","Eq","Exists","Exists.casesOn","Exists.intro","Nat","Nat.Partrec.Code","Nat.Partrec.Code.eval","PFun","Part.bind","Part.map","Part.ofOption","Primcodable","Primcodable.toEncodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.dom_re._simp_1_1","namespace":"_private.Mathlib.Computability.RE.0.Partrec.dom_re","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Membership.mem","Part","Part.Dom","Part.instMembership"],"value_dag_size":31,"value_refs":["Exists","Membership.mem","Part","Part.Dom","Part.dom_iff_mem","Part.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_3","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Part","Part.instMembership","Part.ofOption"],"value_dag_size":37,"value_refs":["Membership.mem","Option","Option.instMembership","Part","Part.instMembership","Part.mem_coe","Part.ofOption","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_4","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.bind","Part.instMembership"],"value_dag_size":66,"value_refs":["And","Exists","Membership.mem","Part","Part.bind","Part.instMembership","Part.mem_bind_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_5","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_6","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map","Part.mem_map_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_7","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Option","Option.some"],"value_dag_size":28,"value_refs":["Eq","Option","Option.some","Option.some_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'._simp_1_8","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Part.some","True"],"value_dag_size":17,"value_refs":["Part.Dom","Part.some","Part.some_dom","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge'.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge'","reducibility":"abbrev","statement_dag_size":389,"type_refs":["And","And.intro","Encodable.decode₂","Encodable.encode","Exists","Exists.intro","Iff","Membership.mem","Nat","Nat.Partrec","Or","PFun","Part","Part.Dom","Part.bind","Part.instMembership","Part.map","Part.ofOption","Primcodable","Primcodable.toEncodable"],"value_dag_size":486,"value_refs":["And","And.casesOn","And.intro","Encodable.decode₂","Encodable.encode","Exists","Exists.casesOn","Exists.intro","Iff","Membership.mem","Nat","Nat.Partrec","Or","PFun","Part","Part.Dom","Part.bind","Part.instMembership","Part.map","Part.ofOption","Primcodable","Primcodable.toEncodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.Partrec.merge.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.Partrec.merge","reducibility":"abbrev","statement_dag_size":263,"type_refs":["And","And.intro","Exists","Exists.intro","Iff","Membership.mem","Or","PFun","Part","Part.Dom","Part.instMembership","Partrec","Primcodable"],"value_dag_size":373,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Iff","Membership.mem","Or","PFun","Part","Part.Dom","Part.instMembership","Partrec","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RE","name":"_private.Mathlib.Computability.RE.0.PrimrecPred.computablePred.match_1_1","namespace":"_private.Mathlib.Computability.RE.0.PrimrecPred.computablePred","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","Decidable.decide","DecidablePred","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"],"value_dag_size":91,"value_refs":["Bool","Decidable.decide","DecidablePred","Exists.casesOn","Exists.intro","Primcodable","Primcodable.bool","Primrec","PrimrecPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RecursiveIn","name":"_private.Mathlib.Computability.RecursiveIn.0.RecursiveIn.partrec_of_oracle._simp_1_1","namespace":"_private.Mathlib.Computability.RecursiveIn.0.RecursiveIn.partrec_of_oracle","reducibility":null,"statement_dag_size":23,"type_refs":["Denumerable.nat","Eq","Nat","Nat.Partrec","PFun","Partrec","Primcodable.ofDenumerable"],"value_dag_size":24,"value_refs":["Denumerable.nat","Nat","Nat.Partrec","PFun","Partrec","Partrec.nat_iff","Primcodable.ofDenumerable","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RecursiveIn","name":"_private.Mathlib.Computability.RecursiveIn.0.RecursiveIn.subst._simp_1_1","namespace":"_private.Mathlib.Computability.RecursiveIn.0.RecursiveIn.subst","reducibility":null,"statement_dag_size":29,"type_refs":["Denumerable.nat","Eq","Nat","Nat.RecursiveIn","PFun","Primcodable.ofDenumerable","RecursiveIn","Set"],"value_dag_size":31,"value_refs":["Denumerable.nat","Nat","Nat.RecursiveIn","PFun","Primcodable.ofDenumerable","RecursiveIn","RecursiveIn.iff_nat","Set","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.Equiv.Computable.trans.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.Equiv.Computable.trans","reducibility":"abbrev","statement_dag_size":269,"type_refs":["And.intro","Computable","DFunLike.coe","Equiv","Equiv.Computable","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Primcodable"],"value_dag_size":362,"value_refs":["And.casesOn","And.intro","Computable","DFunLike.coe","Equiv","Equiv.Computable","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree.add_le._simp_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree.add_le","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","HAdd.hAdd","Inhabited","ManyOneDegree","ManyOneDegree.instAdd","ManyOneDegree.of","Primcodable","Primcodable.sum","Set","Sum","Sum.elim","Sum.instMonad_mathlib","instHAdd","instInhabitedOfMonad"],"value_dag_size":93,"value_refs":["Eq.symm","HAdd.hAdd","Inhabited","ManyOneDegree","ManyOneDegree.add_of","ManyOneDegree.instAdd","ManyOneDegree.of","Primcodable","Primcodable.sum","Set","Sum","Sum.elim","Sum.instMonad_mathlib","instHAdd","instInhabitedOfMonad"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree.le_antisymm","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","LE.le","ManyOneDegree","ManyOneDegree.instLE"],"value_dag_size":161,"value_refs":["And","Denumerable.nat","Eq","Eq.mp","Eq.trans","LE.le","ManyOneDegree","ManyOneDegree.ind_on","ManyOneDegree.instLE","ManyOneDegree.of","ManyOneDegree.of_eq_of._simp_1","ManyOneDegree.of_le_of._simp_1","ManyOneEquiv","ManyOneReducible","Nat","Primcodable.ofDenumerable","Set","True","congr","congrArg","eq_true","id","instInhabitedNat","of_eq_true","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree.le_refl","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree","reducibility":null,"statement_dag_size":9,"type_refs":["LE.le","ManyOneDegree","ManyOneDegree.instLE"],"value_dag_size":63,"value_refs":["Denumerable.nat","Eq","Eq.mpr","LE.le","ManyOneDegree","ManyOneDegree.ind_on","ManyOneDegree.instLE","ManyOneDegree.of","ManyOneDegree.of_le_of._simp_1","ManyOneReducible","Nat","Primcodable.ofDenumerable","Set","id","instInhabitedNat","manyOneReducible_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree.le_trans","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneDegree","reducibility":null,"statement_dag_size":17,"type_refs":["LE.le","ManyOneDegree","ManyOneDegree.instLE"],"value_dag_size":85,"value_refs":["Denumerable.nat","LE.le","ManyOneDegree","ManyOneDegree.ind_on","ManyOneDegree.instLE","ManyOneDegree.of","ManyOneReducible.trans","Nat","Primcodable.ofDenumerable","Set","instInhabitedNat","toNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneEquiv.trans.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneEquiv.trans","reducibility":"abbrev","statement_dag_size":137,"type_refs":["And.intro","ManyOneEquiv","ManyOneReducible","Primcodable"],"value_dag_size":192,"value_refs":["And.casesOn","And.intro","ManyOneEquiv","ManyOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.ManyOneReducible.trans.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.ManyOneReducible.trans","reducibility":"abbrev","statement_dag_size":176,"type_refs":["And","And.intro","Computable","Exists.intro","Iff","ManyOneReducible","Primcodable"],"value_dag_size":357,"value_refs":["And","And.casesOn","And.intro","Computable","Exists.casesOn","Exists.intro","Iff","ManyOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.OneOneEquiv.to_many_one.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.OneOneEquiv.to_many_one","reducibility":"abbrev","statement_dag_size":76,"type_refs":["And.intro","OneOneEquiv","OneOneReducible","Primcodable"],"value_dag_size":99,"value_refs":["And.casesOn","And.intro","OneOneEquiv","OneOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.OneOneEquiv.trans.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.OneOneEquiv.trans","reducibility":"abbrev","statement_dag_size":137,"type_refs":["And.intro","OneOneEquiv","OneOneReducible","Primcodable"],"value_dag_size":192,"value_refs":["And.casesOn","And.intro","OneOneEquiv","OneOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.OneOneReducible.to_many_one.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.OneOneReducible.to_many_one","reducibility":"abbrev","statement_dag_size":119,"type_refs":["And","And.intro","Computable","Exists.intro","Function.Injective","Iff","OneOneReducible","Primcodable"],"value_dag_size":251,"value_refs":["And","And.casesOn","And.intro","Computable","Exists.casesOn","Exists.intro","Function.Injective","Iff","OneOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.OneOneReducible.trans.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.OneOneReducible.trans","reducibility":"abbrev","statement_dag_size":216,"type_refs":["And","And.intro","Computable","Exists.intro","Function.Injective","Iff","OneOneReducible","Primcodable"],"value_dag_size":613,"value_refs":["And","And.casesOn","And.intro","Computable","Exists.casesOn","Exists.intro","Function.Injective","Iff","OneOneReducible","Primcodable"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0._aux_Mathlib_Computability_Reduce___unexpand_Sum_elim_1","namespace":"_private.Mathlib.Computability.Reduce.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":245,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.disjoin_le.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.disjoin_le","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","ManyOneReducible","Primcodable"],"value_dag_size":120,"value_refs":["And","And.casesOn","And.intro","ManyOneReducible","Primcodable"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.disjoin_manyOneReducible.match_1_1","namespace":"_private.Mathlib.Computability.Reduce.0.disjoin_manyOneReducible","reducibility":"abbrev","statement_dag_size":175,"type_refs":["And","And.intro","Computable","Exists.intro","Iff","ManyOneReducible","Primcodable"],"value_dag_size":359,"value_refs":["And","And.casesOn","And.intro","Computable","Exists.casesOn","Exists.intro","Iff","ManyOneReducible","Primcodable"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.«_aux_Mathlib_Computability_Reduce___macroRules__private_Mathlib_Computability_Reduce_0_term_⊕'__1_1»","namespace":"_private.Mathlib.Computability.Reduce.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":230,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.Reduce","name":"_private.Mathlib.Computability.Reduce.0.«term_⊕'__1»","namespace":"_private.Mathlib.Computability.Reduce.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":56,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.add_rmatch_iff._simp_1_11","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.add_rmatch_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.or","Bool.true","Eq","Or"],"value_dag_size":27,"value_refs":["Bool","Bool.or","Bool.or_eq_true_iff","Bool.true","Eq","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":87,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_2","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":87,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_3","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":90,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_4","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":98,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":94,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_5","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":95,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_6","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":91,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.deriv.match_1","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.splitter","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1","reducibility":"abbrev","statement_dag_size":75,"type_refs":["RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero"],"value_dag_size":1,"value_refs":["RegularExpression.deriv.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_id.match_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_id","reducibility":"abbrev","statement_dag_size":61,"type_refs":["RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":90,"value_refs":["RegularExpression","RegularExpression.casesOn","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_map.match_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_map","reducibility":"abbrev","statement_dag_size":61,"type_refs":["RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":90,"value_refs":["RegularExpression","RegularExpression.casesOn","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_pow.match_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.map_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit","Unit.unit"],"value_dag_size":72,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_2","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit","Unit.unit"],"value_dag_size":72,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_3","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":75,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_4","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":80,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_5","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":79,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.eq_6","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":75,"value_refs":["Eq.refl","RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.matches'.match_1","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1.splitter","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'.match_1","reducibility":"abbrev","statement_dag_size":61,"type_refs":["RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":1,"value_refs":["RegularExpression.matches'.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'_map.match_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'_map","reducibility":"abbrev","statement_dag_size":61,"type_refs":["RegularExpression","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit"],"value_dag_size":90,"value_refs":["RegularExpression","RegularExpression.casesOn","RegularExpression.char","RegularExpression.comp","RegularExpression.epsilon","RegularExpression.plus","RegularExpression.star","RegularExpression.zero","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'_pow.match_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.matches'_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1.eq_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","List","List.cons","List.nil","RegularExpression","RegularExpression.rmatch.match_1"],"value_dag_size":51,"value_refs":["Eq.refl","List","List.cons","List.nil","RegularExpression","RegularExpression.rmatch.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1.eq_2","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","List","List.cons","List.nil","RegularExpression","RegularExpression.rmatch.match_1"],"value_dag_size":58,"value_refs":["Eq.refl","List","List.cons","List.nil","RegularExpression","RegularExpression.rmatch.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1.splitter","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","RegularExpression"],"value_dag_size":1,"value_refs":["RegularExpression.rmatch.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'._simp_1_1","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'","reducibility":null,"statement_dag_size":89,"type_refs":["And","Bool","Bool.true","DecidableEq","Eq","Exists","HAppend.hAppend","HMul.hMul","List","List.instAppend","RegularExpression","RegularExpression.instMul","RegularExpression.rmatch","instHAppendOfAppend","instHMul"],"value_dag_size":95,"value_refs":["And","Bool","Bool.true","DecidableEq","Eq","Exists","HAppend.hAppend","HMul.hMul","List","List.instAppend","RegularExpression","RegularExpression.instMul","RegularExpression.mul_rmatch_iff","RegularExpression.rmatch","instHAppendOfAppend","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'._simp_1_2","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Exists","HAppend.hAppend","HMul.hMul","Language","Language.instMembershipList","Language.instMul","List","List.instAppend","Membership.mem","instHAppendOfAppend","instHMul"],"value_dag_size":91,"value_refs":["And","Eq","Exists","HAppend.hAppend","HMul.hMul","Language","Language.instMembershipList","Language.instMul","Language.mem_mul","List","List.instAppend","Membership.mem","instHAppendOfAppend","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'._simp_1_4","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'","reducibility":null,"statement_dag_size":80,"type_refs":["And","Bool","Bool.true","DecidableEq","Eq","Exists","List","List.flatten","List.instMembership","List.nil","Membership.mem","Ne","RegularExpression","RegularExpression.rmatch","RegularExpression.star"],"value_dag_size":85,"value_refs":["And","Bool","Bool.true","DecidableEq","Eq","Exists","List","List.flatten","List.instMembership","List.nil","Membership.mem","Ne","RegularExpression","RegularExpression.rmatch","RegularExpression.star","RegularExpression.star_rmatch_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'._simp_1_5","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'","reducibility":null,"statement_dag_size":78,"type_refs":["And","Eq","Exists","KStar.kstar","Language","Language.instKStar","Language.instMembershipList","List","List.flatten","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":81,"value_refs":["And","Eq","Exists","KStar.kstar","Language","Language.instKStar","Language.instMembershipList","Language.mem_kstar_iff_exists_nonempty","List","List.flatten","List.instMembership","List.nil","Membership.mem","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'._simp_1_6","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.rmatch_iff_matches'","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._proof_1_11","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":173,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._proof_1_17","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":168,"type_refs":["And","Bool","Bool.true","DecidableEq","Eq","Exists","HAppend.hAppend","Iff","LT.lt","List","List.cons","List.flatten","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","RegularExpression","RegularExpression.rmatch","RegularExpression.star","instHAppendOfAppend","instLTNat"],"value_dag_size":1716,"value_refs":["And","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HAdd.hAdd","HAppend.hAppend","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_and","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.ctorIdx","List.flatten","List.instAppend","List.instMembership","List.length","List.length_append","List.length_cons","List.mem_cons","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","RegularExpression","RegularExpression.rmatch","RegularExpression.star","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._simp_1_12","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._simp_1_13","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._simp_1_14","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._simp_1_15","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.RegularExpressions","name":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff._simp_1_16","namespace":"_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.star_rmatch_iff","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","List","List.cons"],"value_dag_size":43,"value_refs":["And","Eq","List","List.cons","List.cons_eq_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches.to₀.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches.to₀","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.refl.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.refl","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.single.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.single","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.trans.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₀.trans","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₁.to₀.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Reaches₁.to₀","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1.eq_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Option","Option.none","Option.some","StateTransition.Respects.match_1","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Option","Option.none","Option.some","StateTransition.Respects.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1.eq_2","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Option","Option.none","Option.some","StateTransition.Respects.match_1","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Option.none","Option.some","StateTransition.Respects.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1.splitter","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.Respects.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["StateTransition.Respects.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Eq","Option","Option.none","StateTransition.Reaches"],"value_dag_size":95,"value_refs":["And","And.casesOn","And.intro","Eq","Option","Option.none","StateTransition.Reaches"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal₁.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal₁","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Eq","Option","Option.none","StateTransition.Reaches"],"value_dag_size":95,"value_refs":["And","And.casesOn","And.intro","Eq","Option","Option.none","StateTransition.Reaches"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal₁.match_1_3","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.eval_maximal₁","reducibility":"abbrev","statement_dag_size":158,"type_refs":["And","And.intro","Exists","Exists.intro","Membership.mem","Option","Option.instMembership","Relation.ReflTransGen"],"value_dag_size":221,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Membership.mem","Option","Option.instMembership","Relation.ReflTransGen"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.frespects_eq.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.frespects_eq","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":39,"value_refs":["Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.fun_respects._simp_1_4","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.fun_respects","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.fun_respects._simp_1_5","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.fun_respects","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.mem_eval.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.mem_eval","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Eq","Option","Option.none","StateTransition.Reaches"],"value_dag_size":95,"value_refs":["And","And.casesOn","And.intro","Eq","Option","Option.none","StateTransition.Reaches"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.reaches_eval.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.reaches_eval","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Eq","Option","Option.none","StateTransition.Reaches"],"value_dag_size":95,"value_refs":["And","And.casesOn","And.intro","Eq","Option","Option.none","StateTransition.Reaches"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.reaches₀_eq.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.reaches₀_eq","reducibility":"abbrev","statement_dag_size":40,"type_refs":["Option","StateTransition.Reaches₁"],"value_dag_size":40,"value_refs":["Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval'.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval'","reducibility":"abbrev","statement_dag_size":133,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Option","Part","Part.instMembership","StateTransition.eval"],"value_dag_size":193,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Option","Part","Part.instMembership","StateTransition.eval"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval_dom.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval_dom","reducibility":"abbrev","statement_dag_size":194,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Option","Part","Part.Dom","Part.get","Part.instMembership","StateTransition.eval"],"value_dag_size":326,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Option","Part","Part.Dom","Part.get","Part.instMembership","StateTransition.eval"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval_dom.match_1_3","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_eval_dom","reducibility":"abbrev","statement_dag_size":194,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Option","Part","Part.Dom","Part.get","Part.instMembership","StateTransition.eval"],"value_dag_size":326,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Option","Part","Part.Dom","Part.get","Part.instMembership","StateTransition.eval"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches.match_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches","reducibility":"abbrev","statement_dag_size":90,"type_refs":["And","And.intro","Exists","Exists.intro","Option","StateTransition.Reaches₁"],"value_dag_size":139,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Option","StateTransition.Reaches₁"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches_rev._simp_1_1","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches_rev","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.StateTransition","name":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches_rev._simp_1_2","namespace":"_private.Mathlib.Computability.StateTransition.0.StateTransition.tr_reaches_rev","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.TuringDegree","name":"_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat","namespace":"_private.Mathlib.Computability.TuringDegree.0","reducibility":"regular","statement_dag_size":6,"type_refs":["Nat","PFun","Preorder"],"value_dag_size":41,"value_refs":["And","LE.mk","LT.mk","Nat","Not","PFun","Preorder.mk","TuringReducible","TuringReducible.refl","TuringReducible.trans","_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat._proof_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringDegree","name":"_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat._proof_1","namespace":"_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat","reducibility":null,"statement_dag_size":21,"type_refs":["And","Iff","Nat","Not","PFun","TuringReducible"],"value_dag_size":20,"value_refs":["And","Iff.rfl","Nat","Not","PFun","TuringReducible"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Computability.TuringMachine.Computable","name":"_private.Mathlib.Computability.TuringMachine.Computable.0.Turing.TM2ComputableInPolyTime.comp","namespace":"_private.Mathlib.Computability.TuringMachine.Computable.0.Turing.TM2ComputableInPolyTime","reducibility":"regular","statement_dag_size":55,"type_refs":["Function.comp","List","Nonempty","ProofWanted","Turing.TM2ComputableInPolyTime"],"value_dag_size":55,"value_refs":["Function.comp","List","Nonempty","ProofWanted.mk","Turing.TM2ComputableInPolyTime"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Computable","name":"_private.Mathlib.Computability.TuringMachine.Computable.0.Turing.idComputableInPolyTime._simp_1","namespace":"_private.Mathlib.Computability.TuringMachine.Computable.0.Turing.idComputableInPolyTime","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.headI.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.headI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.headI.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.headI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.List.headI.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.headI.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit","Unit.unit"],"value_dag_size":65,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit","Unit.unit"],"value_dag_size":65,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit","Unit.unit"],"value_dag_size":65,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"],"value_dag_size":71,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"],"value_dag_size":71,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"],"value_dag_size":71,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.eval.match_1","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1","reducibility":"abbrev","statement_dag_size":53,"type_refs":["Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'","Unit"],"value_dag_size":1,"value_refs":["Turing.ToPartrec.Code.eval.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":21,"type_refs":["Bool","Bool.false","Decidable","Decidable.decide","Eq","Not"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Decidable","Decidable.decide","Eq","Not","false_eq_decide_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_12","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.bind","Part.instMembership"],"value_dag_size":66,"value_refs":["And","Exists","Membership.mem","Part","Part.bind","Part.instMembership","Part.mem_bind_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_13","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map","Part.mem_map_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":51,"type_refs":["And","Bool","Bool.false","Bool.true","Eq","LT.lt","Membership.mem","Nat","Nat.rfind","PFun","Part","Part.instMembership","instLTNat"],"value_dag_size":53,"value_refs":["And","Bool","Bool.false","Bool.true","LT.lt","Membership.mem","Nat","Nat.mem_rfind","Nat.rfind","PFun","Part","Part.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_15","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":19,"type_refs":["Bool","Bool.true","Decidable","Decidable.decide","Eq"],"value_dag_size":23,"value_refs":["Bool","Bool.true","Decidable","Decidable.decide","Eq","propext","true_eq_decide_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_16","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.mem_some_iff","Part.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_17","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":13,"type_refs":["Eq","Exists","False"],"value_dag_size":13,"value_refs":["Exists","False","eq_false","exists_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","Fin","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","List.Vector","List.Vector.get","List.Vector.get_tail._proof_2","List.Vector.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":78,"value_refs":["Eq.symm","Fin","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","List.Vector","List.Vector.get","List.Vector.get_tail","List.Vector.get_tail._proof_2","List.Vector.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_8","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":null,"statement_dag_size":26,"type_refs":["Applicative.toPure","Eq","Monad.toApplicative","Part","Part.instMonad","Part.some","Pure.pure"],"value_dag_size":30,"value_refs":["Applicative.toPure","Eq.symm","Monad.toApplicative","Part","Part.instMonad","Part.pure_eq_some","Part.some","Pure.pure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Eq","List","List.Vector","List.length","List.nil","Nat","OfNat.ofNat","Subtype.mk","instOfNatNat"],"value_dag_size":153,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Vector","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","Subtype.casesOn","Subtype.mk","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code.match_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Eq","List","List.Vector","List.cons","List.length","List.nil","Nat","OfNat.ofNat","Subtype.mk","instOfNatNat"],"value_dag_size":263,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Vector","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","Subtype.casesOn","Subtype.mk","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code.match_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Eq","List","List.Vector","List.cons","List.length","Nat","Nat.succ","Subtype.mk"],"value_dag_size":161,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Vector","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.ctorIdx","Nat.succ","Subtype.casesOn","Subtype.mk","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit","Unit.unit"],"value_dag_size":62,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":71,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.eval.match_1","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Cont.eval.match_1","reducibility":"abbrev","statement_dag_size":51,"type_refs":["List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":1,"value_refs":["Turing.ToPartrec.Cont.eval.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.cont_eval_fix._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.cont_eval_fix","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.bind","Part.instMembership"],"value_dag_size":66,"value_refs":["And","Exists","Membership.mem","Part","Part.bind","Part.instMembership","Part.mem_bind_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.cont_eval_fix._simp_1_17","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.cont_eval_fix","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Part","Part.instMembership","Part.mem_some_iff","Part.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont","Turing.ToPartrec.step.match_1"],"value_dag_size":36,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont","Turing.ToPartrec.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont","Turing.ToPartrec.step.match_1"],"value_dag_size":39,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont","Turing.ToPartrec.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.step.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","Nat","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont"],"value_dag_size":1,"value_refs":["Turing.ToPartrec.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"],"value_dag_size":76,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"],"value_dag_size":85,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"],"value_dag_size":82,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"],"value_dag_size":82,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"],"value_dag_size":82,"value_refs":["Eq.refl","List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet.match_1","reducibility":"abbrev","statement_dag_size":65,"type_refs":["List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt"],"value_dag_size":1,"value_refs":["Turing.ToPartrec.stepRet.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Config","name":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet_eval._simp_1_13","namespace":"_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.stepRet_eval","reducibility":null,"statement_dag_size":64,"type_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq","Functor.map","LawfulMonad","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"],"value_dag_size":74,"value_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq.symm","Functor.map","LawfulMonad","LawfulMonad.bind_pure_comp","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":43,"value_refs":["Eq.refl","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Nat.iterate.match_1","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.iterate.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Option","Option.getD.match_1","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Option","Option.getD.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Option","Option.getD.match_1","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Option.getD.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.getD.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Option.getD.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Option","Option.isSome.match_1","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Option","Option.isSome.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Option","Option.isSome.match_1","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Option.isSome.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Option.isSome.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Cfg.map.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Cfg.map.match_1","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.map.match_1","Turing.TM0.Cfg.mk","Turing.Tape"],"value_dag_size":55,"value_refs":["Eq.refl","Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.map.match_1","Turing.TM0.Cfg.mk","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Cfg.map.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Cfg.map.match_1","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.Tape"],"value_dag_size":1,"value_refs":["Turing.TM0.Cfg.map.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Machine.map_respects.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Machine.map_respects","reducibility":"abbrev","statement_dag_size":196,"type_refs":["And","And.intro","Eq","Eq.refl","Inhabited","Membership.mem","Set","Set.instMembership","Turing.PointedMap","Turing.PointedMap.f","Turing.TM0.Cfg","Turing.TM0.Cfg.map","Turing.TM0.Cfg.q"],"value_dag_size":445,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Inhabited","Membership.mem","Set","Set.instMembership","Turing.PointedMap","Turing.PointedMap.f","Turing.TM0.Cfg","Turing.TM0.Cfg.map","Turing.TM0.Cfg.q","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Machine.map_step.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.Machine.map_step","reducibility":"abbrev","statement_dag_size":91,"type_refs":["Inhabited","Membership.mem","Set","Set.instMembership","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.TM0.Cfg.q","Turing.Tape"],"value_dag_size":127,"value_refs":["Inhabited","Membership.mem","Set","Set.instMembership","Turing.TM0.Cfg","Turing.TM0.Cfg.casesOn","Turing.TM0.Cfg.mk","Turing.TM0.Cfg.q","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Turing.Dir","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0.step.match_1"],"value_dag_size":38,"value_refs":["Eq.refl","Turing.Dir","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Turing.Dir","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0.step.match_1"],"value_dag_size":37,"value_refs":["Eq.refl","Turing.Dir","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1","reducibility":"abbrev","statement_dag_size":28,"type_refs":["Turing.Dir","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write"],"value_dag_size":1,"value_refs":["Turing.TM0.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_5.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_5","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.TM0.step.match_5","Turing.Tape"],"value_dag_size":55,"value_refs":["Eq.refl","Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.TM0.step.match_5","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_5.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_5","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.Tape"],"value_dag_size":1,"value_refs":["Turing.TM0.step.match_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step_supports.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step_supports","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.Tape"],"value_dag_size":56,"value_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.casesOn","Turing.TM0.Cfg.mk","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","Option","Option.none","Option.some","Prod","Prod.mk","Turing.TM0.Stmt","Turing.TM0to1.tr.match_1","Unit","Unit.unit"],"value_dag_size":59,"value_refs":["Eq.refl","Option","Option.none","Option.some","Prod","Prod.mk","Turing.TM0.Stmt","Turing.TM0to1.tr.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","Option","Option.none","Option.some","Prod","Prod.mk","Turing.TM0.Stmt","Turing.TM0to1.tr.match_1","Unit"],"value_dag_size":69,"value_refs":["Eq.refl","Option","Option.none","Option.some","Prod","Prod.mk","Turing.TM0.Stmt","Turing.TM0to1.tr.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_1","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Option","Option.none","Option.some","Prod","Prod.mk","Turing.TM0.Stmt","Unit"],"value_dag_size":1,"value_refs":["Turing.TM0to1.tr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"],"value_dag_size":65,"value_refs":["Eq.refl","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"],"value_dag_size":67,"value_refs":["Eq.refl","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"],"value_dag_size":68,"value_refs":["Eq.refl","Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.tr.match_3","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3","reducibility":"abbrev","statement_dag_size":53,"type_refs":["Turing.Dir","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal"],"value_dag_size":1,"value_refs":["Turing.TM0to1.tr.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects._proof_1_27","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects","reducibility":null,"statement_dag_size":113,"type_refs":["Eq","Inhabited","Membership.mem","Option","Option.instMembership","Option.some","PUnit","PUnit.unit","Prod","Prod.mk","Turing.TM0.Machine","Turing.TM0.Stmt","Turing.TM0to1.tr","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step","Turing.Tape","Turing.Tape.head"],"value_dag_size":699,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Iff","Inhabited","Inhabited.default","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.cond_eq_ite","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Membership.mem","Not","Option","Option.instMembership","Option.isNone","Option.isNone_some","Option.mem_some","Option.some","PUnit","PUnit.unit","Prod","Prod.mk","True","True.intro","Turing.Dir","Turing.TM0.Machine","Turing.TM0.Stmt","Turing.TM0.Stmt.move","Turing.TM0.Stmt.write","Turing.TM0to1.instInhabitedΛ'","Turing.TM0to1.tr","Turing.TM0to1.tr.eq_1","Turing.TM0to1.tr.match_1","Turing.TM0to1.tr.match_1.congr_eq_2","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.step","Turing.TM1.step.eq_2","Turing.TM1.stepAux","Turing.TM1.stepAux.eq_4","Turing.TM1.stepAux.eq_5","Turing.Tape","Turing.Tape.head","Unit","_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0.step.match_1.splitter","cond","congrArg","eq_false","eq_true","heq_eq_eq","id","instDecidableEqBool","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects._proof_1_30","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects","reducibility":null,"statement_dag_size":163,"type_refs":["Bool","Bool.false","Bool.true","Inhabited","Membership.mem","Option","Option.instMembership","Option.isSome.match_1","Option.none","Option.some","PUnit","PUnit.unit","Prod","Relation.ReflTransGen","Turing.Dir","Turing.TM0.Machine","Turing.TM0.Stmt","Turing.TM0.step.match_1","Turing.TM0to1.tr","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.normal","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step","Turing.Tape","Turing.Tape.head","Turing.Tape.move","Turing.Tape.write","cond.match_1"],"value_dag_size":1264,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Iff","Inhabited","Inhabited.default","Lean.Grind.cond_eq_ite","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Option","Option.instMembership","Option.isNone","Option.isNone_none","Option.isSome.match_1","Option.isSome.match_1.congr_eq_1","Option.isSome.match_1.congr_eq_2","Option.mem_some","Option.none","Option.some","Or","PUnit","PUnit.casesOn","PUnit.unit","Prod","Prod.casesOn","Prod.mk","Relation.ReflTransGen","Relation.TransGen","Relation.TransGen.single","Relation.reflTransGen_iff_eq_or_transGen","True","True.intro","Turing.Dir","Turing.TM0.Machine","Turing.TM0.Stmt","Turing.TM0.step.match_1","Turing.TM0to1.instInhabitedΛ'","Turing.TM0to1.tr","Turing.TM0to1.tr.eq_1","Turing.TM0to1.tr.match_1","Turing.TM0to1.Λ'","Turing.TM0to1.Λ'.act","Turing.TM0to1.Λ'.normal","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.step","Turing.TM1.step.eq_2","Turing.TM1.stepAux","Turing.TM1.stepAux.eq_4","Turing.TM1.stepAux.eq_6","Turing.Tape","Turing.Tape.head","Turing.Tape.move","Turing.Tape.write","Unit","_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Option.isSome.match_1.splitter","cond","cond.match_1","cond.match_1.congr_eq_1","cond.match_1.congr_eq_2","congrArg","eq_false","eq_true","heq_eq_eq","id","instDecidableEqBool","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr_respects","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.mk","Turing.Tape"],"value_dag_size":56,"value_refs":["Inhabited","Turing.TM0.Cfg","Turing.TM0.Cfg.casesOn","Turing.TM0.Cfg.mk","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":137,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"],"value_dag_size":134,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"],"value_dag_size":136,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"],"value_dag_size":136,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":143,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"],"value_dag_size":139,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":132,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"],"value_dag_size":130,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":null,"statement_dag_size":124,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit","Unit.unit"],"value_dag_size":121,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.SupportsStmt.match_1","reducibility":"abbrev","statement_dag_size":112,"type_refs":["Bool","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Unit"],"value_dag_size":1,"value_refs":["Turing.TM1.SupportsStmt.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Inhabited","Option.none","Option.some","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step.match_1","Turing.Tape"],"value_dag_size":81,"value_refs":["Eq.refl","Inhabited","Option.none","Option.some","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","Inhabited","Option.none","Option.some","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step.match_1","Turing.Tape"],"value_dag_size":86,"value_refs":["Eq.refl","Inhabited","Option.none","Option.some","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1.step.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step.match_1","reducibility":"abbrev","statement_dag_size":67,"type_refs":["Inhabited","Option.none","Option.some","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.Tape"],"value_dag_size":1,"value_refs":["Turing.TM1.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":193,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":188,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":195,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":190,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":192,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":187,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":202,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":196,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":188,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":184,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":null,"statement_dag_size":180,"type_refs":["Bool","Eq","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"],"value_dag_size":177,"value_refs":["Bool","Eq.refl","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stepAux.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stepAux.match_1","reducibility":"abbrev","statement_dag_size":163,"type_refs":["Bool","Inhabited","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.Tape"],"value_dag_size":1,"value_refs":["Turing.TM1.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step_supports._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step_supports","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step_supports.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.step_supports","reducibility":"abbrev","statement_dag_size":305,"type_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Inhabited","Membership.mem","Option","Option.instMembership","Option.some","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Turing.TM1.Cfg","Turing.TM1.Cfg.l","Turing.TM1.Cfg.mk","Turing.TM1.Stmt","Turing.TM1.step","Turing.Tape","instFunLikeOrderEmbedding"],"value_dag_size":1447,"value_refs":["DFunLike.coe","Eq","Eq.casesOn","Eq.refl","False","False.elim","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","HEq","HEq.refl","Inhabited","Membership.mem","Option","Option.casesOn","Option.ctorIdx","Option.instMembership","Option.none","Option.some","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Turing.ListBlank","Turing.TM1.Cfg","Turing.TM1.Cfg.casesOn","Turing.TM1.Cfg.l","Turing.TM1.Cfg.mk","Turing.TM1.Stmt","Turing.TM1.step","Turing.Tape","Turing.Tape.casesOn","Turing.Tape.mk","instFunLikeOrderEmbedding","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding"],"value_dag_size":90,"value_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insertNone","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_supportsStmt","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding"],"value_dag_size":90,"value_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insertNone","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts_trans","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":null,"statement_dag_size":179,"type_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"],"value_dag_size":171,"value_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":null,"statement_dag_size":178,"type_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"],"value_dag_size":170,"value_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":null,"statement_dag_size":178,"type_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"],"value_dag_size":170,"value_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":null,"statement_dag_size":188,"type_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"],"value_dag_size":179,"value_refs":["Bool","Eq","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":null,"statement_dag_size":237,"type_refs":["Bool","Eq","False","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1.stmts₁.match_1"],"value_dag_size":1468,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","False.elim","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.ctorIdx","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.rec","Turing.TM1.Stmt.write","Turing.TM1.stmts₁._sparseCasesOn_1","Turing.TM1.stmts₁._sparseCasesOn_1.else_eq","Turing.TM1.stmts₁.match_1","_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.splitter._sparseCasesOn_5","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1","reducibility":"abbrev","statement_dag_size":178,"type_refs":["Bool","Eq","False","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write"],"value_dag_size":426,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.ctorIdx","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.splitter._sparseCasesOn_5","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.splitter._sparseCasesOn_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁.match_1.splitter","reducibility":"abbrev","statement_dag_size":105,"type_refs":["Bool","Nat.hasNotBit","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.ctorIdx","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write"],"value_dag_size":310,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.ctorIdx","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.rec","Turing.TM1.Stmt.write","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self._simp_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","True","Turing.TM1.Stmt","Turing.TM1.stmts₁"],"value_dag_size":45,"value_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Turing.TM1.Stmt","Turing.TM1.stmts₁","Turing.TM1.stmts₁_self","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","True"],"value_dag_size":43,"value_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_self","Insert.insert","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self._simp_1_8","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_self","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","True"],"value_dag_size":32,"value_refs":["Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton_self","Membership.mem","SetLike.instMembership","Singleton.singleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono._simp_1_15","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono._simp_1_16","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._proof_1_10","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":141,"type_refs":["Bool","Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.instUnion","Insert.insert","Membership.mem","SetLike.instMembership","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.stmts₁","Union.union"],"value_dag_size":360,"value_refs":["Bool","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.instUnion","Finset.mem_insert","Finset.mem_union","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.stmts₁","Union.union","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._proof_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":141,"type_refs":["Bool","Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.instUnion","Insert.insert","Membership.mem","SetLike.instMembership","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.stmts₁","Union.union"],"value_dag_size":345,"value_refs":["Bool","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.instUnion","Finset.mem_insert","Finset.mem_union","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.stmts₁","Union.union","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._proof_1_12","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":124,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.move","Turing.TM1.stmts₁"],"value_dag_size":283,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.move","Turing.TM1.stmts₁","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._proof_1_13","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":125,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","Turing.TM1.Stmt","Turing.TM1.Stmt.write","Turing.TM1.stmts₁"],"value_dag_size":284,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","Turing.TM1.Stmt","Turing.TM1.Stmt.write","Turing.TM1.stmts₁","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._proof_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":125,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","Turing.TM1.Stmt","Turing.TM1.Stmt.load","Turing.TM1.stmts₁"],"value_dag_size":284,"value_refs":["Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","Turing.TM1.Stmt","Turing.TM1.Stmt.load","Turing.TM1.stmts₁","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._simp_1_8","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans._simp_1_9","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_trans","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","Option","Option.none","Option.some","Prod.mk","Turing.TM1.Stmt","Turing.TM1to0.tr.match_1","Turing.TM1to0.Λ'"],"value_dag_size":87,"value_refs":["Eq.refl","Option","Option.none","Option.some","Prod.mk","Turing.TM1.Stmt","Turing.TM1to0.tr.match_1","Turing.TM1to0.Λ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","Option","Option.none","Option.some","Prod.mk","Turing.TM1.Stmt","Turing.TM1to0.tr.match_1","Turing.TM1to0.Λ'"],"value_dag_size":95,"value_refs":["Eq.refl","Option","Option.none","Option.some","Prod.mk","Turing.TM1.Stmt","Turing.TM1to0.tr.match_1","Turing.TM1to0.Λ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr.match_1","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Option","Option.none","Option.some","Prod.mk","Turing.TM1.Stmt","Turing.TM1to0.Λ'"],"value_dag_size":1,"value_refs":["Turing.TM1to0.tr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":154,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":150,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":156,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":152,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":156,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":152,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":163,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":158,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":146,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":143,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"],"value_dag_size":137,"value_refs":["Bool","Eq.refl","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write","Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trAux.match_1","reducibility":"abbrev","statement_dag_size":127,"type_refs":["Bool","Turing.Dir","Turing.TM1.Stmt","Turing.TM1.Stmt.branch","Turing.TM1.Stmt.goto","Turing.TM1.Stmt.halt","Turing.TM1.Stmt.load","Turing.TM1.Stmt.move","Turing.TM1.Stmt.write"],"value_dag_size":1,"value_refs":["Turing.TM1to0.trAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trCfg.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trCfg.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1to0.trCfg.match_1","Turing.Tape"],"value_dag_size":71,"value_refs":["Eq.refl","Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.TM1to0.trCfg.match_1","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trCfg.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trCfg.match_1","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.Tape"],"value_dag_size":1,"value_refs":["Turing.TM1to0.trCfg.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_respects.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_respects","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.Tape"],"value_dag_size":72,"value_refs":["Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.casesOn","Turing.TM1.Cfg.mk","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding"],"value_dag_size":90,"value_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insertNone","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Option","Option.some"],"value_dag_size":28,"value_refs":["Eq","Option","Option.some","Option.some_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_8","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports._simp_1_9","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.tr_supports","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.stepAux_write._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.stepAux_write","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Nat","Nat.succ"],"value_dag_size":21,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","Turing.TM1.Stmt","Turing.TM1to1.tr.match_1","Turing.TM1to1.Λ'","Turing.TM1to1.Λ'.normal","Turing.TM1to1.Λ'.write"],"value_dag_size":60,"value_refs":["Eq.refl","Turing.TM1.Stmt","Turing.TM1to1.tr.match_1","Turing.TM1to1.Λ'","Turing.TM1to1.Λ'.normal","Turing.TM1to1.Λ'.write"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Turing.TM1.Stmt","Turing.TM1to1.tr.match_1","Turing.TM1to1.Λ'","Turing.TM1to1.Λ'.normal","Turing.TM1to1.Λ'.write"],"value_dag_size":66,"value_refs":["Eq.refl","Turing.TM1.Stmt","Turing.TM1to1.tr.match_1","Turing.TM1to1.Λ'","Turing.TM1to1.Λ'.normal","Turing.TM1to1.Λ'.write"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr.match_1","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Turing.TM1.Stmt","Turing.TM1to1.Λ'","Turing.TM1to1.Λ'.normal","Turing.TM1to1.Λ'.write"],"value_dag_size":1,"value_refs":["Turing.TM1to1.tr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_respects._proof_1_22","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_respects","reducibility":null,"statement_dag_size":313,"type_refs":["Bool","Bool.false","Eq","Inhabited","Inhabited.default","List.Vector","List.Vector.replicate","Nat","StateTransition.Reaches","Turing.ListBlank","Turing.ListBlank.head","Turing.TM1.Cfg","Turing.TM1.Stmt","Turing.TM1.step","Turing.TM1.stepAux","Turing.TM1to1.tr","Turing.TM1to1.trCfg","Turing.TM1to1.trNormal","Turing.TM1to1.trTape'","Turing.TM1to1.Λ'","Turing.Tape.mk'","cond","instInhabitedBool"],"value_dag_size":741,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Inhabited","Inhabited.default","Lean.Grind.alreadyNorm","Lean.Grind.cond_eq_ite","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List.Vector","List.Vector.replicate","Nat","Not","Or","Or.casesOn","StateTransition.Reaches","True","True.intro","Turing.ListBlank","Turing.ListBlank.head","Turing.TM1.Cfg","Turing.TM1.Stmt","Turing.TM1.step","Turing.TM1.stepAux","Turing.TM1to1.tr","Turing.TM1to1.trCfg","Turing.TM1to1.trCfg.congr_simp","Turing.TM1to1.trNormal","Turing.TM1to1.trTape'","Turing.TM1to1.Λ'","Turing.Tape.mk'","cond","congr","congrArg","eq_false","eq_true","id","instDecidableEqBool","instInhabitedBool","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_respects.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_respects","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.mk","Turing.Tape"],"value_dag_size":72,"value_refs":["Inhabited","Option","Turing.TM1.Cfg","Turing.TM1.Cfg.casesOn","Turing.TM1.Cfg.mk","Turing.Tape"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports._simp_1_10","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports._simp_1_21","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports._simp_1_9","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.tr_supports","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1","reducibility":null,"statement_dag_size":72,"type_refs":["Bool","Eq","List","List.cons","List.nil","Turing.TM1.Stmt","Turing.TM1to1.write.match_1","Turing.TM1to1.Λ'"],"value_dag_size":70,"value_refs":["Bool","Eq.refl","List","List.cons","List.nil","Turing.TM1.Stmt","Turing.TM1to1.write.match_1","Turing.TM1to1.Λ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1","reducibility":null,"statement_dag_size":85,"type_refs":["Bool","Eq","List","List.cons","List.nil","Turing.TM1.Stmt","Turing.TM1to1.write.match_1","Turing.TM1to1.Λ'"],"value_dag_size":81,"value_refs":["Bool","Eq.refl","List","List.cons","List.nil","Turing.TM1.Stmt","Turing.TM1to1.write.match_1","Turing.TM1to1.Λ'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to1.write.match_1","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Bool","List","List.cons","List.nil","Turing.TM1.Stmt","Turing.TM1to1.Λ'"],"value_dag_size":1,"value_refs":["Turing.TM1to1.write.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","Unit","Unit.unit","cond.match_1"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Unit","cond.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","Unit","Unit.unit","cond.match_1"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Unit","cond.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.PostTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.cond.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["cond.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.List.getLast?.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.getLast?.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Option","Option.isSome.match_1","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Option","Option.isSome.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Option","Option.isSome.match_1","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Option.isSome.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Option.isSome.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":186,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":182,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":188,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":184,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":188,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":184,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":181,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":178,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":185,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":181,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":173,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"],"value_dag_size":171,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":null,"statement_dag_size":165,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit","Unit.unit"],"value_dag_size":162,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.SupportsStmt.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.SupportsStmt.match_1","reducibility":"abbrev","statement_dag_size":152,"type_refs":["Bool","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Unit"],"value_dag_size":1,"value_refs":["Turing.TM2.SupportsStmt.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"],"value_dag_size":84,"value_refs":["Eq.refl","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"],"value_dag_size":89,"value_refs":["Eq.refl","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk"],"value_dag_size":1,"value_refs":["Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":248,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":242,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":250,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":244,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":246,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":240,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":239,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":234,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":251,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":245,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":235,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":231,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":null,"statement_dag_size":227,"type_refs":["Bool","Eq","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"],"value_dag_size":224,"value_refs":["Bool","Eq.refl","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stepAux.match_1","reducibility":"abbrev","statement_dag_size":210,"type_refs":["Bool","List","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push"],"value_dag_size":1,"value_refs":["Turing.TM2.stepAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step_supports._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step_supports","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step_supports.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.step_supports","reducibility":"abbrev","statement_dag_size":314,"type_refs":["DFunLike.coe","DecidableEq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","List","Membership.mem","Option","Option.instMembership","Option.some","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Turing.TM2.Cfg","Turing.TM2.Cfg.l","Turing.TM2.Cfg.mk","Turing.TM2.Stmt","Turing.TM2.step","instFunLikeOrderEmbedding"],"value_dag_size":1032,"value_refs":["DFunLike.coe","DecidableEq","Eq","Eq.casesOn","Eq.refl","False","False.elim","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","HEq","HEq.refl","List","Membership.mem","Option","Option.casesOn","Option.ctorIdx","Option.instMembership","Option.none","Option.some","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Turing.TM2.Cfg","Turing.TM2.Cfg.casesOn","Turing.TM2.Cfg.l","Turing.TM2.Cfg.mk","Turing.TM2.Stmt","Turing.TM2.step","instFunLikeOrderEmbedding","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding"],"value_dag_size":90,"value_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insertNone","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_supportsStmt","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding"],"value_dag_size":90,"value_refs":["DFunLike.coe","Finset","Finset.insertNone","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insertNone","Membership.mem","Option","Option.instMembership","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instFunLikeOrderEmbedding","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans._simp_1_7","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts_trans","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":284,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":275,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":286,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":277,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":282,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":273,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":275,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":267,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":287,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":278,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":267,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":260,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":null,"statement_dag_size":262,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"],"value_dag_size":256,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.stmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁.match_1","reducibility":"abbrev","statement_dag_size":152,"type_refs":["Bool","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Unit"],"value_dag_size":221,"value_refs":["Bool","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.casesOn","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_self._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_self","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","True"],"value_dag_size":43,"value_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_self","Insert.insert","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_self._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_self","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","True"],"value_dag_size":32,"value_refs":["Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton_self","Membership.mem","SetLike.instMembership","Singleton.singleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono._simp_1_17","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono._simp_1_18","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono._simp_1_19","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_supportsStmt_mono","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans._simp_1_10","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans._simp_1_9","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2.stmts₁_trans","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"],"value_dag_size":85,"value_refs":["Eq.refl","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"],"value_dag_size":87,"value_refs":["Eq.refl","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"],"value_dag_size":83,"value_refs":["Eq.refl","Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push","Turing.TM2to1.stRun.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.stRun.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push"],"value_dag_size":1,"value_refs":["Turing.TM2to1.stRun.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.step_run.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.step_run","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push"],"value_dag_size":95,"value_refs":["Option","Turing.TM2to1.StAct","Turing.TM2to1.StAct.casesOn","Turing.TM2to1.StAct.peek","Turing.TM2to1.StAct.pop","Turing.TM2to1.StAct.push"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"],"value_dag_size":92,"value_refs":["Eq.refl","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"],"value_dag_size":106,"value_refs":["Eq.refl","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"],"value_dag_size":92,"value_refs":["Eq.refl","Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.tr.match_1","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr.match_1","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Turing.TM2.Stmt","Turing.TM2to1.StAct","Turing.TM2to1.Λ'","Turing.TM2to1.Λ'.go","Turing.TM2to1.Λ'.normal","Turing.TM2to1.Λ'.ret"],"value_dag_size":1,"value_refs":["Turing.TM2to1.tr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":169,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":165,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":171,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":167,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":171,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":167,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":164,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":161,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":172,"type_refs":["Bool","Eq","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":168,"value_refs":["Bool","Eq.refl","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":null,"statement_dag_size":269,"type_refs":["Bool","Eq","False","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2to1.trStmts₁.match_1"],"value_dag_size":1744,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","False.elim","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.ctorIdx","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.Stmt.rec","Turing.TM2to1.trStmts₁._sparseCasesOn_1","Turing.TM2to1.trStmts₁._sparseCasesOn_1.else_eq","Turing.TM2to1.trStmts₁.match_1","_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.splitter._sparseCasesOn_6","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1","reducibility":"abbrev","statement_dag_size":251,"type_refs":["Bool","Eq","False","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push"],"value_dag_size":571,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.ctorIdx","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.splitter._sparseCasesOn_6","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.splitter._sparseCasesOn_6","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.trStmts₁.match_1.splitter","reducibility":"abbrev","statement_dag_size":145,"type_refs":["Bool","Nat.hasNotBit","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.ctorIdx","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push"],"value_dag_size":408,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Turing.TM2.Stmt","Turing.TM2.Stmt.branch","Turing.TM2.Stmt.ctorIdx","Turing.TM2.Stmt.goto","Turing.TM2.Stmt.halt","Turing.TM2.Stmt.load","Turing.TM2.Stmt.peek","Turing.TM2.Stmt.pop","Turing.TM2.Stmt.push","Turing.TM2.Stmt.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₁._simp_1_5","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₁","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂._simp_1_12","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂._simp_1_13","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","LT.lt","Nat","Nat.succ","True","instLTNat"],"value_dag_size":16,"value_refs":["LT.lt","Nat","Nat.lt_succ_self","Nat.succ","eq_true","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.add_one_le_iff","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂._simp_1_15","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₂","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","True"],"value_dag_size":38,"value_refs":["LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","eq_true","le_of_lt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₃._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_respects_aux₃","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.StackTuringMachine","name":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Turing.TM2to1.tr_supports","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankExtends.below_of_le._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankExtends.below_of_le","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":35,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.add_le_add_iff_left","instAddNat","instHAdd","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankExtends.below_of_le._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankExtends.below_of_le","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","List.replicate","Nat","instAddNat","instHAdd","instHAppendOfAppend"],"value_dag_size":53,"value_refs":["Eq.symm","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","List.replicate","List.replicate_add","Nat","instAddNat","instHAdd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankRel.trans._proof_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.BlankRel.trans","reducibility":null,"statement_dag_size":34,"type_refs":["Inhabited","List","Turing.BlankRel"],"value_dag_size":755,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Inhabited","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Turing.BlankExtends","Turing.BlankExtends.above_of_le","Turing.BlankExtends.below_of_le","Turing.BlankExtends.trans","Turing.BlankRel","Turing.BlankRel.eq_def","eagerReduce","eq_false","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Inhabited","List","List.cons","List.nil","Turing.ListBlank","Turing.ListBlank.append.match_1"],"value_dag_size":58,"value_refs":["Eq.refl","Inhabited","List","List.cons","List.nil","Turing.ListBlank","Turing.ListBlank.append.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","Inhabited","List","List.cons","List.nil","Turing.ListBlank","Turing.ListBlank.append.match_1"],"value_dag_size":67,"value_refs":["Eq.refl","Inhabited","List","List.cons","List.nil","Turing.ListBlank","Turing.ListBlank.append.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.append.match_1","reducibility":"abbrev","statement_dag_size":51,"type_refs":["Inhabited","List","List.cons","List.nil","Turing.ListBlank"],"value_dag_size":1,"value_refs":["Turing.ListBlank.append.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Inhabited","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.ListBlank.modifyNth.match_1","instOfNatNat"],"value_dag_size":55,"value_refs":["Eq.refl","Inhabited","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.ListBlank.modifyNth.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Inhabited","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.ListBlank.modifyNth.match_1","instOfNatNat"],"value_dag_size":60,"value_refs":["Eq.refl","Inhabited","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.ListBlank.modifyNth.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.modifyNth.match_1","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Inhabited","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","instOfNatNat"],"value_dag_size":1,"value_refs":["Turing.ListBlank.modifyNth.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.nth_map._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.ListBlank.nth_map","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Inhabited","Inhabited.default","List","List.getD","List.getI","Nat"],"value_dag_size":37,"value_refs":["Eq.symm","Inhabited","Inhabited.default","List","List.getD","List.getD_default_eq_getI","List.getI","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Inhabited","Turing.Dir","Turing.Dir.left","Turing.Dir.right","Turing.ListBlank","Turing.Tape","Turing.Tape.mk","Turing.Tape.move.match_1"],"value_dag_size":80,"value_refs":["Eq.refl","Inhabited","Turing.Dir","Turing.Dir.left","Turing.Dir.right","Turing.ListBlank","Turing.Tape","Turing.Tape.mk","Turing.Tape.move.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Inhabited","Turing.Dir","Turing.Dir.left","Turing.Dir.right","Turing.ListBlank","Turing.Tape","Turing.Tape.mk","Turing.Tape.move.match_1"],"value_dag_size":80,"value_refs":["Eq.refl","Inhabited","Turing.Dir","Turing.Dir.left","Turing.Dir.right","Turing.ListBlank","Turing.Tape","Turing.Tape.mk","Turing.Tape.move.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move.match_1","reducibility":"abbrev","statement_dag_size":60,"type_refs":["Inhabited","Turing.Dir","Turing.Dir.left","Turing.Dir.right","Turing.ListBlank","Turing.Tape","Turing.Tape.mk"],"value_dag_size":1,"value_refs":["Turing.Tape.move.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move_left_nth.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.move_left_nth","reducibility":"abbrev","statement_dag_size":106,"type_refs":["Inhabited","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.Tape","Turing.Tape.mk","instOfNat"],"value_dag_size":181,"value_refs":["Inhabited","Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Turing.ListBlank","Turing.Tape","Turing.Tape.casesOn","Turing.Tape.mk","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","Unit.unit","instOfNat"],"value_dag_size":42,"value_refs":["Eq.refl","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","instOfNat"],"value_dag_size":46,"value_refs":["Eq.refl","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","instOfNat"],"value_dag_size":45,"value_refs":["Eq.refl","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape.nth.match_1","Unit","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.nth.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNat"],"value_dag_size":1,"value_refs":["Turing.Tape.nth.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.Tape","name":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.write_nth.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.write_nth","reducibility":"abbrev","statement_dag_size":60,"type_refs":["Inhabited","Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Turing.Tape","instOfNat"],"value_dag_size":84,"value_refs":["Inhabited","Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Turing.Tape","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Option","Option.elim.match_1","Option.none","Option.some"],"value_dag_size":61,"value_refs":["Eq.refl","Option","Option.elim.match_1","Option.none","Option.some"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Option","Option.elim.match_1","Option.none","Option.some"],"value_dag_size":57,"value_refs":["Eq.refl","Option","Option.elim.match_1","Option.none","Option.some"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.elim.match_1","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Option","Option.none","Option.some"],"value_dag_size":1,"value_refs":["Option.elim.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Option","Option.getD.match_1","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Option","Option.getD.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Option","Option.getD.match_1","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Option.getD.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Option.getD.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit","Unit.unit"],"value_dag_size":37,"value_refs":["Eq.refl","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit","Unit.unit"],"value_dag_size":37,"value_refs":["Eq.refl","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit","Unit.unit"],"value_dag_size":37,"value_refs":["Eq.refl","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit","Unit.unit"],"value_dag_size":36,"value_refs":["Eq.refl","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.elim.match_1","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.K'.elim.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.aux","Turing.PartrecToTM2.K'.main","Turing.PartrecToTM2.K'.rev","Turing.PartrecToTM2.K'.stack","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.K'.elim.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.clear_ok._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.clear_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":117,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":123,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":117,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":117,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":132,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":123,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":132,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":123,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":132,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":123,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":null,"statement_dag_size":128,"type_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":120,"value_refs":["Eq","Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.codeSupp'.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Turing.PartrecToTM2.Cont'","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":102,"value_refs":["Turing.PartrecToTM2.Cont'","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.casesOn","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'_supports._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'_supports","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instPartialOrder","Finset.instUnion","Finset.union_subset_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'_supports._simp_1_26","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.codeSupp'_supports","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","DecidableEq","Finset","Finset.insert_subset_iff","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"],"value_dag_size":60,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"],"value_dag_size":57,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"],"value_dag_size":60,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"],"value_dag_size":60,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit","Unit.unit"],"value_dag_size":53,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.contSupp.match_1","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.ToPartrec.Code","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.contSupp.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp_fix._simp_1_16","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp_fix","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp_supports._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.contSupp_supports","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instPartialOrder","Finset.instUnion","Finset.union_subset_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.copy_ok._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.copy_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.head_main_ok._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.head_main_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.head_stack_ok._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.head_stack_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.move_ok._proof_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.move_ok","reducibility":null,"statement_dag_size":149,"type_refs":["Bool","Bool.true","Eq","Function.update","List","List.head?","List.nil","List.tail","Membership.mem","Option","Option.elim","Option.instMembership","Option.some","Prod","Prod.mk","Relation.ReflTransGen","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.instDecidableEqK'","Turing.PartrecToTM2.push'","Turing.PartrecToTM2.splitAtPred","Turing.PartrecToTM2.tr","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.move","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.Stmt.goto","Turing.TM2.step","Turing.TM2.stepAux","cond"],"value_dag_size":1238,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Function.update","HEq","Iff","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.alreadyNorm","Lean.Grind.cond_eq_ite","Lean.Grind.em","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.ctorIdx","List.head?","List.head?_cons","List.head?_nil","List.nil","List.tail","List.tail_cons","List.tail_nil","Membership.mem","Not","Option","Option.elim","Option.elim_none","Option.elim_some","Option.instMembership","Option.none","Option.some","Or","Or.casesOn","PUnit","PUnit.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Relation.ReflTransGen","Relation.TransGen","Relation.reflTransGen_iff_eq_or_transGen","True","True.intro","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.instDecidableEqK'","Turing.PartrecToTM2.push'","Turing.PartrecToTM2.splitAtPred","Turing.PartrecToTM2.splitAtPred.eq_def","Turing.PartrecToTM2.splitAtPred.match_1","Turing.PartrecToTM2.splitAtPred.match_3","Turing.PartrecToTM2.splitAtPred.match_3.congr_eq_1","Turing.PartrecToTM2.splitAtPred.match_3.congr_eq_2","Turing.PartrecToTM2.tr","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.move","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.Stmt.goto","Turing.TM2.step","Turing.TM2.stepAux","Unit","_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3.splitter","cond","congr","congrArg","congrFun'","eq_false","eq_true","funext","heq_eq_eq","id","instDecidableEqBool","ite","ite_cond_eq_false","ite_cond_eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.move₂_ok._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.move₂_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit","Unit.unit"],"value_dag_size":30,"value_refs":["Eq.refl","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit","Unit.unit"],"value_dag_size":30,"value_refs":["Eq.refl","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit"],"value_dag_size":302,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Turing.PartrecToTM2.natEnd._sparseCasesOn_1","Turing.PartrecToTM2.natEnd._sparseCasesOn_1.else_eq","Turing.PartrecToTM2.natEnd.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Turing.PartrecToTM2.Γ'.ctorIdx","Turing.PartrecToTM2.Γ'.rec","Unit","Unit.unit","_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.splitter._sparseCasesOn_3","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Eq","False","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Unit"],"value_dag_size":139,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Turing.PartrecToTM2.Γ'.ctorIdx","Unit","Unit.unit","_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.natEnd.match_1.splitter","reducibility":"abbrev","statement_dag_size":24,"type_refs":["Nat.hasNotBit","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Turing.PartrecToTM2.Γ'.ctorIdx"],"value_dag_size":90,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Turing.PartrecToTM2.Γ'.ctorIdx","Turing.PartrecToTM2.Γ'.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_1","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","List","Option","Prod","Prod.mk","Turing.PartrecToTM2.splitAtPred.match_1"],"value_dag_size":69,"value_refs":["Eq.refl","List","Option","Prod","Prod.mk","Turing.PartrecToTM2.splitAtPred.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_1","reducibility":"abbrev","statement_dag_size":49,"type_refs":["List","Option","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.splitAtPred.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","Turing.PartrecToTM2.splitAtPred.match_3","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","Turing.PartrecToTM2.splitAtPred.match_3","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","Turing.PartrecToTM2.splitAtPred.match_3","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","Turing.PartrecToTM2.splitAtPred.match_3","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred.match_3","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.splitAtPred.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred_eq.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.splitAtPred_eq","reducibility":"abbrev","statement_dag_size":336,"type_refs":["And","And.intro","Bool","Bool.false","Bool.true","Eq","Eq.refl","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Option","Option.elim'","Option.none","Option.some","instHAppendOfAppend"],"value_dag_size":845,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.false","Bool.true","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HAppend.hAppend","HEq","HEq.refl","List","List.casesOn","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Option","Option.casesOn","Option.elim'","Option.none","Option.some","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.succ_ok._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.succ_ok","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.supports_union._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.supports_union","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.supports_union._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.supports_union","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":151,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":146,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_10","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":144,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":141,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_11","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":144,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":141,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_12","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":136,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit","Unit.unit"],"value_dag_size":133,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":147,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":143,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":137,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":147,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":143,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":137,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":137,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":143,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":140,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_8","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":144,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":141,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.eq_9","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":null,"statement_dag_size":140,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":138,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.tr.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr.match_1","reducibility":"abbrev","statement_dag_size":116,"type_refs":["Bool","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.Cont'.comp","Turing.PartrecToTM2.Cont'.cons₁","Turing.PartrecToTM2.Cont'.cons₂","Turing.PartrecToTM2.Cont'.fix","Turing.PartrecToTM2.Cont'.halt","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ","Turing.ToPartrec.Code","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.tr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit","Unit.unit"],"value_dag_size":62,"value_refs":["Eq.refl","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":71,"value_refs":["Eq.refl","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":68,"value_refs":["Eq.refl","List","Nat","Turing.PartrecToTM2.trCont.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trCont.match_1","reducibility":"abbrev","statement_dag_size":51,"type_refs":["List","Nat","Turing.ToPartrec.Code","Turing.ToPartrec.Cont","Turing.ToPartrec.Cont.comp","Turing.ToPartrec.Cont.cons₁","Turing.ToPartrec.Cont.cons₂","Turing.ToPartrec.Cont.fix","Turing.ToPartrec.Cont.halt","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trCont.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trLList.match_1","Unit","Unit.unit"],"value_dag_size":34,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trLList.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trLList.match_1","Unit"],"value_dag_size":40,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trLList.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trLList.match_1","reducibility":"abbrev","statement_dag_size":28,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trLList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trList.match_1","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trList.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trList.match_1","Unit"],"value_dag_size":39,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Turing.PartrecToTM2.trList.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ._simp_1_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ._simp_1_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList_ne_consₗ","reducibility":"abbrev","statement_dag_size":49,"type_refs":["List","List.cons","List.instMembership","Membership.mem","Nat","Turing.PartrecToTM2.trList","Turing.PartrecToTM2.Γ'"],"value_dag_size":355,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.casesOn","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","Nat","Turing.PartrecToTM2.trList","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Turing.PartrecToTM2.Γ'.casesOn","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":82,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":82,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":82,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":88,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":88,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":88,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":85,"value_refs":["Eq.refl","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.trNormal.match_1","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Turing.PartrecToTM2.Cont'","Turing.ToPartrec.Code","Turing.ToPartrec.Code.case","Turing.ToPartrec.Code.comp","Turing.ToPartrec.Code.cons","Turing.ToPartrec.Code.fix","Turing.ToPartrec.Code.succ","Turing.ToPartrec.Code.tail","Turing.ToPartrec.Code.zero'"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trNormal.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal_respects._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal_respects","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal_supports._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNormal_supports","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instPartialOrder","Finset.instUnion","Finset.union_subset_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Num","Num.pos","Num.zero","PosNum","Turing.PartrecToTM2.trNum.match_1","Unit","Unit.unit"],"value_dag_size":27,"value_refs":["Eq.refl","Num","Num.pos","Num.zero","PosNum","Turing.PartrecToTM2.trNum.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Num","Num.pos","Num.zero","PosNum","Turing.PartrecToTM2.trNum.match_1","Unit"],"value_dag_size":30,"value_refs":["Eq.refl","Num","Num.pos","Num.zero","PosNum","Turing.PartrecToTM2.trNum.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum.match_1","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trNum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum_natEnd.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trNum_natEnd","reducibility":"abbrev","statement_dag_size":45,"type_refs":["List","List.instMembership","Membership.mem","Num","Num.pos","PosNum","Turing.PartrecToTM2.trNum","Turing.PartrecToTM2.Γ'"],"value_dag_size":347,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","Num","Num.casesOn","Num.pos","Num.zero","PosNum","Turing.PartrecToTM2.trNum","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Turing.PartrecToTM2.Γ'.casesOn","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.trPosNum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum_natEnd.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trPosNum_natEnd","reducibility":"abbrev","statement_dag_size":102,"type_refs":["List","List.Mem","List.Mem.head","List.Mem.tail","List.instMembership","List.nil","Membership.mem","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Turing.PartrecToTM2.trPosNum","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Unit"],"value_dag_size":1004,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.cons.noConfusion","List.ctorIdx","List.instMembership","List.nil","Membership.mem","PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Turing.PartrecToTM2.trPosNum","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":162,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":152,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":158,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":149,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":150,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":143,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":158,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":149,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":150,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":143,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":150,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":143,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":154,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":146,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.eq_8","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":null,"statement_dag_size":150,"type_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":143,"value_refs":["Bool","Eq","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.trStmts₁.match_1","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁.match_1","reducibility":"abbrev","statement_dag_size":81,"type_refs":["Bool","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":127,"value_refs":["Bool","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.casesOn","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_supports'._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_supports'","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instPartialOrder","Finset.instUnion","Finset.union_subset_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_supports._simp_1_10","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_supports","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_10","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_11","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_12","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_13","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_14","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Finset","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","True"],"value_dag_size":27,"value_refs":["Finset","Finset.Subset.refl","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_15","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_16","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_17","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans._simp_1_18","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trStmts₁_trans","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_eval._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_eval","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Part","Part.instMembership","Part.map","Part.mem_map_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_eval._simp_1_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_eval","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_respects.match_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_respects","reducibility":"abbrev","statement_dag_size":131,"type_refs":["Eq","Eq.refl","Exists.intro","List","List.nil","Nat","Option","Option.some","Turing.PartrecToTM2.Cfg'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.elim","Turing.PartrecToTM2.TrCfg","Turing.PartrecToTM2.halt","Turing.PartrecToTM2.trCont","Turing.PartrecToTM2.trContStack","Turing.PartrecToTM2.trList","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.ret","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont"],"value_dag_size":476,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.nil","Nat","Option","Option.some","Turing.PartrecToTM2.Cfg'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.K'.elim","Turing.PartrecToTM2.TrCfg","Turing.PartrecToTM2.halt","Turing.PartrecToTM2.trCont","Turing.PartrecToTM2.trContStack","Turing.PartrecToTM2.trList","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.ret","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.ToPartrec.Cfg","Turing.ToPartrec.Cfg.casesOn","Turing.ToPartrec.Cfg.halt","Turing.ToPartrec.Cfg.ret","Turing.ToPartrec.Cont","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_ret_respects._simp_1_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.tr_ret_respects","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":110,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":105,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":106,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":102,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_3","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":98,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":96,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_4","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":106,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":102,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":98,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":96,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_6","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":98,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":96,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_7","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":102,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":99,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.eq_8","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":null,"statement_dag_size":98,"type_refs":["Bool","Eq","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":96,"value_refs":["Bool","Eq.refl","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.Supports.match_1","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.Supports.match_1","reducibility":"abbrev","statement_dag_size":81,"type_refs":["Bool","Option","Turing.PartrecToTM2.Cont'","Turing.PartrecToTM2.K'","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Λ'","Turing.PartrecToTM2.Λ'.clear","Turing.PartrecToTM2.Λ'.copy","Turing.PartrecToTM2.Λ'.move","Turing.PartrecToTM2.Λ'.pred","Turing.PartrecToTM2.Λ'.push","Turing.PartrecToTM2.Λ'.read","Turing.PartrecToTM2.Λ'.ret","Turing.PartrecToTM2.Λ'.succ"],"value_dag_size":1,"value_refs":["Turing.PartrecToTM2.Λ'.Supports.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.instDecidableEq._simp_5","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.Λ'.instDecidableEq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1.eq_1","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"],"value_dag_size":84,"value_refs":["Eq.refl","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1.eq_2","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"],"value_dag_size":89,"value_refs":["Eq.refl","List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk","Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1.splitter","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.TM2.step.match_1","reducibility":"abbrev","statement_dag_size":69,"type_refs":["List","Option.none","Option.some","Turing.TM2.Cfg","Turing.TM2.Cfg.mk"],"value_dag_size":1,"value_refs":["Turing.TM2.step.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0._proof_23","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Nat","Option","Option.some","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.ctorIdx","Turing.PartrecToTM2.Γ'.enumList","instLTNat"],"value_dag_size":122,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Nat","Option","Option.some","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.bit0","Turing.PartrecToTM2.Γ'.bit1","Turing.PartrecToTM2.Γ'.casesOn","Turing.PartrecToTM2.Γ'.cons","Turing.PartrecToTM2.Γ'.consₗ","Turing.PartrecToTM2.Γ'.ctorIdx","Turing.PartrecToTM2.Γ'.enumList","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Computability.TuringMachine.ToPartrec","name":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0._proof_26","namespace":"_private.Mathlib.Computability.TuringMachine.ToPartrec.0","reducibility":null,"statement_dag_size":5,"type_refs":["List.Nodup","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.enumList"],"value_dag_size":58,"value_refs":["Eq","Eq.rec","Eq.symm","List","List.Nodup","List.Nodup.of_map","List.map","List.nodup_range","List.range","Nat","OfNat.ofNat","Turing.PartrecToTM2.Γ'","Turing.PartrecToTM2.Γ'.ctorIdx","Turing.PartrecToTM2.Γ'.enumList","instOfNatNat","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedMod.isDiscrete_tfae.match_1_1","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedMod.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":1122,"type_refs":["AddCommGroup.toAddCommMonoid","AddCommGrpCat.hasColimitsOfShape","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.essImage","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.obj","CategoryTheory.Functor.sections","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.instInhabited","CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.PreservesFilteredColimitsOfSize.preserves_filtered_colimits","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.isCofiltered_of_directed_ge_nonempty","CategoryTheory.isFiltered_op_of_isCofiltered","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed.IsDiscrete","Condensed.IsDiscrete._proof_1","CondensedMod","LinearMap","LinearMap.instFunLike","Membership.mem","ModuleCat","ModuleCat.FilteredColimits.forget_preservesFilteredColimits","ModuleCat.carrier","ModuleCat.hasColimitsOfShape","ModuleCat.hasLimit","ModuleCat.instConcreteCategoryLinearMapIdCarrier","ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier","ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier","ModuleCat.isAddCommGroup","ModuleCat.isModule","ModuleCat.moduleCategory","Opposite","Opposite.small","Preorder.smallCategory","Ring","Ring.toSemiring","RingHom.id","SemilatticeInf.instIsCodirectedOrder","Semiring.toNonAssocSemiring","Set","Set.instMembership","TopCat","True","UnivLE.self","UnivLE.small","instNonemptyOfInhabited","small_Pi","small_subtype"],"value_dag_size":1159,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGrpCat.hasColimitsOfShape","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.essImage","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.obj","CategoryTheory.Functor.sections","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.instInhabited","CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.PreservesFilteredColimitsOfSize.preserves_filtered_colimits","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.casesOn","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.isCofiltered_of_directed_ge_nonempty","CategoryTheory.isFiltered_op_of_isCofiltered","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed.IsDiscrete","Condensed.IsDiscrete._proof_1","CondensedMod","LinearMap","LinearMap.instFunLike","Membership.mem","ModuleCat","ModuleCat.FilteredColimits.forget_preservesFilteredColimits","ModuleCat.carrier","ModuleCat.hasColimitsOfShape","ModuleCat.hasLimit","ModuleCat.instConcreteCategoryLinearMapIdCarrier","ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier","ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier","ModuleCat.isAddCommGroup","ModuleCat.isModule","ModuleCat.moduleCategory","Opposite","Opposite.small","Preorder.smallCategory","Ring","Ring.toSemiring","RingHom.id","SemilatticeInf.instIsCodirectedOrder","Semiring.toNonAssocSemiring","Set","Set.instMembership","TopCat","True","UnivLE.self","UnivLE.small","instNonemptyOfInhabited","small_Pi","small_subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedSet.isDiscrete_tfae.match_1_1","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedSet.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":233,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence","CategoryTheory.Functor.isRightAdjoint_of_isEquivalence","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.Types.hasColimitsOfShape","CategoryTheory.Limits.Types.hasLimit","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.Types.instIsEquivalenceForgetTypeFun","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.instReflectsIsomorphismsForgetTypeFun","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed.IsDiscrete","Condensed.IsDiscrete._proof_1","CondensedSet","Opposite","Opposite.small","Preorder.smallCategory","TopCat","True","TypeCat.Fun","TypeCat.instFunLikeFun","UnivLE.self","UnivLE.small","instConcreteCategoryTypeFun"],"value_dag_size":249,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence","CategoryTheory.Functor.isRightAdjoint_of_isEquivalence","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.Types.hasColimitsOfShape","CategoryTheory.Limits.Types.hasLimit","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.casesOn","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.Types.instIsEquivalenceForgetTypeFun","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.instReflectsIsomorphismsForgetTypeFun","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed.IsDiscrete","Condensed.IsDiscrete._proof_1","CondensedSet","Opposite","Opposite.small","Preorder.smallCategory","TopCat","True","TypeCat.Fun","TypeCat.instFunLikeFun","UnivLE.self","UnivLE.small","instConcreteCategoryTypeFun"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedSet.isDiscrete_tfae.match_1_3","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.CondensedSet.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":91,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.obj","CategoryTheory.Iso","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","CondensedSet.LocallyConstant.functor","Exists.intro","Nonempty","Nonempty.intro","Opposite","TopCat","True"],"value_dag_size":123,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.obj","CategoryTheory.Iso","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","CondensedSet.LocallyConstant.functor","Exists.casesOn","Exists.intro","Nonempty","Nonempty.casesOn","Nonempty.intro","Opposite","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondMod.isDiscrete_tfae.match_1_1","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondMod.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":173,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondMod","LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat","LightCondensed.IsDiscrete","LightCondensed.IsDiscrete._proof_1","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":212,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.casesOn","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondMod","LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat","LightCondensed.IsDiscrete","LightCondensed.IsDiscrete._proof_1","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondSet.isDiscrete_tfae.match_1_1","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondSet.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":128,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.types","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondSet","LightCondensed.IsDiscrete","LightCondensed.IsDiscrete._proof_1","LightProfinite","LightProfinite.hasSheafify_type","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":144,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Sheaf.IsConstant.casesOn","CategoryTheory.Sheaf.IsConstant.mk","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.types","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondSet","LightCondensed.IsDiscrete","LightCondensed.IsDiscrete._proof_1","LightProfinite","LightProfinite.hasSheafify_type","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Characterization","name":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondSet.isDiscrete_tfae.match_1_3","namespace":"_private.Mathlib.Condensed.Discrete.Characterization.0.LightCondSet.isDiscrete_tfae","reducibility":"abbrev","statement_dag_size":103,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.obj","CategoryTheory.Iso","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","Exists.intro","LightCondSet","LightCondSet.LocallyConstant.functor","LightCondensed._proof_1","LightProfinite","Nonempty","Nonempty.intro","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":135,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.essImage","CategoryTheory.Functor.obj","CategoryTheory.Iso","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","Exists.casesOn","Exists.intro","LightCondSet","LightCondSet.LocallyConstant.functor","LightCondensed._proof_1","LightProfinite","Nonempty","Nonempty.casesOn","Nonempty.intro","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYoneda._simp_2","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYoneda","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp._simp_1_2","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp._simp_1_3","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp","reducibility":null,"statement_dag_size":79,"type_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op"],"value_dag_size":89,"value_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.op_comp","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp._simp_1_4","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoFinYonedaComponents_inv_comp","reducibility":null,"statement_dag_size":212,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed.isoFinYonedaComponents","DFunLike.coe","EMetricSpace.metrizableSpace","Eq","Finite","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Profinite","Profinite.of","Quiver.Hom.op","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"],"value_dag_size":220,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed.isoFinYonedaComponents","Condensed.isoFinYonedaComponents_hom_apply","DFunLike.coe","EMetricSpace.metrizableSpace","Eq.symm","Finite","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Profinite","Profinite.of","Quiver.Hom.op","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv._simp_1_7","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":80,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq","Quiver.Hom"],"value_dag_size":91,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv._simp_1_8","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":79,"type_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op"],"value_dag_size":89,"value_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.op_comp","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv._simp_1_9","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":212,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed.isoFinYonedaComponents","DFunLike.coe","EMetricSpace.metrizableSpace","Eq","Finite","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Profinite","Profinite.of","Quiver.Hom.op","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"],"value_dag_size":220,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed.isoFinYonedaComponents","Condensed.isoFinYonedaComponents_hom_apply","DFunLike.coe","EMetricSpace.metrizableSpace","Eq.symm","Finite","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Profinite","Profinite.of","Quiver.Hom.op","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv.match_1_2","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.Condensed.isoLocallyConstantOfIsColimit_inv","reducibility":"abbrev","statement_dag_size":106,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Comma.mk","CategoryTheory.CostructuredArrow","CategoryTheory.Discrete","CategoryTheory.Functor.fromPUnit","CategoryTheory.Functor.obj","CategoryTheory.Functor.op","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.discreteCategory","CategoryTheory.types","CompHausLike.category","Finite","FintypeCat","FintypeCat.toProfinite","Opposite","PUnit","Profinite","Quiver.Hom","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":131,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Comma.casesOn","CategoryTheory.Comma.mk","CategoryTheory.CostructuredArrow","CategoryTheory.Discrete","CategoryTheory.Functor.fromPUnit","CategoryTheory.Functor.obj","CategoryTheory.Functor.op","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.discreteCategory","CategoryTheory.types","CompHausLike.category","Finite","FintypeCat","FintypeCat.toProfinite","Opposite","PUnit","Profinite","Quiver.Hom","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoFinYonedaComponents_inv_comp._simp_1_2","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoFinYonedaComponents_inv_comp","reducibility":null,"statement_dag_size":79,"type_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op"],"value_dag_size":89,"value_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.op_comp","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoFinYonedaComponents_inv_comp._simp_1_3","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoFinYonedaComponents_inv_comp","reducibility":null,"statement_dag_size":235,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Countable.LindelofSpace","DFunLike.coe","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Finite","LightCondensed.isoFinYonedaComponents","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","Quiver.Hom.op","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instCountablePUnit","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"],"value_dag_size":243,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Countable.LindelofSpace","DFunLike.coe","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq.symm","Finite","LightCondensed.isoFinYonedaComponents","LightCondensed.isoFinYonedaComponents_hom_apply","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","Quiver.Hom.op","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instCountablePUnit","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv._simp_1_7","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":80,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq","Quiver.Hom"],"value_dag_size":91,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv._simp_1_8","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":79,"type_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op"],"value_dag_size":89,"value_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.op_comp","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv._simp_1_9","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv","reducibility":null,"statement_dag_size":235,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Countable.LindelofSpace","DFunLike.coe","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","Finite","LightCondensed.isoFinYonedaComponents","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","Quiver.Hom.op","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instCountablePUnit","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"],"value_dag_size":243,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.hom","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Countable.LindelofSpace","DFunLike.coe","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq.symm","Finite","LightCondensed.isoFinYonedaComponents","LightCondensed.isoFinYonedaComponents_hom_apply","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","Quiver.Hom.op","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instCompactSpace","instConcreteCategoryTypeFun","instCountablePUnit","instExtremallyDisconnectedOfPreirreducibleSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instPreirreducibleSpaceOfIndiscreteTopology","instTopologicalSpacePUnit","instTotallySeparatedSpaceOfExtremallyDisconnectedOfT2Space"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Discrete.Colimit","name":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv.match_1_2","namespace":"_private.Mathlib.Condensed.Discrete.Colimit.0.LightCondensed.isoLocallyConstantOfIsColimit_inv","reducibility":"abbrev","statement_dag_size":112,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Comma.mk","CategoryTheory.CostructuredArrow","CategoryTheory.Discrete","CategoryTheory.Functor.fromPUnit","CategoryTheory.Functor.obj","CategoryTheory.Functor.op","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.discreteCategory","CategoryTheory.types","CompHausLike.category","Finite","FintypeCat","FintypeCat.toLightProfinite","LightProfinite","Opposite","PUnit","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":137,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Comma.casesOn","CategoryTheory.Comma.mk","CategoryTheory.CostructuredArrow","CategoryTheory.Discrete","CategoryTheory.Functor.fromPUnit","CategoryTheory.Functor.obj","CategoryTheory.Functor.op","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.discreteCategory","CategoryTheory.types","CompHausLike.category","Finite","FintypeCat","FintypeCat.toLightProfinite","LightProfinite","Opposite","PUnit","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction._proof_2","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction","reducibility":null,"statement_dag_size":221,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.Limits.PreservesFiniteProducts","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preregular","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.sheafToPresheaf","CategoryTheory.types","CompHausLike","CompHausLike.HasExplicitFiniteCoproducts","CompHausLike.HasExplicitPullbacks","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","CompHausLike.preregular","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Function.Surjective","Opposite","Quiver.Hom","TopCat","TopCat.carrier","TopCat.str"],"value_dag_size":167,"value_refs":["CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Preregular","CategoryTheory.Presheaf.instPreservesFiniteProductsOppositeObjFunctorIsSheafCoherentTopology","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.types","CompHausLike","CompHausLike.HasExplicitFiniteCoproducts","CompHausLike.HasExplicitPullbacks","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","CompHausLike.preregular","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Function.Surjective","Quiver.Hom","TopCat","TopCat.carrier","TopCat.str"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction._simp_3","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","Function.Fiber","Function.Fiber.image","Membership.mem","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Set.range","Singleton.singleton","Subtype.val"],"value_dag_size":106,"value_refs":["Eq","Function.Fiber","Function.Fiber.image","Function.Fiber.mem_iff_eq_image","Membership.mem","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Set.range","Singleton.singleton","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction._simp_4","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Function.Fiber","Function.Fiber.image","Function.Fiber.preimage"],"value_dag_size":36,"value_refs":["Eq.symm","Function.Fiber","Function.Fiber.image","Function.Fiber.map_preimage_eq_image","Function.Fiber.preimage"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.componentHom._simp_2","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.componentHom","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.componentHom._simp_3","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.componentHom","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counit._simp_3","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counit","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Function.Fiber","Function.Fiber.image","Function.Fiber.preimage","Function.comp"],"value_dag_size":55,"value_refs":["Eq.symm","Function.Fiber","Function.Fiber.image","Function.Fiber.map_preimage_eq_image_map","Function.Fiber.preimage","Function.comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counitApp._simp_3","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counitApp","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counitApp._simp_4","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.counitApp","reducibility":null,"statement_dag_size":79,"type_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op"],"value_dag_size":89,"value_refs":["CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.opposite","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.op_comp","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.incl_of_counitAppApp._simp_1_2","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.incl_of_counitAppApp","reducibility":null,"statement_dag_size":68,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Iso","CategoryTheory.Iso.hom","CategoryTheory.Iso.op","Eq","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"],"value_dag_size":75,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Iso","CategoryTheory.Iso.hom","CategoryTheory.Iso.op","CategoryTheory.Iso.op_hom","Eq.symm","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Quiver.opposite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.incl_of_counitAppApp._simp_1_3","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.incl_of_counitAppApp","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.LocallyConstant","name":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction","reducibility":null,"statement_dag_size":308,"type_refs":["CategoryTheory.Adjunction.unit","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.id","CategoryTheory.Functor.obj","CategoryTheory.IsIso","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.sheafSections","CategoryTheory.types","CompHausLike","CompHausLike.HasExplicitFiniteCoproducts","CompHausLike.HasExplicitPullbacks","CompHausLike.HasProp","CompHausLike.LocallyConstant.adjunction","CompHausLike.LocallyConstant.functor","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","CompHausLike.of","CompHausLike.preregular","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","EMetricSpace.metrizableSpace","Function.Surjective","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Quiver.Hom","Subtype","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","instCompactSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit","instTopologicalSpaceSubtype"],"value_dag_size":298,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.id","CategoryTheory.Functor.obj","CategoryTheory.Iso.isIso_hom","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.sheafSections","CategoryTheory.types","CompHausLike","CompHausLike.HasExplicitFiniteCoproducts","CompHausLike.HasExplicitPullbacks","CompHausLike.HasProp","CompHausLike.LocallyConstant.functor","CompHausLike.LocallyConstant.unitIso","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","CompHausLike.of","CompHausLike.preregular","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","EMetricSpace.metrizableSpace","Function.Surjective","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Quiver.Hom","Subtype","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","instCompactSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.functorIsoDiscrete._simp_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.functorIsoDiscrete","reducibility":null,"statement_dag_size":80,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq","Quiver.Hom"],"value_dag_size":91,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.functorIsoDiscrete._simp_3","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.functorIsoDiscrete","reducibility":null,"statement_dag_size":106,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":118,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf","reducibility":null,"statement_dag_size":616,"type_refs":["AddCommGroup.toAddCommMonoid","AddCommGrpCat.hasColimitsOfShape","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.obj","CategoryTheory.Functor.sections","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.instInhabited","CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.PreservesFilteredColimitsOfSize.preserves_filtered_colimits","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.isCofiltered_of_directed_ge_nonempty","CategoryTheory.isFiltered_op_of_isCofiltered","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LinearMap","LinearMap.instFunLike","Membership.mem","ModuleCat","ModuleCat.FilteredColimits.forget_preservesFilteredColimits","ModuleCat.carrier","ModuleCat.hasColimitsOfShape","ModuleCat.hasLimit","ModuleCat.instConcreteCategoryLinearMapIdCarrier","ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier","ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier","ModuleCat.isAddCommGroup","ModuleCat.isModule","ModuleCat.moduleCategory","Opposite","Opposite.small","Preorder.smallCategory","Ring","Ring.toSemiring","RingHom.id","SemilatticeInf.instIsCodirectedOrder","Semiring.toNonAssocSemiring","Set","Set.instMembership","TopCat","True","UnivLE.self","UnivLE.small","instNonemptyOfInhabited","small_Pi","small_subtype","univLE_of_max"],"value_dag_size":10,"value_refs":["CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete","Ring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf","reducibility":null,"statement_dag_size":616,"type_refs":["AddCommGroup.toAddCommMonoid","AddCommGrpCat.hasColimitsOfShape","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.obj","CategoryTheory.Functor.sections","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.instInhabited","CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.PreservesFilteredColimitsOfSize.preserves_filtered_colimits","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.isCofiltered_of_directed_ge_nonempty","CategoryTheory.isFiltered_op_of_isCofiltered","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LinearMap","LinearMap.instFunLike","Membership.mem","ModuleCat","ModuleCat.FilteredColimits.forget_preservesFilteredColimits","ModuleCat.carrier","ModuleCat.hasColimitsOfShape","ModuleCat.hasLimit","ModuleCat.instConcreteCategoryLinearMapIdCarrier","ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier","ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier","ModuleCat.isAddCommGroup","ModuleCat.isModule","ModuleCat.moduleCategory","Opposite","Opposite.small","Preorder.smallCategory","Ring","Ring.toSemiring","RingHom.id","SemilatticeInf.instIsCodirectedOrder","Semiring.toNonAssocSemiring","Set","Set.instMembership","TopCat","True","UnivLE.self","UnivLE.small","instNonemptyOfInhabited","small_Pi","small_subtype","univLE_of_max"],"value_dag_size":10,"value_refs":["CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete","Ring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor","reducibility":null,"statement_dag_size":208,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence","CategoryTheory.Functor.isRightAdjoint_of_isEquivalence","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.Types.hasColimitsOfShape","CategoryTheory.Limits.Types.hasLimit","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Types.instIsEquivalenceForgetTypeFun","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.instReflectsIsomorphismsForgetTypeFun","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Opposite","Opposite.small","Preorder.smallCategory","TopCat","True","TypeCat.Fun","TypeCat.instFunLikeFun","UnivLE.self","UnivLE.small","instConcreteCategoryTypeFun","univLE_of_max"],"value_dag_size":1,"value_refs":["CondensedSet.LocallyConstant.instFaithfulCondensedTypeDiscrete"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor._proof_2","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor","reducibility":null,"statement_dag_size":208,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.Functor.instPreservesColimitsOfShapeOfIsLeftAdjoint","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence","CategoryTheory.Functor.isRightAdjoint_of_isEquivalence","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.Types.hasColimitsOfShape","CategoryTheory.Limits.Types.hasLimit","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.Types.instIsEquivalenceForgetTypeFun","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.forget","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.instReflectsIsomorphismsForgetTypeFun","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Opposite","Opposite.small","Preorder.smallCategory","TopCat","True","TypeCat.Fun","TypeCat.instFunLikeFun","UnivLE.self","UnivLE.small","instConcreteCategoryTypeFun","univLE_of_max"],"value_dag_size":1,"value_refs":["CondensedSet.LocallyConstant.instFullCondensedTypeDiscrete"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf","reducibility":null,"statement_dag_size":109,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":10,"value_refs":["LightCondMod.LocallyConstant.instFaithfulModuleCatLightCondensedDiscrete","Ring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf","reducibility":null,"statement_dag_size":109,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":10,"value_refs":["LightCondMod.LocallyConstant.instFullModuleCatLightCondensedDiscrete","Ring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor._proof_1","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor","reducibility":null,"statement_dag_size":97,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.types","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite","LightProfinite.hasSheafify_type","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":1,"value_refs":["LightCondSet.LocallyConstant.instFaithfulLightCondensedTypeDiscrete"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Discrete.Module","name":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor._proof_2","namespace":"_private.Mathlib.Condensed.Discrete.Module.0.LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor","reducibility":null,"statement_dag_size":97,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.constantSheaf","CategoryTheory.instHasWeakSheafifyOfHasSheafify","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.types","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite","LightProfinite.hasSheafify_type","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":1,"value_refs":["LightCondSet.LocallyConstant.instFullLightCondensedTypeDiscrete"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.EffectiveEpi","name":"_private.Mathlib.Condensed.EffectiveEpi.0.instIsRegularEpiCategoryCondensedSet._proof_1","namespace":"_private.Mathlib.Condensed.EffectiveEpi.0.instIsRegularEpiCategoryCondensedSet","reducibility":null,"statement_dag_size":42,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.IsRegularEpiCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","TopCat","True"],"value_dag_size":20,"value_refs":["CategoryTheory.coherentTopology","CategoryTheory.instHasSheafifyType","CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify","CompHaus","CompHausLike.category","Condensed._proof_1","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Functors","name":"_private.Mathlib.Condensed.Functors.0.instFaithfulCompHausCondensedSetCompHausToCondensed._proof_1","namespace":"_private.Mathlib.Condensed.Functors.0.instFaithfulCompHausCondensedSetCompHausToCondensed","reducibility":null,"statement_dag_size":46,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","TopCat","True","compHausToCondensed"],"value_dag_size":79,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Faithful.comp","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Condensed.ulift","CondensedSet","Opposite","TopCat","True","compHausToCondensed'","instFaithfulCompHausCondensedTypeCompHausToCondensed'","instFaithfulCondensedTypeCondensedSetUlift"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Functors","name":"_private.Mathlib.Condensed.Functors.0.instFaithfulCompHausCondensedTypeCompHausToCondensed'._proof_1","namespace":"_private.Mathlib.Condensed.Functors.0.instFaithfulCompHausCondensedTypeCompHausToCondensed'","reducibility":null,"statement_dag_size":48,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Opposite","TopCat","True","compHausToCondensed'"],"value_dag_size":39,"value_refs":["CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeYoneda","CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Functors","name":"_private.Mathlib.Condensed.Functors.0.instFullCompHausCondensedSetCompHausToCondensed._proof_1","namespace":"_private.Mathlib.Condensed.Functors.0.instFullCompHausCondensedSetCompHausToCondensed","reducibility":null,"statement_dag_size":46,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","TopCat","True","compHausToCondensed"],"value_dag_size":79,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Full.comp","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Condensed.ulift","CondensedSet","Opposite","TopCat","True","compHausToCondensed'","instFullCompHausCondensedTypeCompHausToCondensed'","instFullCondensedTypeCondensedSetUlift"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Functors","name":"_private.Mathlib.Condensed.Functors.0.instFullCompHausCondensedTypeCompHausToCondensed'._proof_1","namespace":"_private.Mathlib.Condensed.Functors.0.instFullCompHausCondensedTypeCompHausToCondensed'","reducibility":null,"statement_dag_size":48,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Opposite","TopCat","True","compHausToCondensed'"],"value_dag_size":39,"value_refs":["CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.GrothendieckTopology.instFullSheafTypeYoneda","CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Functors","name":"_private.Mathlib.Condensed.Functors.0.instPreservesFiniteCoproductsCompHausCondensedSetCompHausToCondensed._proof_1","namespace":"_private.Mathlib.Condensed.Functors.0.instPreservesFiniteCoproductsCompHausCondensedSetCompHausToCondensed","reducibility":null,"statement_dag_size":46,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.PreservesFiniteCoproducts","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","TopCat","True","compHausToCondensed"],"value_dag_size":26,"value_refs":["CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed.instPreservesFiniteProductsOppositeCompHausObjFunctorIsSheafCoherentTopology","Condensed.ulift._proof_1","TopCat","True","instPreservesFiniteCoproductsSheafTypeUliftYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.EffectiveEpi","name":"_private.Mathlib.Condensed.Light.EffectiveEpi.0.instIsRegularEpiCategoryLightCondSet._proof_1","namespace":"_private.Mathlib.Condensed.Light.EffectiveEpi.0.instIsRegularEpiCategoryLightCondSet","reducibility":null,"statement_dag_size":55,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.IsRegularEpiCategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":30,"value_refs":["And","CategoryTheory.coherentTopology","CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify","CompHausLike.category","LightCondensed._proof_1","LightProfinite","LightProfinite.hasSheafify_type","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Epi","name":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.epi_π_app_zero_of_epi._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.epi_π_app_zero_of_epi","reducibility":null,"statement_dag_size":102,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Function.Surjective","LightProfinite","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":105,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Function.Surjective","LightProfinite","LightProfinite.effectiveEpi_iff_surjective","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.Epi","name":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim.match_1","namespace":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim","reducibility":"abbrev","statement_dag_size":17,"type_refs":["CategoryTheory.Discrete","CategoryTheory.Discrete.mk","Nat"],"value_dag_size":26,"value_refs":["CategoryTheory.Discrete","CategoryTheory.Discrete.casesOn","CategoryTheory.Discrete.mk","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Epi","name":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.Epi.0.LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite","reducibility":null,"statement_dag_size":102,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Function.Surjective","LightProfinite","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":105,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.EffectiveEpi","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Function.Surjective","LightProfinite","LightProfinite.effectiveEpi_iff_surjective","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Functors","name":"_private.Mathlib.Condensed.Light.Functors.0.instFaithfulLightProfiniteLightCondSetLightProfiniteToLightCondSet._proof_1","namespace":"_private.Mathlib.Condensed.Light.Functors.0.instFaithfulLightProfiniteLightCondSetLightProfiniteToLightCondSet","reducibility":null,"statement_dag_size":59,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Faithful","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","lightProfiniteToLightCondSet"],"value_dag_size":52,"value_refs":["And","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.GrothendieckTopology.instFaithfulSheafTypeYoneda","CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Functors","name":"_private.Mathlib.Condensed.Light.Functors.0.instFullLightProfiniteLightCondSetLightProfiniteToLightCondSet._proof_1","namespace":"_private.Mathlib.Condensed.Light.Functors.0.instFullLightProfiniteLightCondSetLightProfiniteToLightCondSet","reducibility":null,"statement_dag_size":59,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.Full","CategoryTheory.Functor.category","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","lightProfiniteToLightCondSet"],"value_dag_size":52,"value_refs":["And","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.GrothendieckTopology.instFullSheafTypeYoneda","CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Functors","name":"_private.Mathlib.Condensed.Light.Functors.0.instPreservesFiniteCoproductsLightProfiniteLightCondSetLightProfiniteToLightCondSet._proof_1","namespace":"_private.Mathlib.Condensed.Light.Functors.0.instPreservesFiniteCoproductsLightProfiniteLightCondSetLightProfiniteToLightCondSet","reducibility":null,"statement_dag_size":59,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.PreservesFiniteCoproducts","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","lightProfiniteToLightCondSet"],"value_dag_size":62,"value_refs":["And","CategoryTheory.Presheaf.instPreservesFiniteProductsOppositeObjFunctorIsSheafCoherentTopology","CategoryTheory.Sheaf","CategoryTheory.coherentTopology","CategoryTheory.coherentTopology.subcanonical","CategoryTheory.types","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instPreservesFiniteCoproductsSheafTypeYonedaOfPreservesFiniteProductsOppositeObjFunctorIsSheaf","lightProfiniteToLightCondSet._proof_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Functors","name":"_private.Mathlib.Condensed.Light.Functors.0.instPreservesLimitsOfShapeLightProfiniteLightCondSetLightProfiniteToLightCondSetOfCountableCategory._proof_1","namespace":"_private.Mathlib.Condensed.Light.Functors.0.instPreservesLimitsOfShapeLightProfiniteLightCondSetLightProfiniteToLightCondSetOfCountableCategory","reducibility":null,"statement_dag_size":40,"type_refs":["And","CategoryTheory.CountableCategory","CategoryTheory.Limits.PreservesLimitsOfShape","CategoryTheory.SmallCategory","CompHausLike.category","LightProfinite","LightProfinite.toTopCat","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":99,"value_refs":["And","CategoryTheory.CountableCategory","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Limits.comp_preservesLimitsOfShape","CategoryTheory.Limits.hasCountableLimits_of_hasLimits","CategoryTheory.Limits.instHasLimitsOfShapeOfHasCountableLimitsOfCountableCategory","CategoryTheory.SmallCategory","CategoryTheory.instIsRightAdjointOfMonadicRightAdjoint","CategoryTheory.monadicOfReflective","CategoryTheory.preservesLimitOfShape_of_createsLimitsOfShape_and_hasLimitsOfShape","CompHausLike.category","LightProfinite","LightProfinite.createsCountableLimits","Profinite","Profinite.hasLimits","Profinite.toTopCat","Profinite.toTopCat.reflective","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.str","TotallyDisconnectedSpace","lightToProfinite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition'._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition'","reducibility":null,"statement_dag_size":163,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","Eq","Quiver.Hom"],"value_dag_size":177,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.LaxMonoidal.μ_natural_left","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition","reducibility":null,"statement_dag_size":80,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq","Quiver.Hom"],"value_dag_size":91,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition._simp_1_2","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_internallyProjective_iff_tensor_condition","reducibility":null,"statement_dag_size":160,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerLeft","Eq","Quiver.Hom"],"value_dag_size":174,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.LaxMonoidal.μ_natural_right","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerLeft","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'","reducibility":null,"statement_dag_size":133,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":147,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_assoc","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'._simp_1_2","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition'","reducibility":null,"statement_dag_size":199,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","Eq","Quiver.Hom"],"value_dag_size":215,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.LaxMonoidal.μ_natural_left_assoc","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition","reducibility":null,"statement_dag_size":133,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":147,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_assoc","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition._simp_1_2","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition","reducibility":null,"statement_dag_size":196,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerLeft","Eq","Quiver.Hom"],"value_dag_size":212,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.LaxMonoidal","CategoryTheory.Functor.LaxMonoidal.μ","CategoryTheory.Functor.LaxMonoidal.μ_natural_right_assoc","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerLeft","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.ihom_map_val_app._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.ihom_map_val_app","reducibility":null,"statement_dag_size":132,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Closed","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalClosed.uncurry","CategoryTheory.ihom","Eq","Quiver.Hom"],"value_dag_size":144,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Closed","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.MonoidalCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalClosed.uncurry","CategoryTheory.MonoidalClosed.uncurry_natural_right","CategoryTheory.ihom","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.ihom_map_val_app._simp_1_2","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.ihom_map_val_app","reducibility":null,"statement_dag_size":205,"type_refs":["CategoryTheory.Adjunction","CategoryTheory.Adjunction.homEquiv","CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Quiver.Hom"],"value_dag_size":219,"value_refs":["CategoryTheory.Adjunction","CategoryTheory.Adjunction.homEquiv","CategoryTheory.Adjunction.homEquiv_naturality_right_symm","CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.InternallyProjective","name":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.internallyProjective_iff_tensor_condition.match_1_1","namespace":"_private.Mathlib.Condensed.Light.InternallyProjective.0.LightCondensed.internallyProjective_iff_tensor_condition","reducibility":"abbrev","statement_dag_size":186,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.InternallyProjective","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.ObjectProperty.Is.mk","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.isInternallyProjective","CommRing","CommRing.toRing","CompHausLike.category","LightCondMod","LightCondensed._proof_1","LightCondensed.instMonoidalCategorySheafLightProfiniteCoherentTopologyModuleCat","LightCondensed.instMonoidalClosedLightCondMod","LightProfinite","ModuleCat","ModuleCat.moduleCategory","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":203,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.InternallyProjective","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.ObjectProperty.Is.casesOn","CategoryTheory.ObjectProperty.Is.mk","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.isInternallyProjective","CommRing","CommRing.toRing","CompHausLike.category","LightCondMod","LightCondensed._proof_1","LightCondensed.instMonoidalCategorySheafLightProfiniteCoherentTopologyModuleCat","LightCondensed.instMonoidalClosedLightCondMod","LightProfinite","ModuleCat","ModuleCat.moduleCategory","Opposite","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite","reducibility":"regular","statement_dag_size":40,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CompHausLike.category","CompHausLike.toTop","LightProfinite","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":177,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","LightProfinite.of","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_4","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","reducibility":null,"statement_dag_size":160,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","CompactSpace","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype"],"value_dag_size":216,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.toTop","CompactSpace","ContinuousMap","ContinuousMap.instContinuousMapClass","ContinuousMap.instFunLike","ContinuousMapClass.map_continuous","DFunLike.coe","Iff.mp","IsClosed.isCompact","IsClosed.preimage","IsCompact","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","T2Space.t1Space","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype","isClosed_singleton","isCompact_iff_compactSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","reducibility":null,"statement_dag_size":130,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","T2Space","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype"],"value_dag_size":125,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_hausdorff","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instT2SpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","reducibility":null,"statement_dag_size":129,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype"],"value_dag_size":124,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre._proof_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","reducibility":null,"statement_dag_size":159,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype"],"value_dag_size":113,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TotallyDisconnectedSpace"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite","reducibility":"regular","statement_dag_size":48,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CompHausLike.category","CompHausLike.toTop","LightProfinite","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre"],"value_dag_size":188,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.InducedCategory.Hom.mk","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.mk","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.ofHom","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl._proof_1","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","reducibility":null,"statement_dag_size":139,"type_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","Continuous","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.val","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceSubtype"],"value_dag_size":123,"value_refs":["And","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","LightProfinite","Membership.mem","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","continuous_subtype_val"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":50,"type_refs":["Function.comp","OnePoint","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton"],"value_dag_size":114,"value_refs":["Eq","Function.comp","Membership.mem","OnePoint","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.ofPred","Set.preimage","Singleton.singleton","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'_compactSpace","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":172,"type_refs":["CompactSpace","Continuous","Function.comp","Membership.mem","OnePoint","OnePoint.instTopologicalSpace","Pi.topologicalSpace","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","T1Space","T2Space","TopologicalSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":694,"value_refs":["CompactSpace","Continuous","Continuous.comp'","Continuous.fst","Continuous.snd","Eq","Eq.mpr","Eq.symm","Eq.trans","Function.comp","Iff","Iff.mp","IsClosed.isCompact","IsClosed.preimage","IsCompact","Membership.mem","OnePoint","OnePoint.instTopologicalSpace","Pi.compactSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.ext","Set.iInter","Set.instMembership","Set.instSingletonSet","Set.mem_iInter._simp_1","Set.ofPred","Set.preimage","Singleton.singleton","Subtype.val","T1Space","T2Space","TopologicalSpace","True","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff._simp_1","congr","congrArg","continuous_apply","continuous_subtype_val","forall_congr","id","iff_self","instTopologicalSpaceProd","instTopologicalSpaceSubtype","isClosed_eq","isClosed_iInter","isClosed_singleton","isCompact_iff_compactSpace","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.aux","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":588,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.IsSplitEpi","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Exists","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","instCompactSpaceSum","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum"],"value_dag_size":8285,"value_refs":["And","And.intro","CategoryTheory.CartesianMonoidalCategory.hom_ext","CategoryTheory.CartesianMonoidalCategory.lift","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.ext","CategoryTheory.ConcreteCategory.hom","CategoryTheory.ConcreteCategory.ofHom","CategoryTheory.Epi","CategoryTheory.InducedCategory.Hom.mk","CategoryTheory.IsSplitEpi","CategoryTheory.IsSplitEpi.mk","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.SplitEpi","CategoryTheory.SplitEpi.mk","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.const","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.condition","CompHausLike.pullback.fst","CompHausLike.pullback.lift","CompHausLike.pullback.snd","CompHausLike.toTop","CompactSpace","Continuous.comp","Continuous.subtype_mk","ContinuousMap","ContinuousMap.ext","ContinuousMap.instContinuousMapClass","ContinuousMap.instFunLike","ContinuousMap.mk","ContinuousMapClass.map_continuous","DFunLike.coe","Eq","Eq.mpr","Eq.symm","Eq.trans","Exists","Exists.intro","Function.Surjective","Function.comp","Iff.mp","IsClosed.isCompact","IsCompact","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.epi_iff_surjective","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instCountableCarrierToTopAndTotallyDisconnectedSpaceSecondCountableTopologyNatUnionInfty","LightProfinite.instEpiCompHausLikeAndTotallyDisconnectedSpaceCarrierSecondCountableTopologySnd","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","LightProfinite.of","Membership.mem","Nat","Nat.instLinearOrder","Nat.instLocallyFiniteOrder","Nonempty.intro","OnePoint","OnePoint.infty","OnePoint.instT1Space","OnePoint.instTopologicalSpace","Option","Option.none","OrderTopology.of_linearLocallyFinite","OrderTopology.t5Space","Pi.t2Space","Pi.topologicalSpace","Pi.totallyDisconnectedSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.ofPred","Set.preimage","Singleton.singleton","Subtype.mk","Subtype.prop","Subtype.totallyDisconnectedSpace","Subtype.val","Sum","T5Space.toT1Space","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.ofHom","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyForallOfCountable","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","True","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'_compactSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_closed","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_continuous","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","congr","congrArg","continuous_apply","continuous_subtype_val","eq_self","id","inferInstance","instCompactSpaceSum","instDiscreteTopologyNat","instT2SpaceSubtype","instT2SpaceSum","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","isCompact_iff_compactSpace","of_eq_true","propext","rfl"]}
+{"definition_height":21,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":885,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.Cocone","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","instCompactSpaceSum","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet"],"value_dag_size":634,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.Cocone.ofCofork","CategoryTheory.Limits.Cofork.ofπ","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.WalkingParallelPair.one","CategoryTheory.Limits.WalkingParallelPair.zero","CategoryTheory.Limits.WalkingParallelPairHom.left","CategoryTheory.Limits.WalkingParallelPairHom.right","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preadditive.fullSubcategory","CategoryTheory.Preadditive.homGroup","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.functorCategoryPreadditive","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","Eq","HAdd.hAdd","HSub.hSub","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","ModuleCat","ModuleCat.instPreadditive","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Quiver.Hom","SecondCountableTopology","SubNegMonoid.toSub","Sum","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","instHAdd","instHSub","instTopologicalSpaceSum","lightProfiniteToLightCondSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","reducibility":null,"statement_dag_size":620,"type_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.WalkingParallelPair.one","CategoryTheory.Limits.WalkingParallelPair.zero","CategoryTheory.Limits.WalkingParallelPairHom.left","CategoryTheory.Limits.WalkingParallelPairHom.right","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preadditive.fullSubcategory","CategoryTheory.Preadditive.homGroup","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.functorCategoryPreadditive","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","Eq","HAdd.hAdd","HSub.hSub","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","ModuleCat","ModuleCat.instPreadditive","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Quiver.Hom","SecondCountableTopology","SubNegMonoid.toSub","Sum","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","instHAdd","instHSub","instTopologicalSpaceSum","lightProfiniteToLightCondSet"],"value_dag_size":7460,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.assoc","CategoryTheory.Category.id_comp","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Discrete","CategoryTheory.Discrete.casesOn","CategoryTheory.Discrete.mk","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.const","CategoryTheory.Functor.instPreservesColimitsOfSizeOfIsLeftAdjoint","CategoryTheory.Functor.map","CategoryTheory.Functor.mapCocone","CategoryTheory.Functor.map_comp","CategoryTheory.Functor.obj","CategoryTheory.Limits.BinaryCofan.IsColimit.desc'","CategoryTheory.Limits.BinaryCofan.IsColimit.desc'_coe","CategoryTheory.Limits.BinaryCofan.inl","CategoryTheory.Limits.BinaryCofan.inr","CategoryTheory.Limits.BinaryCofan.mk","CategoryTheory.Limits.Cocone.pt","CategoryTheory.Limits.Cocone.ι","CategoryTheory.Limits.IsColimit.desc","CategoryTheory.Limits.IsColimit.fac","CategoryTheory.Limits.IsColimit.fac_assoc","CategoryTheory.Limits.IsColimit.hom_ext","CategoryTheory.Limits.PreservesColimits.preservesFiniteColimits","CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit","CategoryTheory.Limits.PreservesFiniteColimits.preservesFiniteColimits","CategoryTheory.Limits.WalkingPair","CategoryTheory.Limits.WalkingPair.casesOn","CategoryTheory.Limits.WalkingPair.left","CategoryTheory.Limits.WalkingPair.right","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.WalkingParallelPair.one","CategoryTheory.Limits.WalkingParallelPair.zero","CategoryTheory.Limits.WalkingParallelPairHom.left","CategoryTheory.Limits.WalkingParallelPairHom.right","CategoryTheory.Limits.comp_preservesColimit","CategoryTheory.Limits.fintypeWalkingPair","CategoryTheory.Limits.instPreservesColimitsOfShapeDiscreteOfFiniteOfPreservesFiniteCoproducts","CategoryTheory.Limits.isColimitOfPreserves","CategoryTheory.Limits.pair","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.NatTrans.app","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preadditive.comp_add","CategoryTheory.Preadditive.comp_sub","CategoryTheory.Preadditive.fullSubcategory","CategoryTheory.Preadditive.homGroup","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.cancel_epi","CategoryTheory.coherentTopology","CategoryTheory.discreteCategory","CategoryTheory.finCategoryDiscreteOfFintype","CategoryTheory.functorCategoryPreadditive","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.HasExplicitPullback","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.coproductCocone","CompHausLike.coproductIsColimit","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.condition","CompHausLike.pullback.fst","CompHausLike.pullback.lift","CompHausLike.pullback.lift_fst","CompHausLike.pullback.lift_snd","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Finite.of_fintype","HAdd.hAdd","HSub.hSub","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.instPreadditive","ModuleCat.moduleCategory","Nat","OfNat.ofNat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","Subtype.totallyDisconnectedSpace","Subtype.val","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","True","Zero.toOfNat0","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","congr","congrArg","congrFun'","eq_self","id","instCompactSpaceSum","instHAdd","instHSub","instIsLeftAdjointLightCondSetLightCondModFree","instPreservesFiniteCoproductsLightProfiniteLightCondSetLightProfiniteToLightCondSet","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet","of_eq_true","propext","rfl","sub_self","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","reducibility":null,"statement_dag_size":133,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":147,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_assoc","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","reducibility":null,"statement_dag_size":106,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":118,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._simp_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","reducibility":null,"statement_dag_size":80,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq","Quiver.Hom"],"value_dag_size":91,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.assoc","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone_pt","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":902,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.Cocone.pt","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","instCompactSpaceSum","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet"],"value_dag_size":901,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.Cocone.pt","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Eq.refl","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","instCompactSpaceSum","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone_ι_app","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":1397,"type_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.const","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.Cocone.pt","CategoryTheory.Limits.Cocone.ι","CategoryTheory.Limits.Cofork.ofπ","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.WalkingParallelPair.one","CategoryTheory.Limits.WalkingParallelPair.rec","CategoryTheory.Limits.WalkingParallelPair.zero","CategoryTheory.Limits.WalkingParallelPairHom.left","CategoryTheory.Limits.WalkingParallelPairHom.right","CategoryTheory.Limits.diagramIsoParallelPair._proof_1","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.NatTrans.app","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preadditive.fullSubcategory","CategoryTheory.Preadditive.homGroup","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.eqToHom","CategoryTheory.functorCategoryPreadditive","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","HAdd.hAdd","HSub.hSub","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.instPreadditive","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cocone._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","instCompactSpaceSum","instHAdd","instHSub","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet"],"value_dag_size":1740,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.assoc","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Epi","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp","CategoryTheory.Functor.obj","CategoryTheory.Limits.WalkingParallelPair","CategoryTheory.Limits.WalkingParallelPair.one","CategoryTheory.Limits.WalkingParallelPair.rec","CategoryTheory.Limits.diagramIsoParallelPair._proof_1","CategoryTheory.Limits.parallelPair","CategoryTheory.Limits.walkingParallelPairHomCategory","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Preadditive.comp_add","CategoryTheory.Preadditive.comp_sub","CategoryTheory.Preadditive.fullSubcategory","CategoryTheory.Preadditive.homGroup","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.fst","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.eqToHom","CategoryTheory.functorCategoryPreadditive","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.pullback.fst","CompHausLike.pullback.snd","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","Eq.trans","HAdd.hAdd","HSub.hSub","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","ModuleCat","ModuleCat.instPreadditive","ModuleCat.moduleCategory","Nat","OnePoint.infty","Opposite","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","SubNegMonoid.toSub","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","congr","congrArg","congrFun","congrFun'","instCompactSpaceSum","instHAdd","instHSub","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum","lightProfiniteToLightCondSet"]}
+{"definition_height":16,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":493,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.of","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instCompactSpaceSum","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum"],"value_dag_size":354,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.InducedCategory.Hom.hom","CategoryTheory.InducedCategory.Hom.mk","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.of","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","ContinuousMap.mk","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Sum","TopCat","TopCat.Hom.hom'","TopCat.carrier","TopCat.instCategory","TopCat.ofHom","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_6","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":283,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":299,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":126,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.pullback","CompHausLike.toTop","CompactSpace","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint.infty","Quiver.Hom","SecondCountableTopology","Sum","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","instTopologicalSpaceSum"],"value_dag_size":330,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instCompactSpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":126,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.pullback","CompHausLike.toTop","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint.infty","Quiver.Hom","SecondCountableTopology","Sum","T2Space","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","instTopologicalSpaceSum"],"value_dag_size":330,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_hausdorff","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instT2SpaceSum","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":127,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp","CompHausLike.category","CompHausLike.pullback","CompHausLike.toTop","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint.infty","Quiver.Hom","SecondCountableTopology","Sum","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","instTopologicalSpaceSum"],"value_dag_size":349,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_5","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":211,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":227,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_6","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover","reducibility":null,"statement_dag_size":319,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.InducedCategory.Hom.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.pullback","CompHausLike.toTop","Continuous","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Nat","OnePoint.infty","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.ofPred","Sum","TopCat","TopCat.Hom.hom'","TopCat.carrier","TopCat.instCategory","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.cover._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum"],"value_dag_size":919,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.InducedCategory.Hom.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.is_hausdorff","CompHausLike.pullback","CompHausLike.toTop","Continuous","Continuous.eval","Continuous.fst","Continuous.prodMk","Continuous.snd","Continuous.subtype_mk","Continuous.sumElim","ContinuousMap","ContinuousMap.compactOpen","ContinuousMap.instContinuousEvalOfLocallyCompactPair","ContinuousMap.instFunLike","ContinuousMap.mk","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint.infty","Option","Prod","Prod.fst","Prod.mk","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.ofPred","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.totallyDisconnectedSpace","Subtype.val","Sum","T2Space.r1Space","TopCat","TopCat.Hom.hom'","TopCat.carrier","TopCat.instCategory","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_2","continuous_const","continuous_id'","continuous_subtype_val","id","instLocallyCompactPairOfWeaklyLocallyCompactSpaceOfR1Space","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instWeaklyLocallyCompactSpaceOfCompactSpace"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":78,"type_refs":["Eq","Option","Prod","Prod.fst","Prod.snd","Subtype","Sum"],"value_dag_size":146,"value_refs":["Eq","Option","Prod","Prod.fst","Prod.mk","Prod.snd","Subtype","Subtype.mk","Subtype.val","Sum.elim","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Option","Prod","Prod.fst","Prod.mk"],"value_dag_size":35,"value_refs":["Option","Prod","Prod.fst","Prod.mk","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun._proof_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Option","Prod","Prod.fst","Prod.snd","Subtype","Subtype.val"],"value_dag_size":75,"value_refs":["Eq","Option","Prod","Prod.fst","Prod.snd","Subtype","Subtype.prop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_apply","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":180,"type_refs":["Eq","Option","Prod","Prod.fst","Prod.mk","Prod.snd","Subtype","Subtype.mk","Subtype.prop","Subtype.val","Sum","Sum.elim","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","rfl"],"value_dag_size":89,"value_refs":["Eq","Option","Prod","Prod.fst","Prod.snd","Subtype","Sum","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":194,"type_refs":["Eq","Function.Surjective","Function.comp","Option","Option.none","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Sum","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":1020,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Function.comp","Iff.mp","Membership.mem","Ne","Not","Option","Option.decidableEqNone","Option.ne_none_iff_exists'","Option.none","Option.some","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Sum","Sum.inl","Sum.inr","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_12","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_9","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective.match_1_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","dite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":52,"type_refs":["Membership.mem","Option","Option.some","Prod","Prod.fst","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":211,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","False.casesOn","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.not_exists","Membership.mem","Not","Option","Option.none","Option.some","Or","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","eq_false","forall_congr","forall_not_of_not_exists","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_11","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","Lean.Grind.nestedProof","Membership.mem","Option","Option.some","Prod","Prod.fst","Prod.mk","Set","Set.instMembership","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":75,"value_refs":["Lean.Grind.nestedProof","Membership.mem","Option","Option.some","Prod","Prod.fst","Set","Set.instMembership","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_6","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_12","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":403,"type_refs":["Eq","Function.comp","Membership.mem","Not","Option","Option.none","Option.some","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Sum.inl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":2450,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Function.comp","HEq","HEq.refl","HEq.trans","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Option","Option.ctorIdx","Option.none","Option.some","Or","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.prop","Subtype.property","Subtype.val","Sum.elim","Sum.elim_inl","Sum.inl","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_apply","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_10","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_11","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_6","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_7","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","congr","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","noConfusion_of_Nat","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":188,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":597,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","Function.comp_apply","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Membership.mem","Not","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.mem_preimage","Set.mem_singleton_iff","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":188,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":582,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","Function.comp_apply","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Membership.mem","Not","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.mem_preimage","Set.mem_singleton_iff","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":270,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":759,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","HEq","HEq.refl","Lean.Grind.nestedProof","Membership.mem","Not","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.mk.inj","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl_apply","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_6","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Membership.mem","Option","Prod","Prod.fst","Prod.mk","Set","Set.instMembership","Subtype","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":76,"value_refs":["Membership.mem","Option","Prod","Prod.fst","Prod.mk","Set","Set.instMembership","Subtype","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_7","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":239,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":231,"value_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.prop","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_8","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":352,"type_refs":["Eq","Function.comp","Lean.Grind.nestedProof","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":343,"value_refs":["Eq","Function.comp","Lean.Grind.nestedProof","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_7","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_9","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":null,"statement_dag_size":385,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Sum.inr","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":1205,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","HEq.refl","HEq.trans","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.prop","Subtype.property","Subtype.val","Sum.elim","Sum.elim_inr","Sum.inr","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_apply","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_6","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_7","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective._proof_1_8","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl_apply","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","congr","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective.match_1_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.coverToFun_surjective","reducibility":"abbrev","statement_dag_size":249,"type_refs":["Eq","Membership.mem","Option","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":615,"value_refs":["Eq","Membership.mem","Option","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Subtype","Subtype.casesOn","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":75,"type_refs":["Function.comp","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":86,"value_refs":["Function.comp","Membership.mem","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl_apply","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":85,"value_refs":["Function.comp","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","rfl"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":21,"type_refs":["Option","Prod","Set"],"value_dag_size":60,"value_refs":["Eq","Option","Option.none","Option.some","Prod","Prod.snd","Set","Set.iUnion","Set.instUnion","Set.ofPred","Set.range","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres.eq_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","Option","Option.none","Option.some","Prod","Prod.snd","Set","Set.iUnion","Set.instUnion","Set.ofPred","Set.range","Union.union","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":32,"value_refs":["Eq.refl","Option","Prod","Set","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_closed","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":105,"type_refs":["CompactSpace","Continuous","DiscreteTopology","Eq","IsClosed","OnePoint","OnePoint.instTopologicalSpace","Option","Prod","Prod.snd","T2Space","TopologicalSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","instTopologicalSpaceProd"],"value_dag_size":386,"value_refs":["And.intro","CompactSpace","Compl.compl","Continuous","Continuous.comp","DiscreteTopology","Eq","Eq.mp","Eq.mpr","Eq.trans","False","False.elim","Function.comp","Inter.inter","IsClosed","IsClosed.mk","IsCompact","IsCompact.isClosed","IsOpen","IsOpen.inter","IsOpen.preimage","Membership.mem","OnePoint","OnePoint.infty","OnePoint.infty_ne_coe._simp_1","OnePoint.instTopologicalSpace","OnePoint.some","Option","Option.some","Prod","Prod.snd","Set","Set.iUnion","Set.instCompl","Set.instInter","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff._simp_1","Set.preimage","Set.range","Singleton.singleton","T2Space","TopologicalSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","congrArg","continuous_snd","id","instTopologicalSpaceProd","isCompact_range","isOpen_compl_iff._simp_1","isOpen_discrete._simp_1","isOpen_iUnion","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":109,"type_refs":["Compl.compl","Eq","Function.comp","Inter.inter","OnePoint","OnePoint.some","Option","Option.some","Prod","Prod.snd","Set","Set.iUnion","Set.instCompl","Set.instInter","Set.instSingletonSet","Set.preimage","Set.range","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":814,"value_refs":["And","And.intro","Bool","Bool.true","Compl.compl","Eq","Eq.mp","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","Function.comp","Iff","Iff.intro","Iff.mp","Inter.inter","Membership.mem","Ne","Not","OnePoint","OnePoint.some","Option","Option.isSome","Option.isSome_iff_ne_none","Option.ne_none_iff_exists'","Option.none","Option.some","Option.some_injective","Or","Prod","Prod.snd","Set","Set.ext","Set.iUnion","Set.instCompl","Set.instInter","Set.instMembership","Set.instSingletonSet","Set.preimage","Set.range","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_5","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_6","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_7","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_8","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion.match_1_11","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion.match_1_9","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congr","congrArg","congrFun'","forall_congr","funext","id","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_5","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_6","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_7","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion._simp_1_8","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion.match_1_11","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":"abbrev","statement_dag_size":165,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Not","OnePoint.some","Option","Option.some","Prod","Prod.snd"],"value_dag_size":243,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Not","OnePoint.some","Option","Option.some","Prod","Prod.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion.match_1_9","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_compl_eq_iUnion","reducibility":"abbrev","statement_dag_size":133,"type_refs":["And","And.intro","Eq","Not","Option","Option.none","Option.some","Prod","Prod.snd"],"value_dag_size":156,"value_refs":["And","And.casesOn","And.intro","Eq","Not","Option","Option.none","Option.some","Prod","Prod.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","Function.Surjective","Membership.mem","Option","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":416,"value_refs":["Eq","Eq.trans","Exists","Exists.casesOn","Exists.intro","Function.Surjective","Membership.mem","Option","Option.casesOn","Option.none","Option.some","Or","Prod","Prod.casesOn","Prod.ext","Prod.fst","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Subtype.mk","Subtype.val","True","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congrArg","exists_apply_eq_apply2._simp_1","of_eq_true","or_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Membership.mem","Option","Option.none","Prod","Prod.mk","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":215,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Option","Option.none","Option.some","Or","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective","reducibility":null,"statement_dag_size":178,"type_refs":["Eq","Eq.trans","Exists","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype.mk","Subtype.val","True","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congrArg","exists_apply_eq_apply2._simp_1","of_eq_true","or_true"],"value_dag_size":233,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Membership.mem","Not","Option","Option.none","Option.some","Or","Prod","Prod.fst","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congrArg","eq_false","eq_true","exists_apply_eq_apply2._simp_1","id","of_eq_true","or_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective._proof_1_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres_surjective","reducibility":null,"statement_dag_size":173,"type_refs":["Eq","Eq.trans","Exists","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype.mk","Subtype.val","True","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congrArg","exists_apply_eq_apply2._simp_1","of_eq_true","or_true"],"value_dag_size":226,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Membership.mem","Not","Option","Option.none","Option.some","Or","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","congrArg","eq_false","eq_true","exists_apply_eq_apply2._simp_1","id","of_eq_true","or_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":151,"type_refs":["Eq","Function.comp","Iff","Membership.mem","OnePoint","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'"],"value_dag_size":90,"value_refs":["Function.comp","Iff.rfl","Membership.mem","OnePoint","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff._simp_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff","reducibility":null,"statement_dag_size":153,"type_refs":["Eq","Function.comp","Membership.mem","OnePoint","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'"],"value_dag_size":158,"value_refs":["Eq","Function.comp","Membership.mem","OnePoint","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","Exists","Iff","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.snd","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":201,"value_refs":["Eq","Eq.trans","Exists","Iff","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.snd","Set","Set.iUnion","Set.instMembership","Set.instUnion","Set.mem_iUnion._simp_1","Set.mem_range._simp_1","Set.mem_union._simp_1","Set.ofPred","Set.range","True","Union.union","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","congrArg","congrFun'","funext","iff_self","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff._simp_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Exists","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.snd","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":83,"value_refs":["Eq","Exists","Membership.mem","Option","Option.none","Option.some","Or","Prod","Prod.snd","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","propext"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":81,"type_refs":["Eq","Function.comp","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":137,"value_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_2","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Membership.mem","Option","Option.none","Prod","Prod.snd","Set","Set.instMembership","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":201,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Option","Option.none","Option.some","Or","Prod","Prod.snd","Set","Set.instMembership","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_fibres_iff","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl","reducibility":null,"statement_dag_size":113,"type_refs":["Eq","Function.comp","Membership.mem","Option","Option.none","Prod","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":437,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.comp","Function.comp_apply","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Membership.mem","Not","Option","Option.none","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.mem_preimage","Set.mem_singleton_iff","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.sectionOfFibreIncl._proof_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","congrArg","eq_false","eq_true","id"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":57,"type_refs":["Function.comp","OnePoint","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'"],"value_dag_size":150,"value_refs":["Function.comp","Membership.mem","OnePoint","OnePoint.infty","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_apply","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":160,"type_refs":["Eq","Function.comp","Membership.mem","OnePoint","OnePoint.infty","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y"],"value_dag_size":66,"value_refs":["Function.comp","OnePoint","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_continuous","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":166,"type_refs":["Continuous","Function.comp","Membership.mem","OnePoint","OnePoint.instTopologicalSpace","Pi.topologicalSpace","Prod","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","TopologicalSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_continuous._auto_1","autoParam","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":323,"value_refs":["Continuous","Continuous.comp","Function.comp","Membership.mem","OnePoint","OnePoint.infty","OnePoint.instTopologicalSpace","Pi.topologicalSpace","Prod","Prod.fst","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.val","TopologicalSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","continuous_apply","continuous_fst","continuous_subtype_val","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_continuous._auto_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_continuous","reducibility":"opaque","statement_dag_size":1,"type_refs":["Lean.Syntax"],"value_dag_size":58,"value_refs":["Array.empty","Array.push","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo.none","Lean.Syntax","Lean.Syntax.node","Lean.mkAtom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":72,"type_refs":["Function.Surjective","Function.comp","OnePoint","Prod","Prod.snd","Set","Set.Elem","Set.instSingletonSet","Set.preimage","Singleton.singleton","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y"],"value_dag_size":222,"value_refs":["Eq","Exists.choose","Exists.choose_spec","Exists.intro","Function.Surjective","Function.comp","Membership.mem","OnePoint","Prod","Prod.mk","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_7"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Exists","Function.Surjective","OnePoint","Prod","Prod.mk"],"value_dag_size":34,"value_refs":["Function.Surjective","OnePoint","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_2","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":85,"type_refs":["Classical.choose","Eq","Exists","Function.Surjective","Lean.Grind.nestedProof","OnePoint","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1"],"value_dag_size":76,"value_refs":["Classical.choose","Eq","Exists","Function.Surjective","Lean.Grind.nestedProof","OnePoint","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Exists.choose","Function.Surjective","Function.comp","Membership.mem","OnePoint","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton"],"value_dag_size":367,"value_refs":["Classical.byContradiction","Classical.choose","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.choose","Exists.choose_spec","False","Function.Surjective","Function.comp","Function.comp_apply","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Membership.mem","Not","OnePoint","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.mem_preimage","Set.mem_singleton_iff","Set.preimage","Singleton.singleton","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":128,"type_refs":["Eq","Exists.choose","Function.Surjective","Function.comp","Membership.mem","OnePoint","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3"],"value_dag_size":709,"value_refs":["Classical.byContradiction","Classical.choose","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","Exists.choose_spec","False","Function.Surjective","Function.comp","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Membership.mem","Not","OnePoint","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.mem_S'_iff","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_5","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Function.Surjective","OnePoint","OnePoint.infty","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Function.Surjective","OnePoint","OnePoint.infty","Prod","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_6","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":83,"type_refs":["Classical.choose","Eq","Exists","Function.Surjective","Lean.Grind.nestedProof","OnePoint","OnePoint.infty","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_5"],"value_dag_size":74,"value_refs":["Classical.choose","Eq","Exists","Function.Surjective","Lean.Grind.nestedProof","OnePoint","OnePoint.infty","Prod","Prod.fst","Prod.mk","Prod.snd","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_7","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective","reducibility":null,"statement_dag_size":182,"type_refs":["Eq","Exists.choose","Function.Surjective","Function.comp","Membership.mem","OnePoint","Prod","Prod.mk","Prod.snd","Set","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_4"],"value_dag_size":609,"value_refs":["Classical.byContradiction","Classical.choose","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.choose","Exists.choose_spec","False","Function.Surjective","Function.comp","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","OnePoint","OnePoint.infty","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Set","Set.Elem","Set.instMembership","Set.instSingletonSet","Set.preimage","Singleton.singleton","Subtype","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.S'","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_apply","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_1","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_4","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.y_surjective._proof_1_5","congrArg","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":"regular","statement_dag_size":35,"type_refs":["Option","Prod","Set.Elem","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"],"value_dag_size":54,"value_refs":["Membership.mem","Option","Prod","Set","Set.Elem","Set.instMembership","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r_apply","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Membership.mem","Option","Prod","Set","Set.Elem","Set.instMembership","Subtype.val","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r"],"value_dag_size":45,"value_refs":["Option","Prod","Set.Elem","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.fibres","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.π_r","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_10","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":10,"type_refs":["Nat","OnePoint","OnePoint.instTopologicalSpace","T2Space","instTopologicalSpaceNat"],"value_dag_size":12,"value_refs":["LightProfinite.instMetrizableSpaceOnePointNat","Nat","OnePoint","OnePoint.instTopologicalSpace","TopologicalSpace.t2Space_of_metrizableSpace","instTopologicalSpaceNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_12","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":549,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.IsIso","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","CategoryTheory.ObjectProperty.FullSubcategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.inv","CategoryTheory.types","CommRing","CommRing.toRing","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.mk","Eq","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.toCondensed","ModuleCat","ModuleCat.moduleCategory","Nat","OnePoint","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Opposite","Quiver.Hom","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceNat","lightProfiniteToLightCondSet"],"value_dag_size":1867,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.assoc","CategoryTheory.Category.id_comp","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.comp.hcongr_7","CategoryTheory.CategoryStruct.id","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.comp_map","CategoryTheory.Functor.comp_obj","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp","CategoryTheory.Functor.obj","CategoryTheory.IsIso","CategoryTheory.IsIso.inv_hom_id","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.MonoidalCategoryStruct.whiskerRight","CategoryTheory.ObjectProperty.FullSubcategory","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CategoryTheory.inv","CategoryTheory.types","Classical.byContradiction","CommRing","CommRing.toRing","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","CompHausLike.mk","CompactSpace","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.trans","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","LightCondMod","LightCondSet","LightCondensed._proof_1","LightCondensed.free","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instMetrizableSpaceOnePointNat","LightProfinite.instPreregular","LightProfinite.toCondensed","ModuleCat","ModuleCat.moduleCategory","Nat","Not","OnePoint","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Opposite","Quiver.Hom","SecondCountableTopology","T2Space","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","True","True.intro","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instTopologicalSpaceNat","lightProfiniteToLightCondSet"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":23,"type_refs":["And","Nat","OnePoint","OnePoint.instTopologicalSpace","SecondCountableTopology","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceNat"],"value_dag_size":35,"value_refs":["And","CompHausLike.HasProp.hasProp","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","Nat","OnePoint","OnePoint.instTopologicalSpace","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","instTopologicalSpaceNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_4","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":269,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.mk","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":339,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.mk","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_5","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":156,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","CompactSpace","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Quiver.Hom","SecondCountableTopology","Sum","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_4","instTopologicalSpaceNat","instTopologicalSpaceSum"],"value_dag_size":370,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_compact","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instCompactSpaceSum","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_6","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":156,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Quiver.Hom","SecondCountableTopology","Sum","T2Space","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_4","instTopologicalSpaceNat","instTopologicalSpaceSum"],"value_dag_size":370,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.is_hausdorff","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instT2SpaceSum","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_7","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":163,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.category","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.instCartesianMonoidalCategory","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Quiver.Hom","SecondCountableTopology","Sum","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_4","instTopologicalSpaceNat","instTopologicalSpaceSum"],"value_dag_size":392,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.snd","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.mk","CompHausLike.pullback","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint","OnePoint.infty","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.totallyDisconnectedSpace","Sum","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TopologicalSpace.instSecondCountableTopologySum","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibre","_private.Mathlib.Condensed.Light.Sequence.0.InternalProjectivityProof.LightProfinite.fibreIncl","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype","instTopologicalSpaceSum","instTotallyDisconnectedSpaceSum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_8","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":207,"type_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.mk","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.instCartesianMonoidalCategory","Membership.mem","Nat","OnePoint","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_3","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"],"value_dag_size":270,"value_refs":["And","CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct","CategoryTheory.MonoidalCategoryStruct.tensorObj","CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory","CompHausLike","CompHausLike.HasProp.hasProp","CompHausLike.category","CompHausLike.concreteCategory","CompHausLike.mk","CompHausLike.toTop","ContinuousMap","ContinuousMap.instFunLike","DFunLike.coe","Eq","LightProfinite","LightProfinite.NatUnionInfty","LightProfinite.NatUnionInfty._proof_1","LightProfinite.NatUnionInfty._proof_2","LightProfinite.NatUnionInfty._proof_3","LightProfinite.instCartesianMonoidalCategory","LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instSecondCountableTopologyCarrierToTopAndTotallyDisconnectedSpace","LightProfinite.instTotallyDisconnectedSpaceCarrierToTopAndSecondCountableTopology","Membership.mem","Nat","OnePoint","OnePoint.instCompactSpace","OnePoint.instTopologicalSpace","Prod","Prod.fst","Prod.snd","Prod.totallyDisconnectedSpace","Quiver.Hom","SecondCountableTopology","Set","Set.instMembership","Set.ofPred","Subtype","Subtype.totallyDisconnectedSpace","TopCat","TopCat.carrier","TopCat.of","TopCat.str","TopologicalSpace.Subtype.secondCountableTopology","TopologicalSpace.instSecondCountableTopologyProd","TotallyDisconnectedSpace","instTopologicalSpaceNat","instTopologicalSpaceProd","instTopologicalSpaceSubtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_9","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":23,"type_refs":["And","CategoryTheory.Precoherent","CompHausLike","CompHausLike.category","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":40,"value_refs":["And","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHausLike","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrierSecondCountableTopology","LightProfinite.instPreregular","SecondCountableTopology","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.Sequence","name":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._simp_1_1","namespace":"_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty","reducibility":null,"statement_dag_size":119,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.comp","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq","Quiver.Hom"],"value_dag_size":132,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.comp","CategoryTheory.Functor.comp_map","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","Eq.symm","Quiver.Hom"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet","reducibility":"regular","statement_dag_size":138,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","Countable.LindelofSpace","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","LightCondSet","LightCondensed._proof_1","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","SecondCountableTopology","Sigma","Sigma.fst","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.of_discrete","TotallySeparatedSpace.totallyDisconnectedSpace","instCompactSpace","instCountablePUnit","instDiscreteTopologyPUnit","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"],"value_dag_size":213,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","DFunLike.coe","LightCondSet","LightCondensed._proof_1","LightProfinite","LightProfinite.of","Opposite","Opposite.op","PUnit","Quiver.Hom.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_1","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_2","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_3","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1","instCompactSpace","instConcreteCategoryTypeFun","instIndiscreteTopologyPUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","reducibility":null,"statement_dag_size":5,"type_refs":["PUnit","T2Space","instTopologicalSpacePUnit"],"value_dag_size":13,"value_refs":["EMetricSpace.metrizableSpace","MetricSpace.toEMetricSpace","PUnit","TopologicalSpace.t2Space_of_metrizableSpace","instMetricSpacePUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_2","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","reducibility":null,"statement_dag_size":5,"type_refs":["PUnit","TotallyDisconnectedSpace","instTopologicalSpacePUnit"],"value_dag_size":11,"value_refs":["PUnit","TotallySeparatedSpace.of_discrete","TotallySeparatedSpace.totallyDisconnectedSpace","instDiscreteTopologyPUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_3","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","reducibility":null,"statement_dag_size":5,"type_refs":["PUnit","SecondCountableTopology","instTopologicalSpacePUnit"],"value_dag_size":22,"value_refs":["Countable.LindelofSpace","EMetricSpace.toPseudoEMetricSpace","MetricSpace.toEMetricSpace","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","instCountablePUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.eq_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","reducibility":null,"statement_dag_size":241,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Countable.LindelofSpace","DFunLike.coe","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq","LightCondSet","LightCondensed._proof_1","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","Quiver.Hom.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.of_discrete","TotallySeparatedSpace.totallyDisconnectedSpace","TypeCat.Fun","TypeCat.instFunLikeFun","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_1","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_2","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod._proof_3","instCompactSpace","instConcreteCategoryTypeFun","instCountablePUnit","instDiscreteTopologyPUnit","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"],"value_dag_size":170,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","Countable.LindelofSpace","EMetricSpace.metrizableSpace","EMetricSpace.toPseudoEMetricSpace","Eq.refl","LightCondSet","LightCondensed._proof_1","LightProfinite","LightProfinite.of","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","PseudoEMetricSpace.pseudoMetrizableSpace","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPseudoMetrizableSpace","TopologicalSpace.t2Space_of_metrizableSpace","TotallyDisconnectedSpace","TotallySeparatedSpace.of_discrete","TotallySeparatedSpace.totallyDisconnectedSpace","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","instCompactSpace","instCountablePUnit","instDiscreteTopologyPUnit","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod","reducibility":"abbrev","statement_dag_size":146,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":209,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.casesOn","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1.eq_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1","reducibility":null,"statement_dag_size":180,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","Eq","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1"],"value_dag_size":176,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","Eq.refl","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace","_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1.splitter","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1","reducibility":"abbrev","statement_dag_size":146,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","CompHausLike.toTop","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":1,"value_refs":["_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction._proof_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction","reducibility":null,"statement_dag_size":102,"type_refs":["And","CategoryTheory.Adjunction.counit","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.id","CategoryTheory.Functor.obj","CategoryTheory.IsIso","CategoryTheory.NatTrans.app","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondSet.lightCondSetToSequential","LightCondSet.sequentialAdjunction","LightCondSet.sequentialToLightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","Sequential","Sequential.instCategory","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":79,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.Iso.isIso_hom","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondSet.lightCondSetToSequential","LightCondSet.sequentialAdjunctionCounitIso","LightCondSet.sequentialToLightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","Sequential","Sequential.instCategory","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat._proof_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.instSequentialSpaceCarrierObjTopCatLightCondSetToTopCat","reducibility":null,"statement_dag_size":67,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","SecondCountableTopology","SequentialSpace","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.str","TotallyDisconnectedSpace","lightCondSetToTopCat"],"value_dag_size":5,"value_refs":["LightCondSet","LightCondSet.instSequentialSpaceCarrierToTopCat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.toTopCatMap.match_1","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.toTopCatMap","reducibility":"abbrev","statement_dag_size":98,"type_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"],"value_dag_size":115,"value_refs":["And","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHausLike.category","LightCondSet","LightCondensed._proof_1","LightProfinite","Opposite","Opposite.op","SecondCountableTopology","Sigma","Sigma.casesOn","Sigma.mk","TopCat","TopCat.carrier","TopCat.str","TotallyDisconnectedSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Light.TopCatAdjunction","name":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.topCatAdjunctionUnit._simp_2","namespace":"_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.topCatAdjunctionUnit","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasColimitsCondensedMod._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasColimitsCondensedMod","reducibility":null,"statement_dag_size":55,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.HasColimits","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedMod","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","TopCat","True"],"value_dag_size":572,"value_refs":["AddCommGroup.toAddCommMonoid","AddCommGrpCat.hasColimitsOfShape","AddCommGrpCat.hasColimitsOfSize","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.comp","CategoryTheory.Functor.instPreservesLimitsOfShapeOfIsRightAdjoint","CategoryTheory.Functor.obj","CategoryTheory.Functor.sections","CategoryTheory.GrothendieckTopology.Cover","CategoryTheory.GrothendieckTopology.Cover.index","CategoryTheory.GrothendieckTopology.Cover.instInhabited","CategoryTheory.GrothendieckTopology.Cover.instSemilatticeInf","CategoryTheory.GrothendieckTopology.Cover.shape","CategoryTheory.GrothendieckTopology.instPreorderCover","CategoryTheory.Limits.MulticospanIndex.multicospan","CategoryTheory.Limits.PreservesFilteredColimitsOfSize.preserves_filtered_colimits","CategoryTheory.Limits.WalkingMulticospan","CategoryTheory.Limits.WalkingMulticospan.instSmallCategory","CategoryTheory.Sheaf.instHasColimitsOfSize","CategoryTheory.coherentTopology","CategoryTheory.forget","CategoryTheory.isCofiltered_of_directed_ge_nonempty","CategoryTheory.isFiltered_op_of_isCofiltered","CategoryTheory.sheafToPresheaf_isRightAdjoint","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","LinearMap","LinearMap.instFunLike","Membership.mem","ModuleCat","ModuleCat.FilteredColimits.forget_preservesFilteredColimits","ModuleCat.carrier","ModuleCat.hasColimitsOfShape","ModuleCat.hasColimitsOfSize","ModuleCat.hasLimit","ModuleCat.instConcreteCategoryLinearMapIdCarrier","ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier","ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier","ModuleCat.isAddCommGroup","ModuleCat.isModule","ModuleCat.moduleCategory","Opposite","Opposite.small","Preorder.smallCategory","Ring","Ring.toSemiring","RingHom.id","SemilatticeInf.instIsCodirectedOrder","Semiring.toNonAssocSemiring","Set","Set.instMembership","TopCat","True","UnivLE.self","UnivLE.small","instNonemptyOfInhabited","small_Pi","small_subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasColimitsOfShapeCondensedOfHasWeakSheafifyCompHausCoherentTopology._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasColimitsOfShapeCondensedOfHasWeakSheafifyCompHausCoherentTopology","reducibility":null,"statement_dag_size":94,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.HasWeakSheafify","CategoryTheory.Limits.HasColimitsOfShape","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed","Condensed._proof_1","Opposite","TopCat","True"],"value_dag_size":71,"value_refs":["CategoryTheory.Category","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.HasWeakSheafify","CategoryTheory.Limits.HasColimitsOfShape","CategoryTheory.Sheaf.instHasColimitsOfShape","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed._proof_1","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasFiniteColimitsCondensedOfHasWeakSheafifyCompHausCoherentTopology._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasFiniteColimitsCondensedOfHasWeakSheafifyCompHausCoherentTopology","reducibility":null,"statement_dag_size":83,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.HasWeakSheafify","CategoryTheory.Limits.HasFiniteColimits","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed","Condensed._proof_1","Opposite","TopCat","True"],"value_dag_size":60,"value_refs":["CategoryTheory.Category","CategoryTheory.FinitaryExtensive.toFinitaryPreExtensive","CategoryTheory.HasWeakSheafify","CategoryTheory.Limits.HasFiniteColimits","CategoryTheory.Sheaf.instHasFiniteColimits","CategoryTheory.coherentTopology","CategoryTheory.instPrecoherentOfFinitaryPreExtensiveOfPreregular","CompHaus","CompHaus.instHasExplicitFiniteCoproductsTrue","CompHaus.instHasExplicitPullbacksTrue","CompHaus.instPreregular","CompHausLike.category","CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions","CompHausLike.instHasExplicitPullbacksOfInclusionsOfHasExplicitPullbacks","Condensed._proof_1","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasFiniteLimitsCondensed._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasFiniteLimitsCondensed","reducibility":null,"statement_dag_size":54,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.HasFiniteLimits","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Opposite","TopCat","True"],"value_dag_size":30,"value_refs":["CategoryTheory.Category","CategoryTheory.Limits.HasFiniteLimits","CategoryTheory.Sheaf.instHasFiniteLimits","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed._proof_1","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasLimitsCondensedMod._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasLimitsCondensedMod","reducibility":null,"statement_dag_size":55,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.HasLimits","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedMod","ModuleCat","ModuleCat.moduleCategory","Opposite","Ring","TopCat","True"],"value_dag_size":34,"value_refs":["CategoryTheory.Sheaf.hasLimitsOfSize","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed._proof_1","ModuleCat","ModuleCat.hasLimits'","ModuleCat.moduleCategory","Ring","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.Limits","name":"_private.Mathlib.Condensed.Limits.0.instHasLimitsOfShapeCondensed._proof_1","namespace":"_private.Mathlib.Condensed.Limits.0.instHasLimitsOfShapeCondensed","reducibility":null,"statement_dag_size":65,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Limits.HasLimitsOfShape","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed","Condensed._proof_1","Opposite","TopCat","True"],"value_dag_size":41,"value_refs":["CategoryTheory.Category","CategoryTheory.Limits.HasLimitsOfShape","CategoryTheory.Sheaf.instHasLimitsOfShape","CategoryTheory.coherentTopology","CompHaus","CompHausLike.category","Condensed._proof_1","TopCat","True"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet","reducibility":"regular","statement_dag_size":101,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHaus.of","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","EMetricSpace.metrizableSpace","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Sigma","Sigma.fst","TopCat","TopCat.carrier","TopologicalSpace.t2Space_of_metrizableSpace","True","instCompactSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"],"value_dag_size":199,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHaus.of","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed._proof_1","CondensedSet","DFunLike.coe","Opposite","Opposite.op","PUnit","Quiver.Hom.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True","TypeCat.Fun","TypeCat.instFunLikeFun","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod._proof_1","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1","instCompactSpace","instConcreteCategoryTypeFun","instIndiscreteTopologyPUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod._proof_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","reducibility":null,"statement_dag_size":5,"type_refs":["PUnit","T2Space","instTopologicalSpacePUnit"],"value_dag_size":13,"value_refs":["EMetricSpace.metrizableSpace","MetricSpace.toEMetricSpace","PUnit","TopologicalSpace.t2Space_of_metrizableSpace","instMetricSpacePUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.eq_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","reducibility":null,"statement_dag_size":200,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHaus.of","CompHausLike","CompHausLike.category","CompHausLike.const","CompHausLike.toTop","Condensed._proof_1","CondensedSet","DFunLike.coe","EMetricSpace.metrizableSpace","Eq","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Quiver.Hom.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopologicalSpace.t2Space_of_metrizableSpace","True","TypeCat.Fun","TypeCat.instFunLikeFun","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod._proof_1","instCompactSpace","instConcreteCategoryTypeFun","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"],"value_dag_size":133,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHaus.of","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","EMetricSpace.metrizableSpace","Eq.refl","MetricSpace.toEMetricSpace","Opposite","Opposite.op","PUnit","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","TopologicalSpace.t2Space_of_metrizableSpace","True","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","instCompactSpace","instIndiscreteTopologyPUnit","instMetricSpacePUnit","instTopologicalSpacePUnit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod","reducibility":"abbrev","statement_dag_size":137,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","Opposite","Opposite.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True"],"value_dag_size":200,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","Opposite","Opposite.op","Sigma","Sigma.casesOn","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1.eq_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1","reducibility":null,"statement_dag_size":171,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","Eq","Opposite","Opposite.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1"],"value_dag_size":167,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","Eq.refl","Opposite","Opposite.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True","_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1.splitter","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1","reducibility":"abbrev","statement_dag_size":137,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompHausLike.toTop","Condensed._proof_1","CondensedSet","Opposite","Opposite.op","Sigma","Sigma.fst","Sigma.mk","TopCat","TopCat.carrier","True"],"value_dag_size":1,"value_refs":["_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.coinducingCoprod.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction._proof_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction","reducibility":null,"statement_dag_size":90,"type_refs":["CategoryTheory.Adjunction.counit","CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.comp","CategoryTheory.Functor.id","CategoryTheory.Functor.obj","CategoryTheory.IsIso","CategoryTheory.NatTrans.app","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompactlyGenerated","CompactlyGenerated.instCategory","Condensed._proof_1","CondensedSet","CondensedSet.compactlyGeneratedAdjunction","CondensedSet.compactlyGeneratedToCondensedSet","CondensedSet.condensedSetToCompactlyGenerated","Opposite","TopCat","True"],"value_dag_size":66,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.Iso.isIso_hom","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","CompactlyGenerated","CompactlyGenerated.instCategory","Condensed._proof_1","CondensedSet","CondensedSet.compactlyGeneratedAdjunctionCounitIso","CondensedSet.compactlyGeneratedToCondensedSet","CondensedSet.condensedSetToCompactlyGenerated","Opposite","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat._proof_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.instUCompactlyGeneratedSpaceCarrierObjTopCatCondensedSetToTopCat","reducibility":null,"statement_dag_size":58,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.category","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","TopCat","TopCat.carrier","TopCat.instCategory","TopCat.str","True","UCompactlyGeneratedSpace","condensedSetToTopCat"],"value_dag_size":5,"value_refs":["CondensedSet","CondensedSet.instUCompactlyGeneratedSpaceCarrierToTopCat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.toTopCatMap.match_1","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.toTopCatMap","reducibility":"abbrev","statement_dag_size":86,"type_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","Opposite.op","Sigma","Sigma.mk","TopCat","True"],"value_dag_size":103,"value_refs":["CategoryTheory.Category.opposite","CategoryTheory.Functor","CategoryTheory.Functor.category","CategoryTheory.Functor.obj","CategoryTheory.ObjectProperty.FullSubcategory.obj","CategoryTheory.Presheaf.IsSheaf","CategoryTheory.coherentTopology","CategoryTheory.types","CompHaus","CompHausLike.category","Condensed._proof_1","CondensedSet","Opposite","Opposite.op","Sigma","Sigma.casesOn","Sigma.mk","TopCat","True"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopCatAdjunction","name":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.topCatAdjunctionUnit._simp_2","namespace":"_private.Mathlib.Condensed.TopCatAdjunction.0.CondensedSet.topCatAdjunctionUnit","reducibility":null,"statement_dag_size":185,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","DFunLike.coe","Eq","FunLike","Quiver.Hom"],"value_dag_size":202,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.map_comp_apply","CategoryTheory.Functor.obj","DFunLike.coe","Eq.symm","FunLike","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Condensed.TopComparison","name":"_private.Mathlib.Condensed.TopComparison.0.equalizerCondition_yonedaPresheaf.match_1_1","namespace":"_private.Mathlib.Condensed.TopComparison.0.equalizerCondition_yonedaPresheaf","reducibility":"abbrev","statement_dag_size":559,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.fst","CategoryTheory.Limits.pullback.snd","CategoryTheory.types","ContinuousMap.yonedaPresheaf","DFunLike.coe","Eq","Membership.mem","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.mk","TopCat","TopCat.instCategory","TopologicalSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instConcreteCategoryTypeFun"],"value_dag_size":639,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.opposite","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.ConcreteCategory.hom","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.fst","CategoryTheory.Limits.pullback.snd","CategoryTheory.types","ContinuousMap.yonedaPresheaf","DFunLike.coe","Eq","Membership.mem","Opposite","Opposite.op","Quiver.Hom","Quiver.Hom.op","Set","Set.Elem","Set.instMembership","Set.ofPred","Subtype.casesOn","Subtype.mk","TopCat","TopCat.instCategory","TopologicalSpace","TypeCat.Fun","TypeCat.instFunLikeFun","instConcreteCategoryTypeFun"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopComparison","name":"_private.Mathlib.Condensed.TopComparison.0.factorsThrough_of_pullbackCondition._simp_1_1","namespace":"_private.Mathlib.Condensed.TopComparison.0.factorsThrough_of_pullbackCondition","reducibility":null,"statement_dag_size":216,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.inv","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.PreservesLimit","CategoryTheory.Limits.PreservesPullback.iso","CategoryTheory.Limits.WalkingCospan","CategoryTheory.Limits.WalkingPair","CategoryTheory.Limits.WidePullbackShape.category","CategoryTheory.Limits.cospan","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.fst","Eq","Quiver.Hom"],"value_dag_size":231,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.inv","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.PreservesLimit","CategoryTheory.Limits.PreservesPullback.iso","CategoryTheory.Limits.PreservesPullback.iso_inv_fst","CategoryTheory.Limits.WalkingCospan","CategoryTheory.Limits.WalkingPair","CategoryTheory.Limits.WidePullbackShape.category","CategoryTheory.Limits.cospan","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.fst","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Condensed.TopComparison","name":"_private.Mathlib.Condensed.TopComparison.0.factorsThrough_of_pullbackCondition._simp_1_2","namespace":"_private.Mathlib.Condensed.TopComparison.0.factorsThrough_of_pullbackCondition","reducibility":null,"statement_dag_size":216,"type_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.inv","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.PreservesLimit","CategoryTheory.Limits.PreservesPullback.iso","CategoryTheory.Limits.WalkingCospan","CategoryTheory.Limits.WalkingPair","CategoryTheory.Limits.WidePullbackShape.category","CategoryTheory.Limits.cospan","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.snd","Eq","Quiver.Hom"],"value_dag_size":231,"value_refs":["CategoryTheory.Category","CategoryTheory.Category.toCategoryStruct","CategoryTheory.CategoryStruct.comp","CategoryTheory.CategoryStruct.toQuiver","CategoryTheory.Functor","CategoryTheory.Functor.map","CategoryTheory.Functor.obj","CategoryTheory.Iso.inv","CategoryTheory.Limits.HasPullback","CategoryTheory.Limits.PreservesLimit","CategoryTheory.Limits.PreservesPullback.iso","CategoryTheory.Limits.PreservesPullback.iso_inv_snd","CategoryTheory.Limits.WalkingCospan","CategoryTheory.Limits.WalkingPair","CategoryTheory.Limits.WidePullbackShape.category","CategoryTheory.Limits.cospan","CategoryTheory.Limits.pullback","CategoryTheory.Limits.pullback.snd","Eq.symm","Quiver.Hom"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Applicative","name":"_private.Mathlib.Control.Applicative.0.Applicative.ext.match_1_1","namespace":"_private.Mathlib.Control.Applicative.0.Applicative.ext","reducibility":"abbrev","statement_dag_size":346,"type_refs":["Applicative","Applicative.mk","Applicative.toPure","Applicative.toSeq","Eq","Functor","LawfulApplicative","Pure.mk","Pure.pure","Seq.mk","Seq.seq","SeqLeft.mk","SeqRight.mk","Unit"],"value_dag_size":1832,"value_refs":["Applicative","Applicative.casesOn","Applicative.mk","Applicative.toPure","Applicative.toSeq","Eq","Functor","LawfulApplicative","Pure","Pure.casesOn","Pure.mk","Pure.pure","Seq","Seq.casesOn","Seq.mk","Seq.seq","SeqLeft","SeqLeft.casesOn","SeqLeft.mk","SeqRight","SeqRight.casesOn","SeqRight.mk","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.joinM_map_joinM._simp_1_2","namespace":"_private.Mathlib.Control.Basic.0.joinM_map_joinM","reducibility":null,"statement_dag_size":64,"type_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq","Functor.map","LawfulMonad","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"],"value_dag_size":74,"value_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq.symm","Functor.map","LawfulMonad","LawfulMonad.bind_pure_comp","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.joinM_map_map._simp_1_2","namespace":"_private.Mathlib.Control.Basic.0.joinM_map_map","reducibility":null,"statement_dag_size":64,"type_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq","Functor.map","LawfulMonad","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"],"value_dag_size":74,"value_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq.symm","Functor.map","LawfulMonad","LawfulMonad.bind_pure_comp","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.joinM_map_pure._simp_1_2","namespace":"_private.Mathlib.Control.Basic.0.joinM_map_pure","reducibility":null,"statement_dag_size":64,"type_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq","Functor.map","LawfulMonad","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"],"value_dag_size":74,"value_refs":["Applicative.toFunctor","Applicative.toPure","Bind.bind","Eq.symm","Functor.map","LawfulMonad","LawfulMonad.bind_pure_comp","Monad","Monad.toApplicative","Monad.toBind","Pure.pure"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.map_seq._simp_1_1","namespace":"_private.Mathlib.Control.Basic.0.map_seq","reducibility":null,"statement_dag_size":59,"type_refs":["Applicative","Applicative.toFunctor","Applicative.toPure","Applicative.toSeq","Eq","Functor.map","LawfulApplicative","Pure.pure","Seq.seq","Unit"],"value_dag_size":69,"value_refs":["Applicative","Applicative.toFunctor","Applicative.toPure","Applicative.toSeq","Eq.symm","Functor.map","LawfulApplicative","LawfulApplicative.pure_seq","Pure.pure","Seq.seq","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.seq_map_assoc._simp_1_1","namespace":"_private.Mathlib.Control.Basic.0.seq_map_assoc","reducibility":null,"statement_dag_size":59,"type_refs":["Applicative","Applicative.toFunctor","Applicative.toPure","Applicative.toSeq","Eq","Functor.map","LawfulApplicative","Pure.pure","Seq.seq","Unit"],"value_dag_size":69,"value_refs":["Applicative","Applicative.toFunctor","Applicative.toPure","Applicative.toSeq","Eq.symm","Functor.map","LawfulApplicative","LawfulApplicative.pure_seq","Pure.pure","Seq.seq","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Basic","name":"_private.Mathlib.Control.Basic.0.seq_map_assoc._simp_1_2","namespace":"_private.Mathlib.Control.Basic.0.seq_map_assoc","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Function.comp","Functor","Functor.map","LawfulFunctor"],"value_dag_size":64,"value_refs":["Eq.symm","Function.comp","Functor","Functor.map","LawfulFunctor","LawfulFunctor.comp_map"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Bitraversable.Instances","name":"_private.Mathlib.Control.Bitraversable.Instances.0.Prod.bitraverse.match_1.eq_1","namespace":"_private.Mathlib.Control.Bitraversable.Instances.0.Prod.bitraverse.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Prod","Prod.bitraverse.match_1","Prod.mk"],"value_dag_size":42,"value_refs":["Eq.refl","Prod","Prod.bitraverse.match_1","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Bitraversable.Instances","name":"_private.Mathlib.Control.Bitraversable.Instances.0.Prod.bitraverse.match_1.splitter","namespace":"_private.Mathlib.Control.Bitraversable.Instances.0.Prod.bitraverse.match_1","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":1,"value_refs":["Prod.bitraverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Bitraversable.Instances","name":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1.eq_1","namespace":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Sum","Sum.bitraverse.match_1","Sum.inl","Sum.inr"],"value_dag_size":45,"value_refs":["Eq.refl","Sum","Sum.bitraverse.match_1","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Bitraversable.Instances","name":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1.eq_2","namespace":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Sum","Sum.bitraverse.match_1","Sum.inl","Sum.inr"],"value_dag_size":43,"value_refs":["Eq.refl","Sum","Sum.bitraverse.match_1","Sum.inl","Sum.inr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Bitraversable.Instances","name":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1.splitter","namespace":"_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Sum","Sum.inl","Sum.inr"],"value_dag_size":1,"value_refs":["Sum.bitraverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.EquivFunctor.Instances","name":"_private.Mathlib.Control.EquivFunctor.Instances.0.EquivFunctorUnique._simp_1","namespace":"_private.Mathlib.Control.EquivFunctor.Instances.0.EquivFunctorUnique","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Fix","name":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1.eq_1","namespace":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","Part.Fix.approx.match_1","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","Part.Fix.approx.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Fix","name":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1.eq_2","namespace":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","Part.Fix.approx.match_1","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","Part.Fix.approx.match_1","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Fix","name":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1.splitter","namespace":"_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Part.Fix.approx.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Fix","name":"_private.Mathlib.Control.Fix.0.Part.fix_def._proof_1_6","namespace":"_private.Mathlib.Control.Fix.0.Part.fix_def","reducibility":null,"statement_dag_size":154,"type_refs":["Classical.propDecidable","Eq","Exists","HAdd.hAdd","LT.lt","Nat","Nat.Upto","Nat.find","Not","OfNat.ofNat","Part","Part.Dom","Part.Fix.approx","Subtype.val","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":566,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.trans","Exists","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.Upto","Nat.find","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Part","Part.Dom","Part.Fix.approx","Subtype.val","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Fix","name":"_private.Mathlib.Control.Fix.0.Part.fix_def._simp_1_5","namespace":"_private.Mathlib.Control.Fix.0.Part.fix_def","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Fold","name":"_private.Mathlib.Control.Fold.0.Traversable.foldlm.ofFreeMonoid_comp_of._simp_1_3","namespace":"_private.Mathlib.Control.Fold.0.Traversable.foldlm.ofFreeMonoid_comp_of","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","MulOpposite","MulOpposite.op"],"value_dag_size":28,"value_refs":["Eq","MulOpposite","MulOpposite.op","MulOpposite.op_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.Comp.comp_map.match_1_1","namespace":"_private.Mathlib.Control.Functor.0.Functor.Comp.comp_map","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Functor.Comp"],"value_dag_size":30,"value_refs":["Functor.Comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.Comp.id_map.match_1_1","namespace":"_private.Mathlib.Control.Functor.0.Functor.Comp.id_map","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Functor.Comp"],"value_dag_size":30,"value_refs":["Functor.Comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.Comp.map.match_1.eq_1","namespace":"_private.Mathlib.Control.Functor.0.Functor.Comp.map.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Functor.Comp","Functor.Comp.map.match_1"],"value_dag_size":39,"value_refs":["Eq.refl","Functor.Comp","Functor.Comp.map.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.Comp.map.match_1.splitter","namespace":"_private.Mathlib.Control.Functor.0.Functor.Comp.map.match_1","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Functor.Comp"],"value_dag_size":1,"value_refs":["Functor.Comp.map.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.Comp.run_pure.match_1_1","namespace":"_private.Mathlib.Control.Functor.0.Functor.Comp.run_pure","reducibility":"abbrev","statement_dag_size":13,"type_refs":[],"value_dag_size":13,"value_refs":[]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor","name":"_private.Mathlib.Control.Functor.0.Functor.ext.match_1_1","namespace":"_private.Mathlib.Control.Functor.0.Functor.ext","reducibility":"abbrev","statement_dag_size":167,"type_refs":["Eq","Functor","Functor.map","Functor.mk","LawfulFunctor"],"value_dag_size":330,"value_refs":["Eq","Functor","Functor.casesOn","Functor.map","Functor.mk","LawfulFunctor"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor","reducibility":"regular","statement_dag_size":74,"type_refs":["Fin2","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","TypeVec","TypeVec.Arrow","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":217,"value_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.mk","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_1","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_2","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f.match_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor","reducibility":"regular","statement_dag_size":99,"type_refs":["Fin2","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.Arrow","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":322,"value_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.mk","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'._proof_1","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'._proof_2","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'.match_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'._proof_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'","reducibility":null,"statement_dag_size":135,"type_refs":["Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":308,"value_refs":["Eq","Eq.mpr","Eq.refl","Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.property","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.append1.match_1","TypeVec.ofRepeat","TypeVec.prod.mk","TypeVec.repeatEq","TypeVec.repeatEq_iff_eq","Unit","_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.eq_1","cast","congrArg","id","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'._proof_2","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'","reducibility":null,"statement_dag_size":123,"type_refs":["Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.val","TypeVec","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":117,"value_refs":["Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.property","TypeVec","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'.match_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f'","reducibility":"abbrev","statement_dag_size":214,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":555,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Fin2","Fin2.casesOn","Fin2.fs","Fin2.fz","HAdd.hAdd","HEq","HEq.refl","Nat","Nat.Internal.elimOffset","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","eq_of_heq","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f","reducibility":null,"statement_dag_size":94,"type_refs":["Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":112,"value_refs":["Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.property","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_7","cast","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_2","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f","reducibility":null,"statement_dag_size":82,"type_refs":["Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.val","TypeVec","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":80,"value_refs":["Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.property","TypeVec","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f._proof_7","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":300,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin2","Fin2.fs","HAdd.hAdd","HEq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Nat","Not","OfNat.ofNat","PUnit","Subtype","Subtype.property","Subtype.val","True","True.intro","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.PredLast.eq_1","TypeVec.append1","TypeVec.append1.match_1","TypeVec.append1.match_1.congr_eq_1","TypeVec.ofRepeat","Unit","congrFun","eq_true","heq_eq_eq","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f.match_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.f","reducibility":"abbrev","statement_dag_size":145,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","TypeVec","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":423,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Fin2","Fin2.casesOn","Fin2.fs","Fin2.fz","HAdd.hAdd","HEq","HEq.refl","Nat","Nat.Internal.elimOffset","OfNat.ofNat","Subtype","TypeVec","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","eq_of_heq","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor","reducibility":"regular","statement_dag_size":74,"type_refs":["Fin2","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","TypeVec","TypeVec.Arrow","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":212,"value_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.mk","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g._proof_1","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g._proof_2","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g.match_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor","reducibility":"regular","statement_dag_size":99,"type_refs":["Fin2","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.Arrow","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":310,"value_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.mk","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'._proof_1","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'._proof_2","_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'.match_1","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'._proof_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'","reducibility":null,"statement_dag_size":126,"type_refs":["Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.ofRepeat","TypeVec.prod.mk","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":362,"value_refs":["Eq","Eq.mpr","Eq.refl","Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.property","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.RelLast'","TypeVec.append1","TypeVec.append1.match_1","TypeVec.ofRepeat","TypeVec.prod.mk","TypeVec.repeatEq","TypeVec.repeatEq_iff_eq","Unit","_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.eq_1","cast","congrArg","congrFun'","id","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'._proof_2","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'","reducibility":null,"statement_dag_size":84,"type_refs":["Fin2.fz","Nat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.val","TypeVec","TypeVec.RelLast","TypeVec.append1"],"value_dag_size":80,"value_refs":["Fin2.fz","Nat","Prod","Prod.fst","Prod.snd","Subtype","Subtype.property","TypeVec","TypeVec.RelLast","TypeVec.append1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'.match_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g'","reducibility":"abbrev","statement_dag_size":184,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.RelLast","TypeVec.append1","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":495,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Fin2","Fin2.casesOn","Fin2.fs","Fin2.fz","HAdd.hAdd","HEq","HEq.refl","Nat","Nat.Internal.elimOffset","OfNat.ofNat","Prod","Prod.fst","Prod.snd","Subtype","TypeVec","TypeVec.RelLast","TypeVec.append1","eq_of_heq","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g._proof_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g","reducibility":null,"statement_dag_size":89,"type_refs":["Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.ofRepeat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":237,"value_refs":["Eq","Eq.mpr","Eq.refl","Fin2","Fin2.fs","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","Subtype.property","Subtype.val","True","TypeVec","TypeVec.PredLast","TypeVec.PredLast'","TypeVec.append1","TypeVec.append1.match_1","TypeVec.const","TypeVec.const_iff_true","TypeVec.ofRepeat","Unit","_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.eq_1","cast","congrArg","congrFun","congrFun'","id","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g._proof_2","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g","reducibility":null,"statement_dag_size":53,"type_refs":["Fin2.fz","Nat","Subtype","Subtype.val","TypeVec","TypeVec.PredLast","TypeVec.append1"],"value_dag_size":52,"value_refs":["Fin2.fz","Nat","Subtype","Subtype.property","TypeVec","TypeVec.PredLast","TypeVec.append1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g.match_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.MvFunctor.g","reducibility":"abbrev","statement_dag_size":130,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Subtype","TypeVec","TypeVec.PredLast","TypeVec.append1","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":394,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Fin2","Fin2.casesOn","Fin2.fs","Fin2.fz","HAdd.hAdd","HEq","HEq.refl","Nat","Nat.Internal.elimOffset","OfNat.ofNat","Subtype","TypeVec","TypeVec.PredLast","TypeVec.append1","eq_of_heq","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.eq_1","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","TypeVec.append1.match_1","Unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq.refl","Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","TypeVec.append1.match_1","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.eq_2","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","TypeVec.append1.match_1","Unit","Unit.unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":53,"value_refs":["Eq.refl","Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","TypeVec.append1.match_1","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Functor.Multivariate","name":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1.splitter","namespace":"_private.Mathlib.Control.Functor.Multivariate.0.TypeVec.append1.match_1","reducibility":"abbrev","statement_dag_size":50,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["TypeVec.append1.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.LawfulFix","name":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.le_f_of_mem_approx._simp_1_1","namespace":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.le_f_of_mem_approx","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.LawfulFix","name":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff._simp_1_1","namespace":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.LawfulFix","name":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff._simp_1_2","namespace":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","Membership.mem","Part","Part.instMembership","Part.none"],"value_dag_size":23,"value_refs":["Membership.mem","Part","Part.instMembership","Part.none","Part.notMem_none","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.LawfulFix","name":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff._simp_1_3","namespace":"_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Membership.mem","Part","Part.Dom","Part.instMembership"],"value_dag_size":31,"value_refs":["Exists","Membership.mem","Part","Part.Dom","Part.dom_iff_mem","Part.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Monad.Cont","name":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1.eq_1","namespace":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Except","Except.error","Except.ok","ExceptT.run_bind.match_1"],"value_dag_size":44,"value_refs":["Eq.refl","Except","Except.error","Except.ok","ExceptT.run_bind.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Monad.Cont","name":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1.eq_2","namespace":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Except","Except.error","Except.ok","ExceptT.run_bind.match_1"],"value_dag_size":42,"value_refs":["Eq.refl","Except","Except.error","Except.ok","ExceptT.run_bind.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Monad.Cont","name":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1.splitter","namespace":"_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Except","Except.error","Except.ok"],"value_dag_size":1,"value_refs":["ExceptT.run_bind.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Monad.Cont","name":"_private.Mathlib.Control.Monad.Cont.0.instLawfulMonadContOptionT.match_1","namespace":"_private.Mathlib.Control.Monad.Cont.0.instLawfulMonadContOptionT","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":39,"value_refs":["Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Basic","name":"_private.Mathlib.Control.Traversable.Basic.0.ApplicativeTransformation.ext._proof_1_1","namespace":"_private.Mathlib.Control.Traversable.Basic.0.ApplicativeTransformation.ext","reducibility":null,"statement_dag_size":75,"type_refs":["Applicative","ApplicativeTransformation","ApplicativeTransformation.app","Eq"],"value_dag_size":296,"value_refs":["Applicative","ApplicativeTransformation","ApplicativeTransformation.app","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.forall_imp_eq_or","Not","Or","True","True.intro","eq_false","eq_true","funext","id","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.List.mem_traverse.match_1_1","namespace":"_private.Mathlib.Control.Traversable.Instances.0.List.mem_traverse","reducibility":"abbrev","statement_dag_size":66,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":110,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1.eq_1","namespace":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.next?.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.next?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1.eq_2","namespace":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.next?.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.next?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1.splitter","namespace":"_private.Mathlib.Control.Traversable.Instances.0.List.next?.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.next?.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.List.traverse_append.match_1_1","namespace":"_private.Mathlib.Control.Traversable.Instances.0.List.traverse_append","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":54,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1.eq_1","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Option","Option.instDecidableEq.match_1","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":34,"value_refs":["Eq.refl","Option","Option.instDecidableEq.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1.eq_2","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Option","Option.instDecidableEq.match_1","Option.none","Option.some","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","Option","Option.instDecidableEq.match_1","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1.splitter","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Option.instDecidableEq.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Option.instDecidableEq.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1.eq_1","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Sum","Sum.inl","Sum.inr","Sum.traverse.match_1"],"value_dag_size":45,"value_refs":["Eq.refl","Sum","Sum.inl","Sum.inr","Sum.traverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1.eq_2","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Sum","Sum.inl","Sum.inr","Sum.traverse.match_1"],"value_dag_size":43,"value_refs":["Eq.refl","Sum","Sum.inl","Sum.inr","Sum.traverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.Traversable.Instances","name":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1.splitter","namespace":"_private.Mathlib.Control.Traversable.Instances.0.Sum.traverse.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Sum","Sum.inl","Sum.inr"],"value_dag_size":1,"value_refs":["Sum.traverse.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.ULift","name":"_private.Mathlib.Control.ULift.0.PLift.instLawfulApplicative_mathlib.match_1","namespace":"_private.Mathlib.Control.ULift.0.PLift.instLawfulApplicative_mathlib","reducibility":"abbrev","statement_dag_size":26,"type_refs":["PLift","PLift.up"],"value_dag_size":35,"value_refs":["PLift","PLift.casesOn","PLift.up"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.ULift","name":"_private.Mathlib.Control.ULift.0.PLift.instLawfulFunctor_mathlib.match_1","namespace":"_private.Mathlib.Control.ULift.0.PLift.instLawfulFunctor_mathlib","reducibility":"abbrev","statement_dag_size":20,"type_refs":["PLift","PLift.up"],"value_dag_size":29,"value_refs":["PLift","PLift.casesOn","PLift.up"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.ULift","name":"_private.Mathlib.Control.ULift.0.ULift.instLawfulApplicative_mathlib.match_1","namespace":"_private.Mathlib.Control.ULift.0.ULift.instLawfulApplicative_mathlib","reducibility":"abbrev","statement_dag_size":26,"type_refs":["ULift","ULift.up"],"value_dag_size":35,"value_refs":["ULift","ULift.casesOn","ULift.up"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Control.ULift","name":"_private.Mathlib.Control.ULift.0.ULift.instLawfulFunctor_mathlib.match_1","namespace":"_private.Mathlib.Control.ULift.0.ULift.instLawfulFunctor_mathlib","reducibility":"abbrev","statement_dag_size":20,"type_refs":["ULift","ULift.up"],"value_dag_size":29,"value_refs":["ULift","ULift.casesOn","ULift.up"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind._simp_3","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind._simp_4","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind._simp_7","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","Set","Set.iUnion","Set.instLE"],"value_dag_size":44,"value_refs":["LE.le","Set","Set.iUnion","Set.iUnion_subset_iff","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind._simp_8","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Exists","Sigma","Sigma.mk"],"value_dag_size":49,"value_refs":["Exists","Sigma","Sigma.exists","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind._simp_9","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":null,"statement_dag_size":78,"type_refs":["And","Eq","Exists","Filter","Filter.bind","Filter.instMembership","Membership.mem","Set","Set.instMembership"],"value_dag_size":83,"value_refs":["And","Exists","Filter","Filter.bind","Filter.instMembership","Filter.mem_bind","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind.match_10","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":"abbrev","statement_dag_size":449,"type_refs":["CFilter","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred"],"value_dag_size":623,"value_refs":["CFilter","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind.match_12","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":"abbrev","statement_dag_size":471,"type_refs":["CFilter","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Membership.mem","Set","Set.Elem","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Subtype.val"],"value_dag_size":514,"value_refs":["CFilter","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Membership.mem","Set","Set.Elem","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind.match_14","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.bind","reducibility":"abbrev","statement_dag_size":431,"type_refs":["And","And.intro","CFilter","CFilter.f","CFilter.toFilter._proof_1","CFilter.toFilter._proof_2","CFilter.toFilter._proof_3","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.instMembership","Filter.mk","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred"],"value_dag_size":729,"value_refs":["And","And.casesOn","And.intro","CFilter","CFilter.f","CFilter.toFilter._proof_1","CFilter.toFilter._proof_2","CFilter.toFilter._proof_3","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.instMembership","Filter.mk","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.comap.match_1","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.comap","reducibility":"abbrev","statement_dag_size":681,"type_refs":["CFilter","CFilter.f","CFilter.inf","CFilter.inf_le_left","CFilter.inf_le_right","CFilter.mk","CFilter.pt","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq.refl","Exists.intro","Filter","Filter.Realizer.F","Filter.Realizer.mk","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.preimage","Set.preimage_mono"],"value_dag_size":782,"value_refs":["CFilter","CFilter.f","CFilter.inf","CFilter.inf_le_left","CFilter.inf_le_right","CFilter.mk","CFilter.pt","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq.refl","Exists.casesOn","Exists.intro","Filter","Filter.Realizer.F","Filter.Realizer.mk","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.preimage","Set.preimage_mono"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.comap.match_3","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.comap","reducibility":"abbrev","statement_dag_size":232,"type_refs":["And","And.intro","CFilter","CFilter.f","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists.intro","Filter","Filter.comap","Filter.instMembership","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.preimage"],"value_dag_size":407,"value_refs":["And","And.casesOn","And.intro","CFilter","CFilter.f","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists.casesOn","Exists.intro","Filter","Filter.comap","Filter.instMembership","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership","Set.preimage"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.inf._simp_1","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.inf","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.le_iff.match_1_1","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.le_iff","reducibility":"abbrev","statement_dag_size":238,"type_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"],"value_dag_size":290,"value_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.le_iff.match_1_3","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.le_iff","reducibility":"abbrev","statement_dag_size":181,"type_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"],"value_dag_size":222,"value_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map._simp_2","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage"],"value_dag_size":53,"value_refs":["LE.le","Set","Set.image","Set.image_subset_iff","Set.instLE","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map._simp_3","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Filter","Filter.instMembership","Filter.sets","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Filter","Filter.instMembership","Filter.mem_sets","Filter.sets","Membership.mem","Set","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map._simp_4","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Filter","Filter.instMembership","Filter.map","Membership.mem","Set","Set.preimage"],"value_dag_size":59,"value_refs":["Filter","Filter.instMembership","Filter.map","Filter.mem_map","Membership.mem","Set","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff._simp_1_1","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff","reducibility":null,"statement_dag_size":27,"type_refs":["EmptyCollection.emptyCollection","Eq","Not","Set","Set.Nonempty","Set.instEmptyCollection"],"value_dag_size":29,"value_refs":["EmptyCollection.emptyCollection","Eq","Not","Set","Set.Nonempty","Set.instEmptyCollection","Set.not_nonempty_iff_eq_empty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff.match_1_2","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff","reducibility":"abbrev","statement_dag_size":183,"type_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","EmptyCollection.emptyCollection","Eq","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instEmptyCollection"],"value_dag_size":225,"value_refs":["CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","EmptyCollection.emptyCollection","Eq","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instEmptyCollection"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff.match_1_4","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff","reducibility":"abbrev","statement_dag_size":249,"type_refs":["Bot.bot","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.bot","Filter.Realizer.σ","Filter.instBot","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Unit.unit"],"value_dag_size":306,"value_refs":["Bot.bot","CFilter.f","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.bot","Filter.Realizer.σ","Filter.instBot","LE.le","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofEquiv.match_1","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofEquiv","reducibility":"abbrev","statement_dag_size":212,"type_refs":["CFilter.f","CFilter.ofEquiv","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Equiv","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership"],"value_dag_size":272,"value_refs":["CFilter.f","CFilter.ofEquiv","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Equiv","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofEquiv.match_3","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofEquiv","reducibility":"abbrev","statement_dag_size":156,"type_refs":["CFilter.f","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership"],"value_dag_size":207,"value_refs":["CFilter.f","CFilter.toFilter","CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Exists.casesOn","Exists.intro","Filter","Filter.Realizer","Filter.Realizer.F","Filter.Realizer.σ","Filter.sets","LE.le","Membership.mem","Set","Set.instCompleteAtomicBooleanAlgebra","Set.instLE","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Filter","name":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofFilter._simp_5","namespace":"_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ofFilter","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Exists","Filter","Filter.instMembership","LE.le","Membership.mem","Set","Set.instLE"],"value_dag_size":52,"value_refs":["And","Exists","Filter","Filter.exists_mem_subset_iff","Filter.instMembership","LE.le","Membership.mem","Set","Set.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.ext.match_1_1","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.ext","reducibility":"abbrev","statement_dag_size":148,"type_refs":["And","And.intro","Ctop","Ctop.f","Exists","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership"],"value_dag_size":218,"value_refs":["And","And.casesOn","And.intro","Ctop","Ctop.f","Exists","Exists.casesOn","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff._simp_1_1","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff._simp_1_2","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff._simp_1_3","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff._simp_1_4","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.Realizer.isClosed_iff","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.mem_nhds_toTopsp.match_1_1","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.mem_nhds_toTopsp","reducibility":"abbrev","statement_dag_size":207,"type_refs":["And","And.intro","Ctop","Ctop.f","Eq","Eq.refl","Exists","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range"],"value_dag_size":680,"value_refs":["And","And.casesOn","And.intro","Ctop","Ctop.f","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.mem_nhds_toTopsp.match_1_3","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.mem_nhds_toTopsp","reducibility":"abbrev","statement_dag_size":122,"type_refs":["And","Ctop","Ctop.f","Exists","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership"],"value_dag_size":154,"value_refs":["And","Ctop","Ctop.f","Exists","Exists.casesOn","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.toTopsp_isTopologicalBasis.match_1_1","namespace":"_private.Mathlib.Data.Analysis.Topology.0.Ctop.toTopsp_isTopologicalBasis","reducibility":"abbrev","statement_dag_size":84,"type_refs":["Ctop","Ctop.f","Eq","Exists.intro","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":114,"value_refs":["Ctop","Ctop.f","Eq","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.instMembership","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer.match_1_1","namespace":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer","reducibility":"abbrev","statement_dag_size":155,"type_refs":["And","And.intro","Filter","Filter.instMembership","Inter.inter","Membership.mem","Set","Set.Finite","Set.Nonempty","Set.instInter","Set.ofPred","TopologicalSpace","nhds"],"value_dag_size":179,"value_refs":["And","And.casesOn","And.intro","Filter","Filter.instMembership","Inter.inter","Membership.mem","Set","Set.Finite","Set.Nonempty","Set.instInter","Set.ofPred","TopologicalSpace","nhds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer.match_1_3","namespace":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer","reducibility":"abbrev","statement_dag_size":168,"type_refs":["And","Ctop.Realizer","Ctop.Realizer.F","Ctop.Realizer.σ","Ctop.f","Exists","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","TopologicalSpace"],"value_dag_size":205,"value_refs":["And","Ctop.Realizer","Ctop.Realizer.F","Ctop.Realizer.σ","Ctop.f","Exists","Exists.casesOn","Exists.intro","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","TopologicalSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer.match_1_5","namespace":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer","reducibility":"abbrev","statement_dag_size":170,"type_refs":["And","Exists","Exists.intro","Filter","Filter.instMembership","Inter.inter","Membership.mem","Set","Set.Finite","Set.Nonempty","Set.instInter","Set.ofPred","TopologicalSpace","nhds"],"value_dag_size":210,"value_refs":["And","Exists","Exists.casesOn","Exists.intro","Filter","Filter.instMembership","Inter.inter","Membership.mem","Set","Set.Finite","Set.Nonempty","Set.instInter","Set.ofPred","TopologicalSpace","nhds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Analysis.Topology","name":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer.match_1_7","namespace":"_private.Mathlib.Data.Analysis.Topology.0.locallyFinite_iff_exists_realizer","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Ctop.Realizer","LocallyFinite.Realizer","Nonempty","Nonempty.intro","Set","TopologicalSpace"],"value_dag_size":67,"value_refs":["Ctop.Realizer","LocallyFinite.Realizer","Nonempty","Nonempty.casesOn","Nonempty.intro","Set","TopologicalSpace"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.BitVec","name":"_private.Mathlib.Data.BitVec.0.BitVec.ofFin_intCast._proof_1_1","namespace":"_private.Mathlib.Data.BitVec.0.BitVec.ofFin_intCast","reducibility":null,"statement_dag_size":84,"type_refs":["False","HAdd.hAdd","HMod.hMod","HPow.hPow","Int","Int.instLEInt","Int.instMod","Int.instNatPow","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Not","OfNat.ofNat","instAddNat","instHAdd","instHMod","instHPow","instNatCastInt","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat"],"value_dag_size":362,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMod.hMod","HPow.hPow","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLt","Int.emod_nonneg","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instNatPow","Int.instNegInt","Int.instSub","Int.ne_of_gt","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.pos_pow_of_pos","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instAddNat","instDecidableEqBool","instHAdd","instHMod","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.BitVec","name":"_private.Mathlib.Data.BitVec.0.BitVec.toFin_injective.match_1_1","namespace":"_private.Mathlib.Data.BitVec.0.BitVec.toFin_injective","reducibility":"abbrev","statement_dag_size":103,"type_refs":["BitVec","BitVec.ofFin","BitVec.toFin","Eq","Eq.refl","Fin","Fin.mk","HPow.hPow","LT.lt","Nat","OfNat.ofNat","instHPow","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":503,"value_refs":["BitVec","BitVec.casesOn","BitVec.ofFin","BitVec.toFin","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Fin","Fin.casesOn","Fin.mk","Fin.mk.noConfusion","HEq","HEq.refl","HPow.hPow","LT.lt","Nat","OfNat.ofNat","eq_of_heq","instHPow","instLTNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.BitVec","name":"_private.Mathlib.Data.BitVec.0.BitVec.toNat_injective.match_1_1","namespace":"_private.Mathlib.Data.BitVec.0.BitVec.toNat_injective","reducibility":"abbrev","statement_dag_size":96,"type_refs":["BitVec","BitVec.ofFin","BitVec.toNat","Eq","Eq.refl","Fin.mk","HPow.hPow","LT.lt","Nat","OfNat.ofNat","instHPow","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":434,"value_refs":["BitVec","BitVec.casesOn","BitVec.ofFin","BitVec.toNat","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Fin","Fin.casesOn","Fin.mk","HEq","HEq.refl","HPow.hPow","LT.lt","Nat","OfNat.ofNat","eq_of_heq","instHPow","instLTNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.and_eq_false_eq_eq_false_or_eq_false._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.and_eq_false_eq_eq_false_or_eq_false","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.and","Bool.false","Eq","Or"],"value_dag_size":390,"value_refs":["And","And.casesOn","Bool","Bool.and","Bool.and_eq_true","Bool.ctorIdx","Bool.false","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.Bool.and_eq_of_eq_true_left","Lean.Grind.Bool.and_eq_of_eq_true_right","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_true","id","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.false","Bool.true","Eq"],"value_dag_size":212,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.ne_of_ne_of_eq_right","Not","eq_of_heq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply._proof_1_2","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.false","Bool.true","Eq"],"value_dag_size":230,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.ne_of_ne_of_eq_right","Not","eq_of_heq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply._proof_1_3","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.false","Bool.true","Eq"],"value_dag_size":230,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.ne_of_ne_of_eq_right","Not","eq_of_heq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply._proof_1_4","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.apply_apply_apply","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Bool.false","Bool.true","Eq"],"value_dag_size":212,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.ne_of_ne_of_eq_right","Not","eq_of_heq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.bool_iff_false._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.bool_iff_false","reducibility":null,"statement_dag_size":15,"type_refs":["Bool","Bool.false","Bool.true","Eq","Iff","Not"],"value_dag_size":84,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Not","True","congrArg","congrFun'","eq_self"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.coe_xor_iff._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.coe_xor_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Bool","Bool.true","Eq","Iff","Xor","bne","instBEqOfDecidableEq","instDecidableEqBool"],"value_dag_size":802,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.not","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.Bool.ne_of_eq_true_of_eq_false","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.bne_eq_decide_not_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Ne.symm","Not","Or","Or.casesOn","True","True.intro","Xor","bne","congr","congrArg","congrFun'","decide_not","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instDecidableNot","instLawfulBEqBool","noConfusion_of_Nat","not_decide_eq_true","of_eq_false","of_eq_true","xor_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.dichotomy._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.dichotomy","reducibility":null,"statement_dag_size":13,"type_refs":["Bool","Bool.false","Bool.true","Eq","Or"],"value_dag_size":108,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Not","Or","congr","congrArg","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.injective_iff._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.injective_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Bool","Bool.false","Bool.true","Eq","Ne"],"value_dag_size":203,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.ne_of_ne_of_eq_right","Ne","Not","True","True.intro","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.not_eq_false_eq_eq_true._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.not_eq_false_eq_eq_true","reducibility":null,"statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.not","Bool.true","Eq"],"value_dag_size":224,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.not","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.Bool.eq_false_of_not_eq_true","Lean.Grind.Bool.eq_true_of_not_eq_false","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.Bool.ne_of_eq_true_of_eq_false","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Not","Or","Or.casesOn","True","congr","congrArg","eq_true","id","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.not_eq_true_eq_eq_false._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.not_eq_true_eq_eq_false","reducibility":null,"statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.not","Bool.true","Eq"],"value_dag_size":224,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.not","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.Bool.eq_false_of_not_eq_true","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Not","Or","Or.casesOn","True","congr","congrArg","eq_true","id","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat._proof_1_2","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat","reducibility":null,"statement_dag_size":46,"type_refs":["Bool","Bool.instLE","Bool.not","Decidable.decide","Eq","LE.le","Nat","OfNat.ofNat","instDecidableEqNat","instOfNatNat"],"value_dag_size":183,"value_refs":["Bool","Bool.false","Bool.false_le","Bool.instLE","Bool.instLT","Bool.linearOrder","Bool.not","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","LE.le","Lean.Grind.Bool.not_eq_of_eq_true","Lean.Grind.Order.le_eq_false_of_lt","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.lt_le_trans","Lean.Grind.Order.lt_of_not_le","Lean.Grind.decide_eq_true","Lean.Grind.nestedDecidable","LinearOrder.toPartialOrder","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","eq_true","id","instDecidableEqNat","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat._proof_1_4","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat","reducibility":null,"statement_dag_size":50,"type_refs":["Bool","Bool.instLE","Bool.not","Decidable.decide","Eq","LE.le","Nat","Not","OfNat.ofNat","instDecidableEqNat","instOfNatNat"],"value_dag_size":203,"value_refs":["Bool","Bool.false","Bool.instLE","Bool.instLT","Bool.linearOrder","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.hcongr_2","Eq","Eq.symm","Eq.trans","False","LE.le","Lean.Grind.Bool.not_eq_of_eq_false","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.lt_of_not_le","Lean.Grind.Order.lt_unsat","Lean.Grind.decide_eq_false","Lean.Grind.nestedDecidable","Lean.Grind.nestedDecidable_congr","LinearOrder.toPartialOrder","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Std.IsLinearOrder.toIsLinearPreorder","eq_false","eq_of_heq","id","instDecidableEqNat","instIsLinearOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat._proof_1_5","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_le_ofNat","reducibility":null,"statement_dag_size":58,"type_refs":["Bool","Bool.instLE","Bool.not","Decidable.decide","Eq","LE.le","Nat","Not","OfNat.ofNat","instDecidableEqNat","instLENat","instOfNatNat"],"value_dag_size":249,"value_refs":["Bool","Bool.instLE","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instDecidableEqNat","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_toNat._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.ofNat_toNat","reducibility":null,"statement_dag_size":11,"type_refs":["Bool","Bool.ofNat","Bool.toNat","Eq"],"value_dag_size":210,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.ofNat","Bool.ofNat_add_one","Bool.ofNat_zero","Bool.toNat","Bool.toNat_false","Bool.toNat_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.ne_of_ne_of_eq_right","Nat","Not","OfNat.ofNat","congrArg","id","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.or_eq_false_eq_eq_false_and_eq_false._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.or_eq_false_eq_eq_false_and_eq_false","reducibility":null,"statement_dag_size":24,"type_refs":["And","Bool","Bool.false","Bool.or","Eq"],"value_dag_size":441,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.instCommutativeOr","Bool.not_eq_false","Bool.not_eq_true","Bool.or","Bool.or_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_aci","Lean.Grind.AC.diseq_unsat","Lean.Grind.Bool.eq_false_of_or_eq_false_right","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.Bool.or_eq_of_eq_false_right","Lean.Grind.eq_congr","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","congr","congrArg","eagerReduce","eq_true","id","instAssociativeBoolOr","instLawfulIdentityBoolOrFalse","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.or_inr._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.or_inr","reducibility":null,"statement_dag_size":17,"type_refs":["Bool","Bool.or","Bool.true","Eq"],"value_dag_size":64,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.not_eq_true","Bool.or","Bool.true","Classical.byContradiction","Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.Bool.eq_false_of_or_eq_false_right","Lean.Grind.intro_with_eq","Not","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Basic","name":"_private.Mathlib.Data.Bool.Basic.0.Bool.toNat_beq_zero._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Basic.0.Bool.toNat_beq_zero","reducibility":null,"statement_dag_size":28,"type_refs":["BEq.beq","Bool","Bool.not","Bool.toNat","Eq","Nat","OfNat.ofNat","instBEqOfDecidableEq","instDecidableEqNat","instOfNatNat"],"value_dag_size":460,"value_refs":["And","And.casesOn","BEq.beq","Bool","Bool.false","Bool.not","Bool.not_eq_false","Bool.not_eq_true","Bool.toNat","Bool.toNat_false","Bool.toNat_true","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Int","Int.instNegInt","Lean.Grind.Bool.eq_false_of_not_eq_true","Lean.Grind.Bool.eq_true_of_not_eq_false","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.beq_eq_decide_eq","Lean.Grind.bool_eq_to_prop","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","Nat","Nat.instLawfulBEq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqNat","instNatCastNat","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_cons._proof_1_3","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_cons","reducibility":null,"statement_dag_size":95,"type_refs":["Bool","Bool.not","Eq","HAdd.hAdd","HMod.hMod","List","List.IsChain","List.cons","List.count","List.length","Nat","Nat.instMod","Ne","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMod","instOfNatNat"],"value_dag_size":3026,"value_refs":["And","BEq.beq","Bool","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_neg","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_split_resolve","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.of_cons","List.cons","List.count","List.count_cons","List.count_not_add_count","List.isChain_cons_cons","List.length","List.length_cons","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instLawfulBEqBool","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_cons.match_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_cons","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Bool","List","List.IsChain","List.cons","List.nil","Ne"],"value_dag_size":88,"value_refs":["Bool","List","List.IsChain","List.casesOn","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_eq_count._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_eq_count","reducibility":null,"statement_dag_size":57,"type_refs":["Bool","Bool.not","Eq","Even","List","List.IsChain","List.cons","List.count","List.length","Nat","Ne","instAddNat","instBEqOfDecidableEq","instDecidableEqBool"],"value_dag_size":3075,"value_refs":["BEq.beq","Bool","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.count_not_cons","List.cons","List.count","List.count_cons","List.count_not_add_count","List.length","List.length_cons","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.even_iff","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instLawfulBEqBool","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_le_count_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_le_count_add_one","reducibility":null,"statement_dag_size":65,"type_refs":["Bool","Bool.not","HAdd.hAdd","LE.le","List","List.IsChain","List.cons","List.count","Nat","Ne","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLENat","instOfNatNat"],"value_dag_size":2766,"value_refs":["BEq.beq","Bool","Bool.false","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.count_not_cons","List.cons","List.count","List.count_cons","List.count_not_add_count","List.length","List.length_cons","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instMod","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instLENat","instLawfulBEqBool","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.length_sub_one_le_two_mul_count_bool._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.length_sub_one_le_two_mul_count_bool","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","HMul.hMul","HSub.hSub","LE.le","List","List.IsChain","List.count","List.length","Nat","Ne","OfNat.ofNat","instBEqOfDecidableEq","instDecidableEqBool","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":2675,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.two_mul_count_bool_eq_ite","List.count","List.head?","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.even_iff","Nat.instDecidablePredEven","Nat.instMod","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.instBEq","Option.instDecidableEq","Option.instLawfulBEq","Option.some","Or","Or.casesOn","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLawfulBEqBool","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.two_mul_count_bool_eq_ite._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.two_mul_count_bool_eq_ite","reducibility":null,"statement_dag_size":134,"type_refs":["BEq.beq","Bool","Bool.true","Eq","Even","HAdd.hAdd","HMul.hMul","HSub.hSub","List","List.IsChain","List.cons","List.count","List.head?","List.length","Nat","Nat.instDecidablePredEven","Ne","Not","OfNat.ofNat","Option","Option.instBEq","Option.some","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat","ite"],"value_dag_size":4348,"value_refs":["And","And.casesOn","BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.tail","List.IsChain.two_mul_count_bool_of_even","List.cons","List.count","List.count_cons","List.count_tail","List.head?","List.head?_cons","List.le_count_tail","List.length","List.length_cons","List.length_tail","List.tail","List.tail_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.even_add","Nat.even_iff","Nat.instDecidablePredEven","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.instBEq","Option.instDecidableEq","Option.instLawfulBEq","Option.some","Option.some.inj","Or","Or.casesOn","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLawfulBEqBool","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.two_mul_count_bool_le_length_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.IsChain.two_mul_count_bool_le_length_add_one","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","HAdd.hAdd","HMul.hMul","LE.le","List","List.IsChain","List.count","List.length","Nat","Ne","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":2705,"value_refs":["BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.two_mul_count_bool_eq_ite","List.count","List.count_le_length","List.head?","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.even_iff","Nat.instDecidablePredEven","Nat.instMod","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.instBEq","Option.instDecidableEq","Option.instLawfulBEq","Option.some","Or","Or.casesOn","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLawfulBEqBool","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Count","name":"_private.Mathlib.Data.Bool.Count.0.List.count_add_count_not._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Count.0.List.count_add_count_not","reducibility":null,"statement_dag_size":39,"type_refs":["Bool","Bool.not","Eq","HAdd.hAdd","List","List.count","List.length","Nat","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd"],"value_dag_size":160,"value_refs":["Bool","Bool.not","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","List.count_not_add_count","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Set","name":"_private.Mathlib.Data.Bool.Set.0.Bool.compl_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Set.0.Bool.compl_singleton","reducibility":null,"statement_dag_size":25,"type_refs":["Bool","Bool.not","Compl.compl","Eq","Set","Set.instCompl","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":452,"value_refs":["Bool","Bool.casesOn","Bool.ctorIdx","Bool.false","Bool.not","Bool.true","Classical.byContradiction","Compl.compl","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.Bool.ne_of_eq_true_of_eq_false","Lean.Grind.Bool.not_eq_of_eq_false","Lean.Grind.Bool.not_eq_of_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instCompl","Set.instMembership","Set.instSingletonSet","Set.mem_compl_iff","Set.mem_singleton_iff","Singleton.singleton","True","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","noConfusion_of_Nat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Set","name":"_private.Mathlib.Data.Bool.Set.0.Bool.range_eq._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Set.0.Bool.range_eq","reducibility":null,"statement_dag_size":36,"type_refs":["Bool","Bool.false","Bool.true","Eq","Insert.insert","Set","Set.instInsert","Set.instSingletonSet","Set.range","Singleton.singleton"],"value_dag_size":791,"value_refs":["And","And.casesOn","Bool","Bool.casesOn","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.ext","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_range","Set.mem_singleton_iff","Set.range","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bool.Set","name":"_private.Mathlib.Data.Bool.Set.0.Bool.univ_eq._proof_1_1","namespace":"_private.Mathlib.Data.Bool.Set.0.Bool.univ_eq","reducibility":null,"statement_dag_size":26,"type_refs":["Bool","Bool.false","Bool.true","Eq","Insert.insert","Set","Set.instInsert","Set.instSingletonSet","Set.univ","Singleton.singleton"],"value_dag_size":325,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Insert.insert","LE.le","Lean.Grind.Bool.eq_true_of_not_eq_false'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Set","Set.ext","Set.instInsert","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_univ","Set.singleton_subset_iff","Set.subset_insert","Set.univ","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_false","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Bundle","name":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.exists.match_1_1","namespace":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.exists","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Bundle.TotalSpace","Exists","Exists.intro"],"value_dag_size":76,"value_refs":["Bundle.TotalSpace","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Bundle","name":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.exists.match_1_3","namespace":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.exists","reducibility":"abbrev","statement_dag_size":99,"type_refs":["Bundle.TotalSpace","Bundle.TotalSpace.mk","Exists","Exists.intro"],"value_dag_size":156,"value_refs":["Bundle.TotalSpace","Bundle.TotalSpace.mk","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Bundle","name":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.ext.match_1","namespace":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.ext","reducibility":"abbrev","statement_dag_size":37,"type_refs":["Bundle.TotalSpace","Bundle.TotalSpace.mk"],"value_dag_size":52,"value_refs":["Bundle.TotalSpace","Bundle.TotalSpace.casesOn","Bundle.TotalSpace.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Bundle","name":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.mk_inj._simp_1_1","namespace":"_private.Mathlib.Data.Bundle.0.Bundle.TotalSpace.mk_inj","reducibility":null,"statement_dag_size":59,"type_refs":["And","Bundle.TotalSpace","Bundle.TotalSpace.proj","Bundle.TotalSpace.snd","Eq","HEq"],"value_dag_size":64,"value_refs":["And","Bundle.TotalSpace","Bundle.TotalSpace.ext_iff","Bundle.TotalSpace.proj","Bundle.TotalSpace.snd","Eq","HEq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_4","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'","reducibility":"abbrev","statement_dag_size":23,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.succ","Nat.hasNotBit"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_5","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'.match_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nat","Option","Option.some"],"value_dag_size":40,"value_refs":["Nat","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'.match_4","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'","reducibility":"abbrev","statement_dag_size":83,"type_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.Simp.SimpM","Lean.Meta.Simp.StepQ","OfNat.ofNat","Qq.Quoted"],"value_dag_size":209,"value_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.Simp.SimpM","Lean.Meta.Simp.StepQ","Nat.hasNotBit","OfNat.ofNat","Qq.Quoted","_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_4","_private.Mathlib.Data.Complex.Basic.0.Complex.I_pow_eq_pow_mod'._sparseCasesOn_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.conj_eq_iff_real.match_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.conj_eq_iff_real","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Complex","Complex.ofReal","Eq","Exists","Exists.intro","Real"],"value_dag_size":57,"value_refs":["Complex","Complex.ofReal","Eq","Exists","Exists.casesOn","Exists.intro","Real"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.eta.match_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.eta","reducibility":"abbrev","statement_dag_size":18,"type_refs":["Complex","Complex.mk","Real"],"value_dag_size":27,"value_refs":["Complex","Complex.casesOn","Complex.mk","Real"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.ext.match_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.ext","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Complex","Complex.im","Complex.mk","Complex.re","Eq","Eq.refl","Real"],"value_dag_size":386,"value_refs":["Complex","Complex.casesOn","Complex.im","Complex.mk","Complex.re","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Real","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.horizontalSegment_eq._simp_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.horizontalSegment_eq","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.horizontalSegment_eq._simp_1_2","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.horizontalSegment_eq","reducibility":null,"statement_dag_size":75,"type_refs":["And","Eq","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd"],"value_dag_size":80,"value_refs":["And","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd","Set.mem_prod","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_eq_empty","reducibility":null,"statement_dag_size":27,"type_refs":["EmptyCollection.emptyCollection","Eq","Not","Set","Set.Nonempty","Set.instEmptyCollection"],"value_dag_size":35,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Not","Set","Set.Nonempty","Set.instEmptyCollection","Set.not_nonempty_iff_eq_empty","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_eq_empty._simp_1_2","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_eq_empty","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_nonempty._simp_1_2","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.reProdIm_nonempty","reducibility":null,"statement_dag_size":26,"type_refs":["Complex","Complex.mk","Eq","Exists","Real"],"value_dag_size":28,"value_refs":["Complex","Complex.exists","Complex.mk","Exists","Real","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq._simp_1_1","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.preimage"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_preimage","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq._simp_1_2","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq","reducibility":null,"statement_dag_size":75,"type_refs":["And","Eq","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd"],"value_dag_size":80,"value_refs":["And","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","Set","Set.instMembership","Set.instSProd","Set.mem_prod","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq._simp_1_3","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Complex.Basic","name":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq._simp_1_4","namespace":"_private.Mathlib.Data.Complex.Basic.0.Complex.verticalSegment_eq","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Basic","name":"_private.Mathlib.Data.Countable.Basic.0.countable_iff_nonempty_embedding.match_1_1","namespace":"_private.Mathlib.Data.Countable.Basic.0.countable_iff_nonempty_embedding","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Countable","Countable.mk","Exists.intro","Function.Injective","Nat"],"value_dag_size":71,"value_refs":["Countable","Countable.casesOn","Countable.mk","Exists","Exists.casesOn","Exists.intro","Function.Injective","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Basic","name":"_private.Mathlib.Data.Countable.Basic.0.countable_iff_nonempty_embedding.match_1_3","namespace":"_private.Mathlib.Data.Countable.Basic.0.countable_iff_nonempty_embedding","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Function.Embedding","Nat","Nonempty","Nonempty.intro"],"value_dag_size":39,"value_refs":["Function.Embedding","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Defs","name":"_private.Mathlib.Data.Countable.Defs.0.Finite.to_countable.match_1","namespace":"_private.Mathlib.Data.Countable.Defs.0.Finite.to_countable","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Equiv","Exists","Exists.intro","Fin","Nat","Nonempty","Nonempty.intro"],"value_dag_size":86,"value_refs":["Equiv","Exists","Exists.casesOn","Exists.intro","Fin","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Defs","name":"_private.Mathlib.Data.Countable.Defs.0.Function.Injective.countable.match_1_1","namespace":"_private.Mathlib.Data.Countable.Defs.0.Function.Injective.countable","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists","Exists.intro","Function.Injective","Nat"],"value_dag_size":66,"value_refs":["Exists","Exists.casesOn","Exists.intro","Function.Injective","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Defs","name":"_private.Mathlib.Data.Countable.Defs.0.countable_iff_exists_surjective.match_1_1","namespace":"_private.Mathlib.Data.Countable.Defs.0.countable_iff_exists_surjective","reducibility":"abbrev","statement_dag_size":44,"type_refs":["Exists","Exists.intro","Function.Surjective","Nat"],"value_dag_size":62,"value_refs":["Exists","Exists.casesOn","Exists.intro","Function.Surjective","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Defs","name":"_private.Mathlib.Data.Countable.Defs.0.exists_surjective_nat.match_1_1","namespace":"_private.Mathlib.Data.Countable.Defs.0.exists_surjective_nat","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists","Exists.intro","Function.Injective","Nat"],"value_dag_size":66,"value_refs":["Exists","Exists.casesOn","Exists.intro","Function.Injective","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Countable.Defs","name":"_private.Mathlib.Data.Countable.Defs.0.instCountableQuotient._proof_1","namespace":"_private.Mathlib.Data.Countable.Defs.0.instCountableQuotient","reducibility":null,"statement_dag_size":15,"type_refs":["Countable","Quotient","Setoid"],"value_dag_size":18,"value_refs":["Countable","Quotient.countable","Setoid","Setoid.r"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Countable.Small","name":"_private.Mathlib.Data.Countable.Small.0.Countable.toSmall.match_1","namespace":"_private.Mathlib.Data.Countable.Small.0.Countable.toSmall","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists","Exists.intro","Function.Injective","Nat"],"value_dag_size":66,"value_refs":["Exists","Exists.casesOn","Exists.intro","Function.Injective","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index._simp_1_3","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_mapRange_index","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_of_support_subset._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_of_support_subset","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_of_support_subset._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.prod_of_support_subset","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.sumAddHom._simp_1","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.sumAddHom","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Or","instHAdd"],"value_dag_size":49,"value_refs":["HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.mem_add","Or","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.sumZeroHom._simp_1","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.sumZeroHom","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum._simp_1_3","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum._simp_1_4","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_iff","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum._simp_1_5","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.BigOperators","name":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum.match_1_1","namespace":"_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.support_sum","reducibility":"abbrev","statement_dag_size":523,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Exists","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":668,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single","reducibility":null,"statement_dag_size":26,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_3","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single","reducibility":null,"statement_dag_size":24,"type_refs":["Eq"],"value_dag_size":72,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_2","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_4","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single","reducibility":null,"statement_dag_size":80,"type_refs":["DFinsupp","DFinsupp.comapDomain'","DFinsupp.single","DecidableEq","Eq","Function.LeftInverse","Zero"],"value_dag_size":1190,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.comapDomain'","DFinsupp.comapDomain'_apply","DFinsupp.ext","DFinsupp.instDFunLike","DFinsupp.single","DFinsupp.single_apply","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.recOn","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Function.LeftInverse","Function.LeftInverse.eq_1","HEq","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_1","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_2","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.comapDomain'_single._proof_1_3","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.equivFunOnFintype_symm_single._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.equivFunOnFintype_symm_single","reducibility":null,"statement_dag_size":57,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFunLike.coe","DecidableEq","Eq","Pi.single","Zero"],"value_dag_size":65,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFinsupp.single_eq_pi_single","DFunLike.coe","DecidableEq","Eq.symm","Pi.single","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.erase_def._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.erase_def","reducibility":null,"statement_dag_size":163,"type_refs":["DFinsupp","DFinsupp.erase","DFinsupp.instDFunLike","DFinsupp.mk","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","SetLike.coe","Subtype","Subtype.val","Zero","Zero.toOfNat0"],"value_dag_size":1171,"value_refs":["And","Classical.byContradiction","DFinsupp","DFinsupp.erase","DFinsupp.erase_apply","DFinsupp.ext","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.mk","DFinsupp.mk_apply","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.erase","Finset.instSetLike","Finset.mem_erase","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","True","True.intro","Zero","Zero.toOfNat0","congrArg","dite","dite_congr","dite_eq_ite","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_apply_neg._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_apply_neg","reducibility":null,"statement_dag_size":74,"type_refs":["DFinsupp","DFinsupp.filter","DFinsupp.instDFunLike","DFunLike.coe","DecidablePred","Eq","Not","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":209,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFunLike.coe","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_apply_pos._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_apply_pos","reducibility":null,"statement_dag_size":65,"type_refs":["DFinsupp","DFinsupp.filter","DFinsupp.instDFunLike","DFunLike.coe","DecidablePred","Eq","Zero"],"value_dag_size":206,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFunLike.coe","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_def._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_def","reducibility":null,"statement_dag_size":170,"type_refs":["DFinsupp","DFinsupp.filter","DFinsupp.instDFunLike","DFinsupp.mk","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","SetLike.coe","Subtype","Subtype.val","Zero","Zero.toOfNat0"],"value_dag_size":1110,"value_refs":["And","Classical.byContradiction","DFinsupp","DFinsupp.ext","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.mk","DFinsupp.mk_apply","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","True","True.intro","Zero","Zero.toOfNat0","congrArg","dite","dite_congr","dite_eq_ite","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_eq'._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_eq'","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_ne_eq_erase'._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_ne_eq_erase'","reducibility":null,"statement_dag_size":64,"type_refs":["DFinsupp","DFinsupp.erase","DFinsupp.filter","DecidableEq","Eq","Not","Zero","instDecidableNot"],"value_dag_size":470,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.erase","DFinsupp.erase_apply","DFinsupp.ext","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","instDecidableNot","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_ne_eq_erase._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_ne_eq_erase","reducibility":null,"statement_dag_size":63,"type_refs":["DFinsupp","DFinsupp.erase","DFinsupp.filter","DecidableEq","Eq","Not","Zero","instDecidableNot"],"value_dag_size":444,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.erase","DFinsupp.erase_apply","DFinsupp.ext","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","instDecidableNot","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_single._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_single","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_single._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_single","reducibility":null,"statement_dag_size":150,"type_refs":["DFinsupp","DFinsupp.filter","DFinsupp.instDFunLike","DFinsupp.instZero","DFinsupp.single","DFunLike.coe","DecidableEq","DecidablePred","Eq","OfNat.ofNat","Zero","Zero.toOfNat0","ite"],"value_dag_size":986,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFinsupp.instZero","DFinsupp.single","DFinsupp.single_apply","DFunLike.coe","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.recOn","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.filter_single._proof_1_1","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.induction._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.induction","reducibility":null,"statement_dag_size":102,"type_refs":["AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","DecidableEq","Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","OfNat.ofNat","Or","Zero.toOfNat0","ite"],"value_dag_size":406,"value_refs":["AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.induction._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.induction","reducibility":null,"statement_dag_size":332,"type_refs":["AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","DFinsupp","DFinsupp.erase","DFinsupp.instAdd","DFinsupp.instDFunLike","DFinsupp.mk'","DFinsupp.single","DFunLike.coe","DecidableEq","Eq","HAdd.hAdd","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Ne","Not","OfNat.ofNat","Or","Subtype","Subtype.mk","Trunc.mk","Zero.toOfNat0","instHAdd"],"value_dag_size":893,"value_refs":["AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Classical.byContradiction","DFinsupp","DFinsupp.erase","DFinsupp.erase_apply","DFinsupp.instAdd","DFinsupp.instDFunLike","DFinsupp.mk'","DFinsupp.single","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Ne","Not","OfNat.ofNat","Or","Subtype","Subtype.mk","True","True.intro","Trunc.mk","Zero.toOfNat0","congrArg","eq_false","eq_self","eq_true","id","instHAdd","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mem_support_toFun._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mem_support_toFun","reducibility":null,"statement_dag_size":107,"type_refs":["And","Eq","Iff","Membership.mem","Multiset","Multiset.instMembership","Not","OfNat.ofNat","Or","Subtype","Subtype.val","Zero","Zero.toOfNat0"],"value_dag_size":613,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Multiset","Multiset.instMembership","Not","OfNat.ofNat","Or","Or.casesOn","Subtype","Subtype.casesOn","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective","reducibility":null,"statement_dag_size":158,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mk","DFunLike.coe","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.coe","Subtype.val","Zero"],"value_dag_size":286,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.mk","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Membership.mem","Not","Set","Set.Elem","Set.instMembership","SetLike.coe","Subtype.val","True","True.intro","Zero","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective","reducibility":null,"statement_dag_size":47,"type_refs":["Finset","Finset.instSetLike","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype.val"],"value_dag_size":106,"value_refs":["Eq","Eq.mp","Eq.symm","Eq.trans","Finset","Finset.instSetLike","Finset.mem_coe","Iff","Lean.Grind.iff_eq","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype.property","Subtype.val","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective._proof_1_3","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective","reducibility":null,"statement_dag_size":166,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mk","DFunLike.coe","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.Elem","Set.instMembership","SetLike.coe","Subtype.val","Zero"],"value_dag_size":649,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.mk","DFinsupp.mk_apply","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.decidableMem","Finset.instSetLike","Finset.mem_coe","HEq","HEq.refl","Iff","Lean.Grind.dite_cond_eq_true'","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","OfNat.ofNat","Set","Set.Elem","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.mk_injective._proof_1_2","congrArg","dite","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_of_ne._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_of_ne","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_of_ne._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_of_ne","reducibility":null,"statement_dag_size":68,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFunLike.coe","DecidableEq","Eq","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":305,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFinsupp.single_apply","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.rec","Eq.recOn","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_congr'","Lean.Grind.nestedDecidable","Ne","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_of_ne._proof_1_1","congrArg","dite","dite_congr","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_same._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.single_eq_same","reducibility":null,"statement_dag_size":51,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFunLike.coe","DecidableEq","Eq","Zero"],"value_dag_size":201,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.single","DFinsupp.single_apply","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.recOn","Eq.symm","Eq.trans","False","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","congrArg","dite","dite_cond_eq_true","eq_false","eq_self","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_eq_empty","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_filter._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_filter","reducibility":null,"statement_dag_size":82,"type_refs":["DFinsupp","DFinsupp.filter","DFinsupp.support","Decidable","DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":1124,"value_refs":["And","And.casesOn","Classical.byContradiction","DFinsupp","DFinsupp.filter","DFinsupp.filter_apply","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single","reducibility":null,"statement_dag_size":120,"type_refs":["DFinsupp.single","DFinsupp.support","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","Ne","Not","OfNat.ofNat","SetLike.instMembership","Singleton.singleton","Zero","Zero.toOfNat0"],"value_dag_size":221,"value_refs":["DFinsupp.single","DFinsupp.support","Decidable","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Membership.mem","Ne","Not","OfNat.ofNat","SetLike.instMembership","Singleton.singleton","True","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_1","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_5","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single","reducibility":null,"statement_dag_size":82,"type_refs":["DFinsupp.single","DFinsupp.support","Decidable","DecidableEq","Eq","Finset","Finset.instSingleton","Ne","OfNat.ofNat","Singleton.singleton","Zero","Zero.toOfNat0"],"value_dag_size":909,"value_refs":["And","And.casesOn","Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.single","DFinsupp.single_apply","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.recOn","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","HEq","HEq.refl","HEq.symm","HEq.trans","Iff","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eqRec_heq","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Nat","Ne","Not","OfNat.ofNat","OfNat.ofNat.hcongr_3","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","Zero","Zero.toOfNat0","Zero.toOfNat0.hcongr_2","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_1","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_single._proof_1_2","congrArg","congrFun'","dite","dite_congr","eq_false","eq_of_heq","eq_true","forall_congr","funext","heq_of_eq","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_zipWith._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.support_zipWith","reducibility":null,"statement_dag_size":196,"type_refs":["DFinsupp","DFinsupp.support","DFinsupp.zipWith","Decidable","DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","Ne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Union.union","Zero","Zero.toOfNat0"],"value_dag_size":1018,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.support","DFinsupp.zipWith","DFinsupp.zipWith_apply","DFunLike.coe","Decidable","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Finset.subset_iff","HEq","HEq.refl","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","Union.union","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_def._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_def","reducibility":null,"statement_dag_size":290,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mk","DFinsupp.support","DFinsupp.zipWith","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","SetLike.coe","Subtype","Subtype.val","Union.union","Zero","Zero.toOfNat0"],"value_dag_size":1351,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.ext","DFinsupp.instDFunLike","DFinsupp.mem_support_toFun","DFinsupp.mk","DFinsupp.mk_apply","DFinsupp.support","DFinsupp.zipWith","DFinsupp.zipWith_apply","DFunLike.coe","Decidable","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instSetLike","Finset.instUnion","Finset.mem_union","HEq","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","True","True.intro","Union.union","Zero","Zero.toOfNat0","congrArg","dite","dite_congr","dite_eq_ite","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_single_single._proof_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_single_single","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Eq.mpr_prop","Eq.refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Defs","name":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_single_single._proof_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_single_single","reducibility":null,"statement_dag_size":133,"type_refs":["DFinsupp","DFinsupp.single","DFinsupp.zipWith","DecidableEq","Eq","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":1422,"value_refs":["Classical.byContradiction","DFinsupp","DFinsupp.ext","DFinsupp.instDFunLike","DFinsupp.single","DFinsupp.single_apply","DFinsupp.zipWith","DFinsupp.zipWith_apply","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.recOn","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.DFinsupp.Defs.0.DFinsupp.zipWith_single_single._proof_1_1","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Ext","name":"_private.Mathlib.Data.DFinsupp.Ext.0.DFinsupp.addHom_ext._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Ext.0.DFinsupp.addHom_ext","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Ext","name":"_private.Mathlib.Data.DFinsupp.Ext.0.DFinsupp.addHom_ext._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Ext.0.DFinsupp.addHom_ext","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Interval","name":"_private.Mathlib.Data.DFinsupp.Interval.0.DFinsupp.instLocallyFiniteOrder._simp_1","namespace":"_private.Mathlib.Data.DFinsupp.Interval.0.DFinsupp.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":128,"type_refs":["And","DFinsupp","DFinsupp.instDFunLike","DFinsupp.rangeIcc","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.zero","LE.le","LocallyFiniteOrder","Membership.mem","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero"],"value_dag_size":137,"value_refs":["And","DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_rangeIcc_apply_iff","DFinsupp.rangeIcc","DFunLike.coe","Finset","Finset.instSetLike","Finset.zero","LE.le","LocallyFiniteOrder","Membership.mem","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Interval","name":"_private.Mathlib.Data.DFinsupp.Interval.0.DFinsupp.instLocallyFiniteOrder._simp_2","namespace":"_private.Mathlib.Data.DFinsupp.Interval.0.DFinsupp.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.Lex.addLeftStrictMono.match_1","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.Lex.addLeftStrictMono","reducibility":"abbrev","statement_dag_size":656,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLTLex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.intro","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","ofLex"],"value_dag_size":939,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLTLex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.casesOn","Exists.intro","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","ofLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lex_lt_of_lt._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lex_lt_of_lt","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp","reducibility":"regular","statement_dag_size":269,"type_refs":["DFinsupp","DFinsupp.instLTLex","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Zero","instDistribLatticeOfLinearOrder","toLex"],"value_dag_size":542,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLTLex","DFinsupp.neLocus","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finset.min","LT.lt","Lattice.toSemilatticeInf","Lex","Lex.rec","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toDecidableLT","LinearOrder.toPartialOrder","Or.by_cases","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Top.top","WithTop","WithTop.some","WithTop.top","Zero","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_1","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_2","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_3","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_4","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_5","_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec.match_1","instDistribLatticeOfLinearOrder","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_1","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":null,"statement_dag_size":77,"type_refs":["DFinsupp","DFinsupp.neLocus","Eq","Finset.min","LinearOrder","LinearOrder.toDecidableEq","WithTop","Zero"],"value_dag_size":76,"value_refs":["DFinsupp","DFinsupp.neLocus","Finset.min","LinearOrder","LinearOrder.toDecidableEq","WithTop","Zero","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_2","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":null,"statement_dag_size":122,"type_refs":["DFinsupp","DFinsupp.neLocus","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finset.min","Lex","LinearOrder","LinearOrder.toDecidableEq","Top.top","WithTop","WithTop.top","Zero","toLex"],"value_dag_size":187,"value_refs":["DFinsupp","DFinsupp.neLocus","DFinsupp.neLocus_eq_empty","DFunLike.coe","EmptyCollection.emptyCollection","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finset","Finset.instEmptyCollection","Finset.min","Finset.min_eq_top","Iff.mp","Lex","LinearOrder","LinearOrder.toDecidableEq","Top.top","WithTop","WithTop.top","Zero","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_3","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":null,"statement_dag_size":122,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.neLocus","DFunLike.coe","Eq","Finset.min","LT.lt","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","Or","PartialOrder.toPreorder","Preorder.toLT","WithTop","WithTop.some","Zero"],"value_dag_size":171,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_neLocus","DFinsupp.neLocus","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.mem_of_min","Finset.min","Iff.mp","LinearOrder","LinearOrder.toDecidableEq","Membership.mem","Ne","Ne.lt_or_gt","SetLike.instMembership","WithTop","WithTop.some","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_4","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":null,"statement_dag_size":340,"type_refs":["And","DFinsupp","DFinsupp.instDFunLike","DFinsupp.neLocus","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Finset.min","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","WithTop","WithTop.some","Zero","instDistribLatticeOfLinearOrder","ofLex","toLex"],"value_dag_size":610,"value_refs":["And","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.neLocus","DFinsupp.notMem_neLocus","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.intro","Finset","Finset.instSetLike","Finset.min","Finset.notMem_of_lt_min","Iff.mp","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","WithTop","WithTop.some","Zero","instDistribLatticeOfLinearOrder","ofLex","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_5","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":null,"statement_dag_size":340,"type_refs":["And","DFinsupp","DFinsupp.instDFunLike","DFinsupp.neLocus","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Finset.min","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","WithTop","WithTop.some","Zero","instDistribLatticeOfLinearOrder","ofLex","toLex"],"value_dag_size":662,"value_refs":["And","And.intro","DFinsupp","DFinsupp.instDFunLike","DFinsupp.neLocus","DFinsupp.neLocus_comm","DFinsupp.notMem_neLocus","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mpr","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.intro","Finset","Finset.instSetLike","Finset.min","Finset.notMem_of_lt_min","Iff.mp","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toPartialOrder","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","WithTop","WithTop.some","Zero","congrArg","id","instDistribLatticeOfLinearOrder","ofLex","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.Lex","name":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec.match_1","namespace":"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec","reducibility":"abbrev","statement_dag_size":205,"type_refs":["DFinsupp","DFinsupp.neLocus","Eq","Finset.min","LinearOrder","LinearOrder.toDecidableEq","Option.none","Option.some","Top.top","WithTop","WithTop.some","WithTop.top","Zero"],"value_dag_size":255,"value_refs":["DFinsupp","DFinsupp.neLocus","Eq","Finset.min","LinearOrder","LinearOrder.toDecidableEq","Option.casesOn","Option.none","Option.some","Top.top","WithTop","WithTop.some","WithTop.top","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Multiset","name":"_private.Mathlib.Data.DFinsupp.Multiset.0.DFinsupp.toMultiset_le_toMultiset._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Multiset.0.DFinsupp.toMultiset_le_toMultiset","reducibility":null,"statement_dag_size":107,"type_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFinsupp","DFinsupp.addZeroClass'","DFinsupp.instLE","DFunLike.coe","DecidableEq","Eq","LE.le","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.instPartialOrder","Multiset.toDFinsupp","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":117,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFinsupp","DFinsupp.addZeroClass'","DFinsupp.instLE","DFunLike.coe","DecidableEq","Eq.symm","LE.le","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.instPartialOrder","Multiset.toDFinsupp","Multiset.toDFinsupp_le_toDFinsupp","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Multiset","name":"_private.Mathlib.Data.DFinsupp.Multiset.0.DFinsupp.toMultiset_lt_toMultiset._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Multiset.0.DFinsupp.toMultiset_lt_toMultiset","reducibility":null,"statement_dag_size":109,"type_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFinsupp","DFinsupp.addZeroClass'","DFinsupp.instPreorder","DFunLike.coe","DecidableEq","Eq","LT.lt","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.instPartialOrder","Multiset.toDFinsupp","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instPreorder","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":119,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFinsupp","DFinsupp.addZeroClass'","DFinsupp.instPreorder","DFunLike.coe","DecidableEq","Eq.symm","LT.lt","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.instPartialOrder","Multiset.toDFinsupp","Multiset.toDFinsupp_lt_toDFinsupp","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instPreorder","PartialOrder.toPreorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Multiset","name":"_private.Mathlib.Data.DFinsupp.Multiset.0.Multiset.toDFinsupp_le_toDFinsupp._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Multiset.0.Multiset.toDFinsupp_le_toDFinsupp","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","Eq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":52,"value_refs":["DecidableEq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Multiset.le_iff_count","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Multiset","name":"_private.Mathlib.Data.DFinsupp.Multiset.0.Multiset.toDFinsupp_le_toDFinsupp._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Multiset.0.Multiset.toDFinsupp_le_toDFinsupp","reducibility":null,"statement_dag_size":79,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLE","DFunLike.coe","Eq","LE","LE.le","Zero"],"value_dag_size":85,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLE","DFinsupp.le_def","DFunLike.coe","LE","LE.le","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus._simp_1_3","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus._simp_1_4","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_iff","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus._simp_1_5","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.mem_neLocus","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.neLocus_comm._simp_1_3","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.neLocus_comm","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.neLocus_eq_empty._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.neLocus_eq_empty","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.NeLocus","name":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.subset_mapRange_neLocus._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.NeLocus.0.DFinsupp.subset_mapRange_neLocus","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.Notation","name":"_private.Mathlib.Data.DFinsupp.Notation.0.DFinsupp.Internal.elabSingle₀._sparseCasesOn_1","namespace":"_private.Mathlib.Data.DFinsupp.Notation.0.DFinsupp.Internal.elabSingle₀","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.Notation","name":"_private.Mathlib.Data.DFinsupp.Notation.0.DFinsupp.Internal.elabSingle₀.match_1","namespace":"_private.Mathlib.Data.DFinsupp.Notation.0.DFinsupp.Internal.elabSingle₀","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Expr","Option","Option.some"],"value_dag_size":40,"value_refs":["Lean.Expr","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","_private.Mathlib.Data.DFinsupp.Notation.0.DFinsupp.Internal.elabSingle₀._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.add_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.add_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.add_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.add_eq_zero_iff","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.disjoint_iff._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.disjoint_iff","reducibility":null,"statement_dag_size":61,"type_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder"],"value_dag_size":66,"value_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.disjoint_iff._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.disjoint_iff","reducibility":null,"statement_dag_size":89,"type_refs":["DFinsupp","DFinsupp.instZero","DFinsupp.support","Decidable","DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":101,"value_refs":["DFinsupp","DFinsupp.instZero","DFinsupp.support","DFinsupp.support_eq_empty","Decidable","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.instEmptyCollection","Ne","OfNat.ofNat","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.instOrderBotOfIsBotZeroClass._simp_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.instOrderBotOfIsBotZeroClass","reducibility":null,"statement_dag_size":79,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLE","DFunLike.coe","Eq","LE","LE.le","Zero"],"value_dag_size":85,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.instLE","DFinsupp.le_def","DFunLike.coe","LE","LE.le","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.subset_support_tsub._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.subset_support_tsub","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_inf_union_support_sup._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_inf_union_support_sup","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Lattice","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Max.max","Min.min","SemilatticeInf.toMin","SemilatticeSup.toMax"],"value_dag_size":60,"value_refs":["And","Eq","Lattice","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Max.max","Min.min","SemilatticeInf.toMin","SemilatticeSup.toMax","inf_eq_and_sup_eq_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_sup._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_sup","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Not","Or","imp_iff_not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_1","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_2","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":105,"type_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub"],"value_dag_size":113,"value_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub","propext","tsub_eq_zero_iff_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_3","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_iff","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_4","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_5","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","IsBotZeroClass","LE","LE.le","OfNat.ofNat","True","Zero","Zero.toOfNat0"],"value_dag_size":41,"value_refs":["IsBotZeroClass","LE","LE.le","OfNat.ofNat","Zero","Zero.toOfNat0","eq_true","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.DFinsupp.Order","name":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub._simp_1_6","namespace":"_private.Mathlib.Data.DFinsupp.Order.0.DFinsupp.support_tsub","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.DFinsupp.WellFounded","name":"_private.Mathlib.Data.DFinsupp.WellFounded.0.DFinsupp.Lex.acc_zero.match_1_1","namespace":"_private.Mathlib.Data.DFinsupp.WellFounded.0.DFinsupp.Lex.acc_zero","reducibility":"abbrev","statement_dag_size":270,"type_refs":["And","And.intro","DFinsupp","DFinsupp.Lex","DFinsupp.instDFunLike","DFinsupp.instZero","DFunLike.coe","Eq","Exists.intro","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":386,"value_refs":["And","And.casesOn","And.intro","DFinsupp","DFinsupp.Lex","DFinsupp.instDFunLike","DFinsupp.instZero","DFunLike.coe","Eq","Exists.casesOn","Exists.intro","OfNat.ofNat","Zero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Action","name":"_private.Mathlib.Data.ENNReal.Action.0.ENNReal.smul_top._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Action.0.ENNReal.smul_top","reducibility":null,"statement_dag_size":136,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HSMul.hSMul","IsCancelMulZero","Module","Module.IsTorsionFree","Module.toDistribMulAction","MulZeroClass.toZero","OfNat.ofNat","Or","SMulZeroClass.toSMul","Semiring","Semiring.toMonoid","Zero.toOfNat0","instDistribOfSemiring","instHSMul","instMulZeroClassOfSemiring"],"value_dag_size":145,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","Eq","HSMul.hSMul","IsCancelMulZero","Module","Module.IsTorsionFree","Module.toDistribMulAction","MulZeroClass.toZero","OfNat.ofNat","Or","SMulZeroClass.toSMul","Semiring","Semiring.toMonoid","Zero.toOfNat0","instDistribOfSemiring","instHSMul","instMulZeroClassOfSemiring","propext","smul_eq_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_mem_upperBounds._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_mem_upperBounds","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":59,"value_refs":["Membership.mem","Set","Set.forall_mem_image","Set.image","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_toNNReal.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_toNNReal","reducibility":"abbrev","statement_dag_size":43,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.ofNNReal","NNReal","Ne","Option.none","Option.some","Top.top"],"value_dag_size":64,"value_refs":["ENNReal","ENNReal.instTop","ENNReal.ofNNReal","NNReal","Ne","Option.casesOn","Option.none","Option.some","Top.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_toNNReal_le_self.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.coe_toNNReal_le_self","reducibility":"abbrev","statement_dag_size":22,"type_refs":["ENNReal","NNReal","Option.none","Option.some","Unit"],"value_dag_size":34,"value_refs":["ENNReal","NNReal","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat","reducibility":null,"statement_dag_size":44,"type_refs":["Compl.compl","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Ici","Set.Iio","Set.instCompl","instDistribLatticeOfLinearOrder"],"value_dag_size":49,"value_refs":["Compl.compl","DistribLattice.toLattice","Eq.symm","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Ici","Set.Iio","Set.compl_Iio","Set.instCompl","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat","reducibility":null,"statement_dag_size":38,"type_refs":["Compl.compl","Eq","Set","Set.iInter","Set.iUnion","Set.instCompl"],"value_dag_size":43,"value_refs":["Compl.compl","Eq.symm","Set","Set.compl_iUnion","Set.iInter","Set.iUnion","Set.instCompl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ioi_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ioi_coe_nat","reducibility":null,"statement_dag_size":44,"type_refs":["Compl.compl","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Iic","Set.Ioi","Set.instCompl","instDistribLatticeOfLinearOrder"],"value_dag_size":49,"value_refs":["Compl.compl","DistribLattice.toLattice","Eq.symm","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Iic","Set.Ioi","Set.compl_Iic","Set.instCompl","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ioi_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ioi_coe_nat","reducibility":null,"statement_dag_size":38,"type_refs":["Compl.compl","Eq","Set","Set.iInter","Set.iUnion","Set.instCompl"],"value_dag_size":43,"value_refs":["Compl.compl","Eq.symm","Set","Set.compl_iUnion","Set.iInter","Set.iUnion","Set.instCompl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Icc_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Icc_coe_nat","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Icc","Set.Ici","Set.Iic","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Icc","Set.Ici","Set.Ici_inter_Iic","Set.Iic","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Icc_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Icc_coe_nat","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Set","Set.iUnion","Set.instInter"],"value_dag_size":46,"value_refs":["Eq.symm","Inter.inter","Set","Set.iUnion","Set.instInter","Set.inter_iUnion"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ico_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ico_coe_nat","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Ici","Set.Ico","Set.Iio","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Ici","Set.Ici_inter_Iio","Set.Ico","Set.Iio","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ico_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ico_coe_nat","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Set","Set.iUnion","Set.instInter"],"value_dag_size":46,"value_refs":["Eq.symm","Inter.inter","Set","Set.iUnion","Set.instInter","Set.inter_iUnion"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Iio_coe_nat.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Iio_coe_nat","reducibility":"abbrev","statement_dag_size":61,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","Exists","Exists.intro","Membership.mem","Nat","Nat.cast","PartialOrder.toPreorder","Set","Set.Iio","Set.instMembership"],"value_dag_size":76,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instPartialOrder","Exists","Exists.casesOn","Exists.intro","Membership.mem","Nat","Nat.cast","PartialOrder.toPreorder","Set","Set.Iio","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioc_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioc_coe_nat","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Iic","Set.Ioc","Set.Ioi","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Iic","Set.Ioc","Set.Ioi","Set.Ioi_inter_Iic","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioc_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioc_coe_nat","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Set","Set.iUnion","Set.instInter"],"value_dag_size":46,"value_refs":["Eq.symm","Inter.inter","Set","Set.iUnion","Set.instInter","Set.inter_iUnion"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioo_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioo_coe_nat","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Iio","Set.Ioi","Set.Ioo","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Iio","Set.Ioi","Set.Ioi_inter_Iio","Set.Ioo","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioo_coe_nat._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioo_coe_nat","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Inter.inter","Set","Set.iUnion","Set.instInter"],"value_dag_size":46,"value_refs":["Eq.symm","Inter.inter","Set","Set.iUnion","Set.instInter","Set.inter_iUnion"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instCanonicallyOrderedAdd._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instCanonicallyOrderedAdd","reducibility":null,"statement_dag_size":7,"type_refs":["CanonicallyOrderedAdd","ENNReal","ENNReal.instAdd","ENNReal.instLE"],"value_dag_size":18,"value_refs":["Distrib.toAdd","NNReal","NNReal.instCanonicallyOrderedAdd","NNReal.instPartialOrder","NNReal.instSemiring","PartialOrder.toPreorder","WithTop.canonicallyOrderedAdd","instDistribOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instCharZero._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instCharZero","reducibility":null,"statement_dag_size":8,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","CharZero","ENNReal","ENNReal.instAddCommMonoidWithOne"],"value_dag_size":22,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","IsStrictOrderedRing.toCharZero","NNReal","NNReal.instIsStrictOrderedRing_1","NNReal.instPartialOrder","NNReal.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Semiring.toNonAssocSemiring","WithTop.charZero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instDenselyOrdered._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instDenselyOrdered","reducibility":null,"statement_dag_size":11,"type_refs":["DenselyOrdered","ENNReal","ENNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":21,"value_refs":["IsStrictOrderedRing.toNoMaxOrder","NNReal","NNReal.instDenselyOrdered","NNReal.instIsStrictOrderedRing_1","NNReal.instPartialOrder","NNReal.instSemiring","PartialOrder.toPreorder","Preorder.toLT","WithTop.denselyOrdered"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instIsOrderedAddMonoid._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instIsOrderedAddMonoid","reducibility":null,"statement_dag_size":10,"type_refs":["ENNReal","ENNReal.instAddCommMonoid","ENNReal.instPartialOrder","IsOrderedAddMonoid","PartialOrder.toPreorder"],"value_dag_size":17,"value_refs":["IsOrderedRing.toIsOrderedAddMonoid","NNReal","NNReal.instIsOrderedRing_1","NNReal.instPartialOrder","NNReal.instSemiring","Semiring.toAddCommMonoid","WithTop.isOrderedAddMonoid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instIsOrderedRing._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instIsOrderedRing","reducibility":null,"statement_dag_size":10,"type_refs":["CommSemiring.toSemiring","ENNReal","ENNReal.instCommSemiring","ENNReal.instPartialOrder","IsOrderedRing"],"value_dag_size":24,"value_refs":["LinearOrder.toDecidableEq","NNReal","NNReal.instCanonicallyOrderedAdd","NNReal.instCommSemiring","NNReal.instLinearOrder","NNReal.instNoZeroDivisors","NNReal.instNontrivial","NNReal.instPartialOrder","WithTop.instIsOrderedRing"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instNoZeroDivisors._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instNoZeroDivisors","reducibility":null,"statement_dag_size":16,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instZero","NoZeroDivisors","instDistribOfSemiring"],"value_dag_size":27,"value_refs":["LinearOrder.toDecidableEq","NNReal","NNReal.instLinearOrder","NNReal.instNoZeroDivisors","NNReal.instSemiring","NonUnitalNonAssocSemiring.toMulZeroClass","NonUnitalSemiring.toNonUnitalNonAssocSemiring","Semiring.toNonUnitalSemiring","WithTop.instNoZeroDivisors"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instOrderedSub._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.instOrderedSub","reducibility":null,"statement_dag_size":9,"type_refs":["ENNReal","ENNReal.instAdd","ENNReal.instLE","ENNReal.instSub","OrderedSub"],"value_dag_size":25,"value_refs":["Distrib.toAdd","NNReal","NNReal.instOrderBot","NNReal.instOrderedSub","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instSub","PartialOrder.toPreorder","Preorder.toLE","WithTop.instOrderedSub","instDistribOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_add_pos_lt.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_add_pos_lt","reducibility":"abbrev","statement_dag_size":106,"type_refs":["And","And.intro","ENNReal","ENNReal.instAdd","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.intro","HAdd.hAdd","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHAdd"],"value_dag_size":153,"value_refs":["And","And.casesOn","And.intro","ENNReal","ENNReal.instAdd","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_rat_btwn.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_rat_btwn","reducibility":"abbrev","statement_dag_size":119,"type_refs":["And","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"],"value_dag_size":208,"value_refs":["And","And.casesOn","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_real_btwn.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_real_btwn","reducibility":"abbrev","statement_dag_size":118,"type_refs":["And","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"],"value_dag_size":203,"value_refs":["And","And.casesOn","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_real_btwn.match_1_3","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.lt_iff_exists_real_btwn","reducibility":"abbrev","statement_dag_size":107,"type_refs":["And","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofReal","Exists","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLE","Real.instZero","Zero.toOfNat0"],"value_dag_size":192,"value_refs":["And","And.casesOn","And.intro","ENNReal","ENNReal.instPartialOrder","ENNReal.ofReal","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLE","Real.instZero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.natCast_le_ofNNReal._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.natCast_le_ofNNReal","reducibility":null,"statement_dag_size":31,"type_refs":["ENNReal","ENNReal.instLE","ENNReal.ofNNReal","Eq","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":39,"value_refs":["ENNReal","ENNReal.coe_le_coe","ENNReal.instLE","ENNReal.ofNNReal","Eq.symm","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.ofNNReal_le_natCast._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.ofNNReal_le_natCast","reducibility":null,"statement_dag_size":31,"type_refs":["ENNReal","ENNReal.instLE","ENNReal.ofNNReal","Eq","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":39,"value_refs":["ENNReal","ENNReal.coe_le_coe","ENNReal.instLE","ENNReal.ofNNReal","Eq.symm","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff'._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff'","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","NNReal","NNReal.toReal","Real"],"value_dag_size":23,"value_refs":["Eq","NNReal","NNReal.coe_inj","NNReal.toReal","Real","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","NNReal","NNReal.toReal","Real"],"value_dag_size":23,"value_refs":["Eq","NNReal","NNReal.coe_inj","NNReal.toReal","Real","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff","reducibility":null,"statement_dag_size":48,"type_refs":["And","ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.toNNReal","Eq","NNReal","OfNat.ofNat","Or","Top.top","Zero.toOfNat0"],"value_dag_size":51,"value_refs":["And","ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.toNNReal","ENNReal.toNNReal_eq_toNNReal_iff","Eq","NNReal","OfNat.ofNat","Or","Top.top","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_zero_iff","reducibility":null,"statement_dag_size":40,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.toNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Or","Top.top","Zero.toOfNat0"],"value_dag_size":42,"value_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.toNNReal","ENNReal.toNNReal_eq_zero_iff","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Or","Top.top","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal._proof_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal.match_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal","reducibility":"abbrev","statement_dag_size":178,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":393,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealOfNNReal._sparseCasesOn_1","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal._proof_2","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal.match_1","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Basic","name":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal.match_4","namespace":"_private.Mathlib.Data.ENNReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealtoReal","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.finsetSum_iSup_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.finsetSum_iSup_of_monotone","reducibility":"abbrev","statement_dag_size":74,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":89,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.ofReal_prod_of_nonneg._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.ofReal_prod_of_nonneg","reducibility":null,"statement_dag_size":20,"type_refs":["ENNReal","ENNReal.ofNNReal","Eq","NNReal"],"value_dag_size":23,"value_refs":["ENNReal","ENNReal.coe_inj","ENNReal.ofNNReal","Eq","NNReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.ofReal_sum_of_nonneg._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.ofReal_sum_of_nonneg","reducibility":null,"statement_dag_size":20,"type_refs":["ENNReal","ENNReal.ofNNReal","Eq","NNReal"],"value_dag_size":23,"value_refs":["ENNReal","ENNReal.coe_inj","ENNReal.ofNNReal","Eq","NNReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib","reducibility":null,"statement_dag_size":75,"type_refs":["CommMonoid","CommMonoid.toMonoid","Eq","Finset","Finset.prod","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"],"value_dag_size":83,"value_refs":["CommMonoid","CommMonoid.toMonoid","Eq.symm","Finset","Finset.prod","Finset.prod_mul_distrib","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib_of_ne_top._proof_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib_of_ne_top","reducibility":null,"statement_dag_size":72,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","Not","OfNat.ofNat","Or","Set.Pairwise","SetLike.coe","SetLike.instMembership","Top.top","Zero.toOfNat0"],"value_dag_size":500,"value_refs":["Classical.byContradiction","ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Set","Set.Pairwise","Set.Pairwise.eq_1","Set.instMembership","SetLike.coe","SetLike.instMembership","Top.top","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib_of_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.prod_div_distrib_of_ne_zero","reducibility":null,"statement_dag_size":72,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","Not","OfNat.ofNat","Or","Set.Pairwise","SetLike.coe","SetLike.instMembership","Top.top","Zero.toOfNat0"],"value_dag_size":567,"value_refs":["Classical.byContradiction","ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Set","Set.Pairwise","Set.Pairwise.eq_1","Set.instMembership","SetLike.coe","SetLike.instMembership","Top.top","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.BigOperators","name":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.sum_lt_sum_of_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.BigOperators.0.ENNReal.sum_lt_sum_of_nonempty","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Finset","Finset.cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":67,"value_refs":["And","Finset","Finset.cons","Finset.forall_mem_cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Holder","name":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderConjugate.sub_one_mul_inv._proof_1_1","namespace":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderConjugate.sub_one_mul_inv","reducibility":null,"statement_dag_size":19,"type_refs":["ENNReal","ENNReal.instTop","Eq","Ne","Not","Top.top"],"value_dag_size":65,"value_refs":["Classical.byContradiction","ENNReal","ENNReal.instTop","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Ne","Not","Top.top","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Holder","name":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.inv_le_inv._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.inv_le_inv","reducibility":null,"statement_dag_size":24,"type_refs":["ENNReal","ENNReal.instInv","ENNReal.instLE","Eq","Inv.inv","LE.le"],"value_dag_size":26,"value_refs":["ENNReal","ENNReal.instInv","ENNReal.instLE","ENNReal.inv_le_inv","Inv.inv","LE.le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Holder","name":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.inv_sub_inv_eq_inv'._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.inv_sub_inv_eq_inv'","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Holder","name":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.le._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.HolderTriple.le","reducibility":null,"statement_dag_size":24,"type_refs":["ENNReal","ENNReal.instInv","ENNReal.instLE","Eq","Inv.inv","LE.le"],"value_dag_size":32,"value_refs":["ENNReal","ENNReal.instInv","ENNReal.instLE","ENNReal.inv_le_inv","Eq.symm","Inv.inv","LE.le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Holder","name":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.holderConjugate_iff._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Holder.0.ENNReal.holderConjugate_iff","reducibility":null,"statement_dag_size":41,"type_refs":["ENNReal","ENNReal.HolderTriple","ENNReal.instAdd","ENNReal.instInv","Eq","HAdd.hAdd","Inv.inv","instHAdd","semiOutParam"],"value_dag_size":45,"value_refs":["ENNReal","ENNReal.HolderTriple","ENNReal.holderTriple_iff","ENNReal.instAdd","ENNReal.instInv","Eq","HAdd.hAdd","Inv.inv","instHAdd","propext","semiOutParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Ioo","Set.instMembership"],"value_dag_size":51,"value_refs":["And","LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Set.mem_Ioo","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","LE.le","LT.lt","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","Set","Set.Ico","Set.instMembership"],"value_dag_size":57,"value_refs":["And","LE.le","LT.lt","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","Set","Set.Ico","Set.instMembership","Set.mem_Ico","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_eq_top._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_eq_top","reducibility":null,"statement_dag_size":64,"type_refs":["And","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instTop","ENNReal.instZero","Eq","HMul.hMul","Ne","OfNat.ofNat","Or","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul"],"value_dag_size":67,"value_refs":["And","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instTop","ENNReal.instZero","ENNReal.mul_eq_top","Eq","HMul.hMul","Ne","OfNat.ofNat","Or","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_pos_iff._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_pos_iff","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_pos_iff._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.div_pos_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_lt_mul_left","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal","reducibility":null,"statement_dag_size":54,"type_refs":["And","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instPartialOrder","Exists","HMul.hMul","LT.lt","PartialOrder.toPreorder","Preorder.toLT","instDistribOfSemiring","instHMul"],"value_dag_size":345,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","And","And.casesOn","And.intro","CommSemiring.toSemiring","Distrib.toMul","DivInvMonoid.toDiv","ENNReal","ENNReal.div_lt_iff","ENNReal.div_lt_of_lt_mul","ENNReal.instAddCommMonoidWithOne","ENNReal.instCanonicallyOrderedAdd","ENNReal.instCommSemiring","ENNReal.instDenselyOrdered","ENNReal.instDivInvMonoid","ENNReal.instOrderTop","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","False.elim","HDiv.hDiv","HMul.hMul","Iff.mp","LT.lt","MulZeroClass.mul_zero","MulZeroClass.toZero","Ne","OfNat.ofNat","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","Zero.toOfNat0","congrArg","exists_between","instDistribOfSemiring","instHDiv","instHMul","instIsBotZeroClass","instMulZeroClassOfSemiring","not_lt_zero._simp_1","not_top_lt._simp_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_lt_mul_right","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal","reducibility":null,"statement_dag_size":54,"type_refs":["And","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instPartialOrder","Exists","HMul.hMul","LT.lt","PartialOrder.toPreorder","Preorder.toLT","instDistribOfSemiring","instHMul"],"value_dag_size":148,"value_refs":["And","CommMagma.toMul","CommSemiring.toNonUnitalCommSemiring","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instPartialOrder","Eq","Eq.mp","Eq.mpr","Exists","HMul.hMul","LT.lt","NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring","NonUnitalNonAssocCommSemiring.toCommMagma","PartialOrder.toPreorder","Preorder.toLT","_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_lt_mul_left","congrArg","funext","id","instDistribOfSemiring","instHMul","mul_comm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_mem_Ico_zpow._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_mem_Ico_zpow","reducibility":null,"statement_dag_size":32,"type_refs":["ENNReal","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":34,"value_refs":["ENNReal","ENNReal.coe_eq_zero","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_mem_Ioc_zpow._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_mem_Ioc_zpow","reducibility":null,"statement_dag_size":32,"type_refs":["ENNReal","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":34,"value_refs":["ENNReal","ENNReal.coe_eq_zero","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_nat_pos_mul_gt.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_nat_pos_mul_gt","reducibility":"abbrev","statement_dag_size":81,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instDivInvMonoid","ENNReal.instPartialOrder","Exists","Exists.intro","HDiv.hDiv","LT.lt","Nat","Nat.cast","PartialOrder.toPreorder","Preorder.toLT","instHDiv"],"value_dag_size":98,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","DivInvMonoid.toDiv","ENNReal","ENNReal.instAddCommMonoidWithOne","ENNReal.instDivInvMonoid","ENNReal.instPartialOrder","Exists","Exists.casesOn","Exists.intro","HDiv.hDiv","LT.lt","Nat","Nat.cast","PartialOrder.toPreorder","Preorder.toLT","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_pos_mul_lt._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.exists_pos_mul_lt","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top","reducibility":null,"statement_dag_size":32,"type_refs":["ENNReal","ENNReal.instInv","ENNReal.instTop","ENNReal.instZero","Eq","Inv.inv","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0"],"value_dag_size":33,"value_refs":["ENNReal","ENNReal.instInv","ENNReal.instTop","ENNReal.instZero","ENNReal.inv_ne_top","Inv.inv","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_lt_top","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_mul_cancel_left'._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_mul_cancel_left'","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_pow.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.inv_pow","reducibility":"abbrev","statement_dag_size":44,"type_refs":["ENNReal","NNReal","Nat","Nat.succ","OfNat.ofNat","Option.none","Option.some","instOfNatNat"],"value_dag_size":67,"value_refs":["ENNReal","NNReal","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Option.casesOn","Option.none","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mulLeftOrderIso._simp_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mulLeftOrderIso","reducibility":null,"statement_dag_size":62,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instLE","ENNReal.instTop","ENNReal.instZero","Eq","HMul.hMul","LE.le","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul"],"value_dag_size":69,"value_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instLE","ENNReal.instTop","ENNReal.instZero","ENNReal.mul_le_mul_iff_right","HMul.hMul","LE.le","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mulRightOrderIso._simp_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mulRightOrderIso","reducibility":null,"statement_dag_size":65,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instLE","ENNReal.instTop","ENNReal.instZero","Eq","HMul.hMul","LE.le","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul"],"value_dag_size":70,"value_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instLE","ENNReal.instTop","ENNReal.instZero","ENNReal.mul_le_mul_iff_left","HMul.hMul","LE.le","Ne","OfNat.ofNat","Top.top","Zero.toOfNat0","instDistribOfSemiring","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv._proof_1_4","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv","reducibility":null,"statement_dag_size":42,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.ofNNReal","Eq","HMul.hMul","Inv.inv","NNReal","instDistribOfSemiring","instHMul"],"value_dag_size":1054,"value_refs":["And","And.casesOn","Classical.byContradiction","CommGroupWithZero.toDivisionCommMonoid","CommSemiring.toSemiring","Distrib.toMul","DivInvMonoid.toMonoid","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvMonoid","DivisionMonoid.toDivInvOneMonoid","ENNReal","ENNReal.coe_inv","ENNReal.coe_mul","ENNReal.coe_ne_top","ENNReal.coe_zero","ENNReal.instCommSemiring","ENNReal.instInv","ENNReal.instNoZeroDivisors","ENNReal.instTop","ENNReal.instZero","ENNReal.inv_eq_zero","ENNReal.inv_zero","ENNReal.mul_top","ENNReal.ofNNReal","ENNReal.top_mul","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HMul.hMul","Iff","Inv.inv","InvOneClass.toInv","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","LinearOrderedCommGroupWithZero.toCommGroupWithZero","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","NNReal","NNReal.instInv","NNReal.instLinearOrderedCommGroupWithZero","NNReal.instNoZeroDivisors","NNReal.instSemiring","NNReal.instZero","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Top.top","True","True.intro","Zero.toOfNat0","congr","congrArg","eq_false","eq_true","id","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring","mul_eq_zero","mul_inv","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv","reducibility":null,"statement_dag_size":23,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","False","OfNat.ofNat","Top.top","Zero.toOfNat0"],"value_dag_size":22,"value_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.top_ne_zero","Eq","OfNat.ofNat","Top.top","Zero.toOfNat0","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv","reducibility":null,"statement_dag_size":19,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.ofNNReal","Eq","False","NNReal","Top.top"],"value_dag_size":19,"value_refs":["ENNReal","ENNReal.coe_ne_top","ENNReal.instTop","ENNReal.ofNNReal","Eq","NNReal","Top.top","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv","reducibility":null,"statement_dag_size":32,"type_refs":["ENNReal","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":34,"value_refs":["ENNReal","ENNReal.coe_eq_zero","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv_cancel_left'._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.mul_inv_cancel_left'","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe._simp_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE","LE.le","Subtype","Subtype.instLE","Subtype.mk"],"value_dag_size":56,"value_refs":["LE","LE.le","Subtype","Subtype.instLE","Subtype.mk","Subtype.mk_le_mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe._simp_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe","reducibility":null,"statement_dag_size":31,"type_refs":["ENNReal","ENNReal.instLE","ENNReal.ofNNReal","Eq","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":33,"value_refs":["ENNReal","ENNReal.coe_le_coe","ENNReal.instLE","ENNReal.ofNNReal","LE.le","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe._simp_3","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.orderIsoIicCoe","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","LE","LE.le","Subtype","Subtype.instLE","Subtype.val"],"value_dag_size":50,"value_refs":["LE","LE.le","Subtype","Subtype.coe_le_coe","Subtype.instLE","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_add._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_add","reducibility":null,"statement_dag_size":32,"type_refs":["ENNReal","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":34,"value_refs":["ENNReal","ENNReal.coe_eq_zero","ENNReal.instZero","ENNReal.ofNNReal","Eq","NNReal","NNReal.instZero","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_le_of_le._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_le_of_le","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_le_of_le._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_le_of_le","reducibility":null,"statement_dag_size":81,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","LE","LE.le","Neg.neg","NegZeroClass.toNeg","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid"],"value_dag_size":88,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","LE","LE.le","Neg.neg","NegZeroClass.toNeg","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","neg_le_neg_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","Preorder","Preorder.toLT","eq_false","ne_of_lt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","Preorder","Preorder.toLT","eq_false","ne_of_gt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_neg","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":36,"value_refs":["LT.lt","Preorder","Preorder.toLT","eq_false","lt_asymm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Inv","name":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_pos._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Inv.0.ENNReal.zpow_pos","reducibility":null,"statement_dag_size":58,"type_refs":["And","CommSemiring.toSemiring","ENNReal","ENNReal.instCommSemiring","ENNReal.instTop","Eq","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Ne","OfNat.ofNat","Semiring.toMonoid","Top.top","instHPow","instOfNatNat"],"value_dag_size":61,"value_refs":["And","CommSemiring.toSemiring","ENNReal","ENNReal.instCommSemiring","ENNReal.instTop","ENNReal.pow_eq_top_iff","Eq","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Ne","OfNat.ofNat","Semiring.toMonoid","Top.top","instHPow","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.add_ne_top._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.add_ne_top","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top"],"value_dag_size":52,"value_refs":["LT.lt","Ne","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Top.top","lt_top_iff_ne_top","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iInf_add_iInf.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iInf_add_iInf","reducibility":"abbrev","statement_dag_size":89,"type_refs":["ENNReal","ENNReal.instAdd","ENNReal.instLE","Exists","Exists.intro","HAdd.hAdd","LE.le","instHAdd"],"value_dag_size":108,"value_refs":["ENNReal","ENNReal.instAdd","ENNReal.instLE","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","LE.le","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iInf_add_iInf_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iInf_add_iInf_of_monotone","reducibility":"abbrev","statement_dag_size":71,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":85,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iSup_add_iSup_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.iSup_add_iSup_of_monotone","reducibility":"abbrev","statement_dag_size":74,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":89,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.ofReal_iInf._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.ofReal_iInf","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","lowerBounds"],"value_dag_size":56,"value_refs":["LE.le","Membership.mem","Preorder","Preorder.toLE","Set","Set.instMembership","lowerBounds","mem_lowerBounds","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.pow_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.pow_ne_zero","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_add_eq_add_sub._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_add_eq_add_sub","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iInf._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iInf","reducibility":null,"statement_dag_size":60,"type_refs":["Add","Eq","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub"],"value_dag_size":68,"value_refs":["Add","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub","propext","tsub_le_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iSup._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iSup","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iSup._simp_1_2","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.sub_iSup","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_iInf._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_iInf","reducibility":null,"statement_dag_size":60,"type_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENNReal","ENNReal.instCompleteLinearOrder","ENNReal.ofNNReal","Eq","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","Nonempty","iInf"],"value_dag_size":65,"value_refs":["CompleteLinearOrder.toConditionallyCompleteLinearOrderBot","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrderInf.toInfSet","ENNReal","ENNReal.coe_iInf","ENNReal.instCompleteLinearOrder","ENNReal.ofNNReal","Eq.symm","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","Nonempty","iInf"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","InfSet","InfSet.sInf","Set.range","iInf"],"value_dag_size":36,"value_refs":["Eq.symm","InfSet","InfSet.sInf","Set.range","iInf","sInf_range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf._simp_1_4","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","Set.range","Subtype.val"],"value_dag_size":55,"value_refs":["Eq.symm","Membership.mem","Set","Set.Elem","Set.image","Set.image_eq_range","Set.instMembership","Set.range","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sInf","reducibility":"abbrev","statement_dag_size":44,"type_refs":["ENNReal","Membership.mem","Set","Set.instMembership","Subtype","Subtype.mk"],"value_dag_size":60,"value_refs":["ENNReal","Membership.mem","Set","Set.instMembership","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup._simp_1_3","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Set.range","SupSet","SupSet.sSup","iSup"],"value_dag_size":36,"value_refs":["Eq.symm","Set.range","SupSet","SupSet.sSup","iSup","sSup_range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup._simp_1_4","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Membership.mem","Set","Set.Elem","Set.image","Set.instMembership","Set.range","Subtype.val"],"value_dag_size":55,"value_refs":["Eq.symm","Membership.mem","Set","Set.Elem","Set.image","Set.image_eq_range","Set.instMembership","Set.range","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup.match_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_sSup","reducibility":"abbrev","statement_dag_size":44,"type_refs":["ENNReal","Membership.mem","Set","Set.instMembership","Subtype","Subtype.mk"],"value_dag_size":60,"value_refs":["ENNReal","Membership.mem","Set","Set.instMembership","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Operations","name":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toReal_le_add'._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toReal_le_add'","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.Bound.ofReal_pos_of_pos","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.Bound","reducibility":null,"statement_dag_size":40,"type_refs":["ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.ofReal","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0"],"value_dag_size":44,"value_refs":["ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_pos","Iff.mpr","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.coe_lt_ofReal._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.coe_lt_ofReal","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.toNNReal"],"value_dag_size":34,"value_refs":["LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.lt_toNNReal_iff_coe_lt","Real.toNNReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.natCast_le_ofReal._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.natCast_le_ofReal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.ofReal_le_coe._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.ofReal_le_coe","reducibility":null,"statement_dag_size":38,"type_refs":["ENNReal","ENNReal.instLE","ENNReal.ofReal","Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0"],"value_dag_size":47,"value_refs":["ENNReal","ENNReal.instLE","ENNReal.ofReal","ENNReal.ofReal_le_ofReal_iff","Eq.symm","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.ofReal_mul._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.ofReal_mul","reducibility":null,"statement_dag_size":47,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofNNReal","Eq","HMul.hMul","NNReal","NNReal.instSemiring","instDistribOfSemiring","instHMul"],"value_dag_size":51,"value_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.coe_mul","ENNReal.instCommSemiring","ENNReal.ofNNReal","Eq.symm","HMul.hMul","NNReal","NNReal.instSemiring","instDistribOfSemiring","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.toNNReal_strict_mono._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.toNNReal_strict_mono","reducibility":null,"statement_dag_size":35,"type_refs":["ENNReal","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq","LT.lt","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":43,"value_refs":["ENNReal","ENNReal.coe_lt_coe","ENNReal.instPartialOrder","ENNReal.ofNNReal","Eq.symm","LT.lt","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.toReal_add_le._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.toReal_add_le","reducibility":null,"statement_dag_size":27,"type_refs":["ENNReal","ENNReal.toReal","Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","True","Zero.toOfNat0"],"value_dag_size":26,"value_refs":["ENNReal","ENNReal.toReal","ENNReal.toReal_nonneg","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.trichotomy._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.trichotomy","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Classical.or_iff_not_imp_left","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.trichotomy₂._simp_1_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.ENNReal.trichotomy₂","reducibility":null,"statement_dag_size":52,"type_refs":["And","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.toReal","Eq","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Top.top","Zero.toOfNat0"],"value_dag_size":53,"value_refs":["And","ENNReal","ENNReal.instPartialOrder","ENNReal.instTop","ENNReal.instZero","ENNReal.toReal","ENNReal.toReal_pos_iff","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Top.top","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._proof_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._proof_2","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._sparseCasesOn_6","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal.match_1","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal.match_4","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENNReal.Real","name":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal.match_6","namespace":"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal","reducibility":"abbrev","statement_dag_size":178,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":393,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._sparseCasesOn_6","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.add_one_le_natCast_iff._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.add_one_le_natCast_iff","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","HAdd.hAdd","LE.le","LT.lt","Ne","OfNat.ofNat","One.toOfNat1","Top.top","instAddENat","instAddMonoidWithOneENat","instHAdd","instLEENat","instLTENat","instTopENat"],"value_dag_size":58,"value_refs":["AddMonoidWithOne.toOne","ENat","ENat.add_one_le_iff'","HAdd.hAdd","LE.le","LT.lt","Ne","OfNat.ofNat","One.toOfNat1","Top.top","instAddENat","instAddMonoidWithOneENat","instHAdd","instLEENat","instLTENat","instTopENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.lt_add_one_iff._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.lt_add_one_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.lt_add_one_iff._simp_1_2","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.lt_add_one_iff","reducibility":null,"statement_dag_size":33,"type_refs":["Bot.bot","Eq","LT","LT.lt","True","WithBot","WithBot.bot","WithBot.instLT","WithBot.some"],"value_dag_size":34,"value_refs":["Bot.bot","LT","LT.lt","WithBot","WithBot.bot","WithBot.bot_lt_coe","WithBot.instLT","WithBot.some","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_eq_coe_top_iff.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_eq_coe_top_iff","reducibility":"abbrev","statement_dag_size":32,"type_refs":["ENat","Nat","Option.none","Option.some","Unit","WithTop"],"value_dag_size":54,"value_refs":["ENat","Nat","Option.casesOn","Option.none","Option.some","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt._simp_1_3","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt","reducibility":null,"statement_dag_size":95,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","LE.le","Nat","Nat.cast","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat"],"value_dag_size":103,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","LE.le","Nat","Nat.cast","Nat.cast_le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","ZeroLEOneClass","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt._simp_1_4","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","GE.ge","LE","LE.le"],"value_dag_size":30,"value_refs":["GE.ge","LE","LE.le","ge_iff_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt._simp_1_5","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt","reducibility":null,"statement_dag_size":96,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","Eq","LT.lt","Nat","Nat.cast","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","ZeroLEOneClass","instLTNat"],"value_dag_size":104,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CharZero","LT.lt","Nat","Nat.cast","Nat.cast_lt","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","ZeroLEOneClass","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.add_one_natCast_le_withTop_of_lt","reducibility":"abbrev","statement_dag_size":86,"type_refs":["ENat","ENat.instNatCast","LT.lt","Nat","Nat.cast","Option.none","Option.some","Preorder.toLT","Top.top","WithTop","WithTop.instPreorder","WithTop.natCast","WithTop.some","WithTop.top","instPreorderENat","instTopENat"],"value_dag_size":133,"value_refs":["ENat","ENat.instNatCast","LT.lt","Nat","Nat.cast","Option.casesOn","Option.none","Option.some","Preorder.toLT","Top.top","WithTop","WithTop.instPreorder","WithTop.natCast","WithTop.some","WithTop.top","instPreorderENat","instTopENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.exists_nat_gt._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.exists_nat_gt","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","lt_iff_not_ge","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.natCast_ne_coe_top.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.natCast_ne_coe_top","reducibility":"abbrev","statement_dag_size":34,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.cast","Top.top","WithTop","WithTop.natCast","WithTop.some","instTopENat"],"value_dag_size":137,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.cast","Option","Option.ctorIdx","Option.none","Option.some","Option.some.noConfusion","Top.top","WithTop","WithTop.natCast","WithTop.some","eq_of_heq","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.natCast_ne_top.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.natCast_ne_top","reducibility":"abbrev","statement_dag_size":26,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.cast","Top.top","instTopENat"],"value_dag_size":96,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.cast","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.ofNat_ne_top.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.ofNat_ne_top","reducibility":"abbrev","statement_dag_size":41,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.AtLeastTwo","OfNat.ofNat","Top.top","instOfNatAtLeastTwo","instTopENat"],"value_dag_size":127,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.AtLeastTwo","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instOfNatAtLeastTwo","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.one_ne_top.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.one_ne_top","reducibility":"abbrev","statement_dag_size":28,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","OfNat.ofNat","One.toOfNat1","Top.top","instAddMonoidWithOneENat","instTopENat"],"value_dag_size":96,"value_refs":["AddMonoidWithOne.toOne","ENat","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.instAddMonoidWithOne","OfNat.ofNat","One.toOfNat1","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instAddMonoidWithOneENat","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_natCast.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_natCast","reducibility":"abbrev","statement_dag_size":25,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.cast","Top.top","instTopENat"],"value_dag_size":95,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.cast","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_ofNat.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_ofNat","reducibility":"abbrev","statement_dag_size":40,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.AtLeastTwo","OfNat.ofNat","Top.top","instOfNatAtLeastTwo","instTopENat"],"value_dag_size":130,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.AtLeastTwo","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instOfNatAtLeastTwo","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_one.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_one","reducibility":"abbrev","statement_dag_size":28,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","OfNat.ofNat","One.toOfNat1","Top.top","instAddMonoidWithOneENat","instTopENat"],"value_dag_size":96,"value_refs":["AddMonoidWithOne.toOne","ENat","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.instAddMonoidWithOne","OfNat.ofNat","One.toOfNat1","Option","Option.ctorIdx","Option.none","Option.some","Top.top","instAddMonoidWithOneENat","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_zero.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_zero","reducibility":"abbrev","statement_dag_size":34,"type_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","Top.top","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","instTopENat"],"value_dag_size":112,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ENat","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","MulZeroClass.toZero","Nat","Nat.instAddMonoidWithOne","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Top.top","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.ENat.zero_ne_top.match_1_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.ENat.zero_ne_top","reducibility":"abbrev","statement_dag_size":34,"type_refs":["CommSemiring.toSemiring","ENat","Eq","MulZeroClass.toZero","OfNat.ofNat","Top.top","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","instTopENat"],"value_dag_size":112,"value_refs":["AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","CommSemiring.toSemiring","ENat","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","MulZeroClass.toZero","Nat","Nat.instAddMonoidWithOne","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Top.top","Zero.toOfNat0","instCommSemiringENat","instMulZeroClassOfSemiring","instTopENat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Basic","name":"_private.Mathlib.Data.ENat.Basic.0.MonoidWithZeroHom.ENatMap._simp_1","namespace":"_private.Mathlib.Data.ENat.Basic.0.MonoidWithZeroHom.ENatMap","reducibility":null,"statement_dag_size":61,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","HMul.hMul","Nat","Nat.cast","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"],"value_dag_size":67,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq.symm","HMul.hMul","Nat","Nat.cast","Nat.cast_mul","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.BigOperators","name":"_private.Mathlib.Data.ENat.BigOperators.0.ENat.sum_iSup_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENat.BigOperators.0.ENat.sum_iSup_of_monotone","reducibility":"abbrev","statement_dag_size":74,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":89,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.BigOperators","name":"_private.Mathlib.Data.ENat.BigOperators.0.ENat.sum_lt_sum_of_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.ENat.BigOperators.0.ENat.sum_lt_sum_of_nonempty","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Finset","Finset.cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":67,"value_refs":["And","Finset","Finset.cons","Finset.forall_mem_cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.finite_of_sSup_lt_top._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.finite_of_sSup_lt_top","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top"],"value_dag_size":49,"value_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top","propext","top_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_add_iInf.match_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_add_iInf","reducibility":"abbrev","statement_dag_size":89,"type_refs":["ENat","Exists","Exists.intro","HAdd.hAdd","LE.le","instAddENat","instHAdd","instLEENat"],"value_dag_size":108,"value_refs":["ENat","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","LE.le","instAddENat","instHAdd","instLEENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_add_iInf_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_add_iInf_of_monotone","reducibility":"abbrev","statement_dag_size":71,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":85,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iInf_eq_zero","reducibility":null,"statement_dag_size":149,"type_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LT.lt","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder"],"value_dag_size":156,"value_refs":["AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","IsBotZeroClass","LT.lt","Lattice.toSemilatticeInf","LinearOrder","NeZero","OfNat.ofNat","One.toOfNat1","Order.lt_one_iff","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iSup_add_iSup_of_monotone.match_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.iSup_add_iSup_of_monotone","reducibility":"abbrev","statement_dag_size":74,"type_refs":["And","And.intro","LE.le","Preorder","Preorder.toLE"],"value_dag_size":89,"value_refs":["And","And.casesOn","And.intro","LE.le","Preorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.mul_iInf'._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.mul_iInf'","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iInf._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iInf","reducibility":null,"statement_dag_size":60,"type_refs":["Add","Eq","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub"],"value_dag_size":68,"value_refs":["Add","HAdd.hAdd","HSub.hSub","LE","LE.le","OrderedSub","Sub","instHAdd","instHSub","propext","tsub_le_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iSup._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iSup","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Lattice","name":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iSup._simp_1_2","namespace":"_private.Mathlib.Data.ENat.Lattice.0.ENat.sub_iSup","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_add._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_add","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_def._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_def","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_def._simp_1_2","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_def","reducibility":null,"statement_dag_size":25,"type_refs":["ENat","ENat.instNatCast","Eq","LT.lt","Nat","Nat.cast","Top.top","True","instLTENat","instTopENat"],"value_dag_size":24,"value_refs":["ENat","ENat.instNatCast","ENat.natCast_lt_top","LT.lt","Nat","Nat.cast","Top.top","eq_true","instLTENat","instTopENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_mul._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_mul","reducibility":null,"statement_dag_size":61,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","HMul.hMul","Nat","Nat.cast","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"],"value_dag_size":67,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq.symm","HMul.hMul","Nat","Nat.cast","Nat.cast_mul","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_right_mono._simp_1_1","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_right_mono","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_right_mono._simp_1_2","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_right_mono","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LE","LE.le","OrderTop","OrderTop.toTop","Top.top","True"],"value_dag_size":34,"value_refs":["LE","LE.le","OrderTop","OrderTop.toTop","Top.top","eq_true","le_top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top._proof_1_1","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top","reducibility":null,"statement_dag_size":29,"type_refs":["AddMonoidWithOne.toOne","ENat","Eq","LT.lt","Not","OfNat.ofNat","One.toOfNat1","instAddMonoidWithOneENat","instLTENat"],"value_dag_size":81,"value_refs":["AddMonoidWithOne.toOne","Classical.byContradiction","ENat","Eq","False","LT.lt","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.lt_unsat","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Not","OfNat.ofNat","One.toOfNat1","id","instAddMonoidWithOneENat","instIsPreorder_mathlib","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instPreorderENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top._proof_1_2","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top","reducibility":null,"statement_dag_size":52,"type_refs":["AddMonoidWithOne.toOne","CommSemiring.toSemiring","ENat","Eq","LE.le","LT.lt","MulZeroClass.toZero","Not","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instAddMonoidWithOneENat","instCommSemiringENat","instLEENat","instLTENat","instMulZeroClassOfSemiring"],"value_dag_size":109,"value_refs":["AddMonoidWithOne.toOne","Classical.byContradiction","CommSemiring.toSemiring","ENat","Eq","False","LE.le","LT.lt","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.lt_unsat","Lean.Grind.intro_with_eq","Lean.Grind.not_not","MulZeroClass.toZero","Not","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","id","instAddMonoidWithOneENat","instCommSemiringENat","instIsPreorder_mathlib","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instMulZeroClassOfSemiring","instPreorderENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.ENat.Pow","name":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top._proof_1_3","namespace":"_private.Mathlib.Data.ENat.Pow.0.ENat.epow_top","reducibility":null,"statement_dag_size":13,"type_refs":["ENat","LT.lt","Not","Top.top","instLTENat","instTopENat"],"value_dag_size":65,"value_refs":["Classical.byContradiction","ENat","Eq.mp","Eq.symm","Eq.trans","False","LT.lt","Lean.Grind.Order.lt_eq_false","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Not","Top.top","True","True.intro","eq_true","id","instLEENat","instLTENat","instLawfulOrderLT_mathlib","instPreorderENat","instTopENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_mul._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_mul","reducibility":null,"statement_dag_size":47,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.ofNNReal","Eq","HMul.hMul","NNReal","NNReal.instSemiring","instDistribOfSemiring","instHMul"],"value_dag_size":51,"value_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.coe_mul","ENNReal.instCommSemiring","ENNReal.ofNNReal","Eq.symm","HMul.hMul","NNReal","NNReal.instSemiring","instDistribOfSemiring","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_mul.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_mul","reducibility":"abbrev","statement_dag_size":41,"type_refs":["ENNReal","NNReal","Option.none","Option.some","Unit"],"value_dag_size":72,"value_refs":["ENNReal","NNReal","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_top_mul","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal","reducibility":null,"statement_dag_size":50,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.instTop","ENNReal.ofNNReal","ENNReal.toEReal","EReal","EReal.instMul","Eq","HMul.hMul","NNReal","Top.top","instDistribOfSemiring","instHMul","instTopEReal"],"value_dag_size":308,"value_refs":["Bot.bot","CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.coe_ne_zero","ENNReal.instCommSemiring","ENNReal.instTop","ENNReal.instZero","ENNReal.ofNNReal","ENNReal.toEReal","ENNReal.top_mul","EReal","EReal.instMul","EReal.instMulZeroOneClass","Eq","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","HMul.hMul","Iff.mpr","LE.le","LT.lt","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NNReal","NNReal.coe_pos","NNReal.instOrderBot","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","Ne","Ne.bot_lt","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Real","Real.decidableEq","Real.decidableLT","Real.instLE","Real.instLT","Real.instZero","Subtype.val","Top.top","True","Zero.toOfNat0","congr","congrArg","eq_or_ne","eq_self","id","if_pos","instBotEReal","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring","instTopEReal","instZeroEReal","ite","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toENNReal._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toENNReal","reducibility":null,"statement_dag_size":46,"type_refs":["EReal","EReal.toReal","Eq","LE.le","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instZero","True","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal"],"value_dag_size":46,"value_refs":["EReal","EReal.toReal","EReal.toReal_nonneg","LE.le","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instZero","Zero.toOfNat0","eq_true","instPartialOrderEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toENNReal._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toENNReal","reducibility":null,"statement_dag_size":45,"type_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":49,"value_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_bot_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LE","LE.le","OrderTop","OrderTop.toTop","Top.top","True"],"value_dag_size":34,"value_refs":["LE","LE.le","OrderTop","OrderTop.toTop","Top.top","eq_true","le_top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt","reducibility":"abbrev","statement_dag_size":70,"type_refs":["DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":86,"value_refs":["DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt.match_1_3","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt","reducibility":"abbrev","statement_dag_size":67,"type_refs":["DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":82,"value_refs":["DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt.match_1_5","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.exists_rat_btwn_of_lt","reducibility":"abbrev","statement_dag_size":109,"type_refs":["Bot.bot","EReal","LT.lt","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","instBotEReal","instPartialOrderEReal","instTopEReal"],"value_dag_size":244,"value_refs":["Bot.bot","EReal","LT.lt","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","instBotEReal","instPartialOrderEReal","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.induction₂.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.induction₂","reducibility":"abbrev","statement_dag_size":71,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":156,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.le_coe_toReal._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.le_coe_toReal","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.le_coe_toReal._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.le_coe_toReal","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_rat_btwn.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_rat_btwn","reducibility":"abbrev","statement_dag_size":86,"type_refs":["And","And.intro","EReal","Exists","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instRatCast","Real.toEReal","instPartialOrderEReal"],"value_dag_size":130,"value_refs":["And","And.casesOn","And.intro","EReal","Exists","Exists.casesOn","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instRatCast","Real.toEReal","instPartialOrderEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_real_btwn.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_real_btwn","reducibility":"abbrev","statement_dag_size":86,"type_refs":["And","And.intro","EReal","Exists","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instRatCast","Real.toEReal","instPartialOrderEReal"],"value_dag_size":130,"value_refs":["And","And.casesOn","And.intro","EReal","Exists","Exists.casesOn","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instRatCast","Real.toEReal","instPartialOrderEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_real_btwn.match_1_3","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.lt_iff_exists_real_btwn","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","EReal","Exists","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","instPartialOrderEReal"],"value_dag_size":122,"value_refs":["And","And.casesOn","And.intro","EReal","Exists","Exists.casesOn","Exists.intro","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","instPartialOrderEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.neTopBotEquivReal._simp_4","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.neTopBotEquivReal","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.neTopBotEquivReal._simp_5","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.neTopBotEquivReal","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.one_mul.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.one_mul","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":56,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Icc._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Icc","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Icc","Set.Ici","Set.Iic","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Icc","Set.Ici","Set.Ici_inter_Iic","Set.Iic","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ico._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ico","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Ici","Set.Ico","Set.Iio","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Ici","Set.Ici_inter_Iio","Set.Ico","Set.Iio","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ioc._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ioc","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Iic","Set.Ioc","Set.Ioi","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Iic","Set.Ioc","Set.Ioi","Set.Ioi_inter_Iic","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ioo._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.preimage_coe_Ioo","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Inter.inter","Preorder","Set","Set.Iio","Set.Ioi","Set.Ioo","Set.instInter"],"value_dag_size":43,"value_refs":["Eq.symm","Inter.inter","Preorder","Set","Set.Iio","Set.Ioi","Set.Ioi_inter_Iio","Set.Ioo","Set.instInter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.range_coe_ennreal.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.range_coe_ennreal","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":54,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_coe_ennreal.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_coe_ennreal","reducibility":"abbrev","statement_dag_size":22,"type_refs":["ENNReal","NNReal","Option.none","Option.some","Unit"],"value_dag_size":35,"value_refs":["ENNReal","NNReal","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_ne_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_ne_zero_iff","reducibility":null,"statement_dag_size":47,"type_refs":["Bot.bot","EReal","EReal.toReal","Eq","OfNat.ofNat","Or","Real","Real.instZero","Top.top","Zero.toOfNat0","instBotEReal","instTopEReal","instZeroEReal"],"value_dag_size":49,"value_refs":["Bot.bot","EReal","EReal.toReal","EReal.toReal_eq_zero_iff","Eq","OfNat.ofNat","Or","Real","Real.instZero","Top.top","Zero.toOfNat0","instBotEReal","instTopEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_ne_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.toReal_ne_zero_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.EReal.zero_mul.match_1_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.EReal.zero_mul","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":56,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealToEReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealToEReal","reducibility":"abbrev","statement_dag_size":221,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":449,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealToEReal.match_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealToEReal","reducibility":"abbrev","statement_dag_size":201,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":462,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalENNRealToEReal._sparseCasesOn_1","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal._proof_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal._proof_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal.match_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal","reducibility":"abbrev","statement_dag_size":176,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":391,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToENNReal._sparseCasesOn_1","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal._proof_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal._proof_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal.match_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal","reducibility":"abbrev","statement_dag_size":147,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Option","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":169,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._proof_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._proof_2","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._sparseCasesOn_6","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":"abbrev","statement_dag_size":282,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":497,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal.match_1","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal.match_4","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Basic","name":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal.match_6","namespace":"_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal","reducibility":"abbrev","statement_dag_size":235,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":552,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalRealToEReal._sparseCasesOn_6","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff","reducibility":null,"statement_dag_size":32,"type_refs":["EReal","Eq","OfNat.ofNat","Real","Real.instZero","Real.toEReal","Zero.toOfNat0","instZeroEReal"],"value_dag_size":34,"value_refs":["EReal","EReal.coe_eq_zero","Eq","OfNat.ofNat","Real","Real.instZero","Real.toEReal","Zero.toOfNat0","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff","reducibility":null,"statement_dag_size":35,"type_refs":["ENNReal","ENNReal.instZero","ENNReal.ofReal","Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0"],"value_dag_size":37,"value_refs":["ENNReal","ENNReal.instZero","ENNReal.ofReal","ENNReal.ofReal_eq_zero","Eq","LE.le","OfNat.ofNat","Real","Real.instLE","Real.instZero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff","reducibility":null,"statement_dag_size":131,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeInf","LinearOrder","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","instDistribLatticeOfLinearOrder"],"value_dag_size":137,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeInf","LinearOrder","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","abs_nonpos_iff","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff._simp_1_4","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff","reducibility":null,"statement_dag_size":23,"type_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","Eq","False","OfNat.ofNat","Top.top","Zero.toOfNat0"],"value_dag_size":22,"value_refs":["ENNReal","ENNReal.instTop","ENNReal.instZero","ENNReal.top_ne_zero","Eq","OfNat.ofNat","Top.top","Zero.toOfNat0","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff._simp_1_5","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_eq_zero_iff","reducibility":null,"statement_dag_size":23,"type_refs":["EReal","Eq","False","OfNat.ofNat","Top.top","Zero.toOfNat0","instTopEReal","instZeroEReal"],"value_dag_size":22,"value_refs":["EReal","EReal.top_ne_zero","Eq","OfNat.ofNat","Top.top","Zero.toOfNat0","eq_false","instTopEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_mul._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_mul","reducibility":null,"statement_dag_size":34,"type_refs":["EReal","EReal.instMul","Eq","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"],"value_dag_size":38,"value_refs":["EReal","EReal.coe_mul","EReal.instMul","Eq.symm","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_neg.match_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.abs_neg","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":56,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_lt_mul_left_of_nonneg","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal","reducibility":null,"statement_dag_size":81,"type_refs":["And","EReal","EReal.instMul","Exists","HMul.hMul","LE.le","LT.lt","Membership.mem","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal"],"value_dag_size":541,"value_refs":["And","And.casesOn","And.intro","DivInvMonoid.toDiv","EReal","EReal.div_lt_iff","EReal.div_nonneg","EReal.instDivInvMonoid","EReal.instMul","EReal.instMulZeroOneClass","EReal.instPosMulReflectLT","EReal.mul_top_of_pos","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.symm","Exists","Exists.casesOn","Exists.intro","False","False.rec","HDiv.hDiv","HMul.hMul","Iff.mp","Iff.mpr","LE.le","LE.le.trans_lt","LT.lt","LT.lt.le","Membership.mem","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Set.mem_Ioo","Top.top","Zero.toOfNat0","congrArg","eq_or_lt_of_le","eq_or_ne","exists_between","id","instDenselyOrderedEReal","instHDiv","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal","not_le_of_gt","pos_of_mul_pos_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_lt_mul_right_of_nonneg","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal","reducibility":null,"statement_dag_size":81,"type_refs":["And","EReal","EReal.instMul","Exists","HMul.hMul","LE.le","LT.lt","Membership.mem","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal"],"value_dag_size":219,"value_refs":["And","CommMagma.toMul","CommMonoid.toCommSemigroup","CommMonoidWithZero.toCommMonoid","CommSemigroup.toCommMagma","EReal","EReal.instCommMonoidWithZero","EReal.instMul","EReal.instMulZeroOneClass","EReal.instPosMulReflectLT","Eq","Eq.mp","Eq.mpr","Exists","HMul.hMul","LE.le","LE.le.trans_lt","LT.lt","LT.lt.le","Membership.mem","MulZeroClass.toMul","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Zero.toOfNat0","_private.Mathlib.Data.EReal.Inv.0.EReal.exists_lt_mul_left_of_nonneg","congrArg","funext","id","instHMul","instPartialOrderEReal","instZeroEReal","mul_comm","pos_of_mul_pos_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_mul_left_lt","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal","reducibility":null,"statement_dag_size":91,"type_refs":["And","EReal","EReal.instMul","Exists","HMul.hMul","LT.lt","Membership.mem","Ne","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Top.top","Zero.toOfNat0","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":977,"value_refs":["And","And.casesOn","And.intro","Bot.bot","CoheytingAlgebra.toOrderTop","CompleteDistribLattice.toCoframe","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteDistribLattice","DivInvMonoid.toDiv","EReal","EReal.instDivInvMonoid","EReal.instMul","EReal.lt_div_iff","EReal.mul_le_mul_of_nonpos_right","EReal.mul_top_of_neg","EReal.mul_top_of_pos","EReal.top_mul_of_pos","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.symm","Exists","Exists.casesOn","Exists.intro","False","False.rec","HDiv.hDiv","HMul.hMul","Iff.mp","Iff.mpr","LE.le","LT.lt","LT.lt.le","LT.lt.ne","LinearOrder.toPartialOrder","Membership.mem","Ne","OfNat.ofNat","Or","Or.casesOn","Order.Coframe.toCoheytingAlgebra","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Set.mem_Ioo","Top.top","Zero.toOfNat0","congrArg","eq_top_or_lt_top","exists_between","false_or","instBotEReal","instCompleteLinearOrderEReal","instDenselyOrderedEReal","instHDiv","instHMul","instLinearOrderEReal","instPartialOrderEReal","instTopEReal","instZeroEReal","le_or_gt","lt_of_le_of_lt","lt_top_of_lt","lt_trichotomy","ne_self_iff_false","not_top_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_mul_right_lt","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal","reducibility":null,"statement_dag_size":91,"type_refs":["And","EReal","EReal.instMul","Exists","HMul.hMul","LT.lt","Membership.mem","Ne","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Top.top","Zero.toOfNat0","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":214,"value_refs":["And","CommMagma.toMul","CommMonoid.toCommSemigroup","CommMonoidWithZero.toCommMonoid","CommSemigroup.toCommMagma","EReal","EReal.instCommMonoidWithZero","EReal.instMul","Eq","Eq.mp","Eq.mpr","Exists","HMul.hMul","LT.lt","Membership.mem","Ne","OfNat.ofNat","Or","Or.symm","PartialOrder.toPreorder","Preorder.toLT","Set","Set.Ioo","Set.instMembership","Top.top","Zero.toOfNat0","_private.Mathlib.Data.EReal.Inv.0.EReal.exists_mul_left_lt","congrArg","congrFun'","funext","id","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal","mul_comm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_nat_ge_mul.match_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.exists_nat_ge_mul","reducibility":"abbrev","statement_dag_size":60,"type_refs":["Bot.bot","EReal","Ne","Option.none","Option.some","Real","Real.toEReal","Top.top","WithTop","instBotEReal","instTopEReal"],"value_dag_size":104,"value_refs":["Bot.bot","EReal","Ne","Option.casesOn","Option.none","Option.some","Real","Real.toEReal","Top.top","WithTop","instBotEReal","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.instCommMonoidWithZero._simp_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.instCommMonoidWithZero","reducibility":null,"statement_dag_size":10,"type_refs":["And","Eq"],"value_dag_size":12,"value_refs":["And","and_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.instPosMulMono._simp_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.instPosMulMono","reducibility":null,"statement_dag_size":116,"type_refs":["And","DFunLike.coe","DistribLattice.toLattice","ENNReal","ENNReal.instLE","EReal","EReal.abs","Eq","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableLT","Or","OrderHom","OrderHom.instFunLike","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SignType","SignType.instLinearOrder","SignType.neg","SignType.pos","SignType.sign","SignType.zero","instDistribLatticeOfLinearOrder","instLinearOrderEReal","instPartialOrderEReal","instZeroEReal"],"value_dag_size":119,"value_refs":["And","DFunLike.coe","DistribLattice.toLattice","ENNReal","ENNReal.instLE","EReal","EReal.abs","EReal.le_iff_sign","Eq","LE.le","LT.lt","Lattice.toSemilatticeInf","LinearOrder.toDecidableLT","Or","OrderHom","OrderHom.instFunLike","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SignType","SignType.instLinearOrder","SignType.neg","SignType.pos","SignType.sign","SignType.zero","instDistribLatticeOfLinearOrder","instLinearOrderEReal","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.inv_strictAntiOn.match_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.inv_strictAntiOn","reducibility":"abbrev","statement_dag_size":102,"type_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":170,"value_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_coe._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_coe","reducibility":null,"statement_dag_size":43,"type_refs":["EReal","Eq","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal"],"value_dag_size":44,"value_refs":["EReal","EReal.coe_pos","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_coe._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_coe","reducibility":null,"statement_dag_size":43,"type_refs":["EReal","Eq","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal"],"value_dag_size":44,"value_refs":["EReal","EReal.coe_neg'","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul","reducibility":null,"statement_dag_size":34,"type_refs":["EReal","EReal.instMul","Eq","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"],"value_dag_size":38,"value_refs":["EReal","EReal.coe_mul","EReal.instMul","Eq.symm","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul_abs.match_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul_abs","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":54,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul_inv_abs._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_mul_inv_abs","reducibility":null,"statement_dag_size":114,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","LE.le","Lattice","Lattice.toSemilatticeInf","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","abs"],"value_dag_size":118,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddLeftMono","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","LE.le","Lattice","Lattice.toSemilatticeInf","NegZeroClass.toZero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","abs","abs_nonneg","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_neg.match_1_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.EReal.sign_neg","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":56,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealDiv._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealDiv","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealDiv.match_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealDiv","reducibility":"abbrev","statement_dag_size":193,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":235,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Nat.hasNotBit","OfNat.ofNat","Option","Option.ctorIdx","Option.some","Qq.Quoted","_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealDiv._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv._proof_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv._proof_2","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv._sparseCasesOn_3","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv.match_1","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":"abbrev","statement_dag_size":218,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":230,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv.match_3","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv._sparseCasesOn_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Inv","name":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv.match_6","namespace":"_private.Mathlib.Data.EReal.Inv.0.Mathlib.Meta.Positivity.evalERealInv","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.ENNReal.toEReal_sub._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.ENNReal.toEReal_sub","reducibility":null,"statement_dag_size":34,"type_refs":["ENNReal","ENNReal.instSub","ENNReal.ofNNReal","Eq","HSub.hSub","NNReal","NNReal.instSub","instHSub"],"value_dag_size":38,"value_refs":["ENNReal","ENNReal.coe_sub","ENNReal.instSub","ENNReal.ofNNReal","Eq.symm","HSub.hSub","NNReal","NNReal.instSub","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._simp_1_4","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":null,"statement_dag_size":43,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","EReal","Eq","HAdd.hAdd","Real","Real.instAdd","Real.toEReal","instAddCommMonoidEReal","instHAdd"],"value_dag_size":47,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","EReal","EReal.coe_add","Eq.symm","HAdd.hAdd","Real","Real.instAdd","Real.toEReal","instAddCommMonoidEReal","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._simp_1_5","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top"],"value_dag_size":49,"value_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top","propext","top_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._simp_1_6","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":null,"statement_dag_size":19,"type_refs":["EReal","Eq","False","Real","Real.toEReal","Top.top","instTopEReal"],"value_dag_size":19,"value_refs":["EReal","EReal.coe_ne_top","Eq","Real","Real.toEReal","Top.top","eq_false","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._simp_1_7","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":null,"statement_dag_size":31,"type_refs":["EReal","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.toEReal","instPartialOrderEReal"],"value_dag_size":33,"value_refs":["EReal","EReal.coe_le_coe_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.toEReal","instPartialOrderEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._simp_1_8","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":null,"statement_dag_size":52,"type_refs":["Add","AddLeftMono","AddLeftReflectLE","Eq","HAdd.hAdd","LE","LE.le","instHAdd"],"value_dag_size":60,"value_refs":["Add","AddLeftMono","AddLeftReflectLE","HAdd.hAdd","LE","LE.le","add_le_add_iff_left","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.none"],"value_dag_size":83,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe","reducibility":"abbrev","statement_dag_size":148,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Bot.bot","EReal","HAdd.hAdd","LE.le","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLE","Real","Real.toEReal","Top.top","WithTop","instAddCommMonoidEReal","instBotEReal","instHAdd","instPartialOrderEReal","instTopEReal"],"value_dag_size":316,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","Bot.bot","EReal","HAdd.hAdd","LE.le","Nat.hasNotBit","Option.casesOn","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLE","Real","Real.toEReal","Top.top","WithTop","_private.Mathlib.Data.EReal.Operations.0.EReal.addLECancellable_coe._sparseCasesOn_1_1","instAddCommMonoidEReal","instBotEReal","instHAdd","instPartialOrderEReal","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top_left._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top_left","reducibility":null,"statement_dag_size":54,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","Bot.bot","EReal","Eq","HAdd.hAdd","Ne","Top.top","instAddCommMonoidEReal","instBotEReal","instHAdd","instTopEReal"],"value_dag_size":59,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","Bot.bot","EReal","EReal.add_ne_top_iff_ne_top₂","HAdd.hAdd","Ne","Top.top","instAddCommMonoidEReal","instBotEReal","instHAdd","instTopEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","IsEmpty","True"],"value_dag_size":22,"value_refs":["IsEmpty","IsEmpty.forall_iff","True","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂","reducibility":null,"statement_dag_size":19,"type_refs":["EReal","Eq","False","Real","Real.toEReal","Top.top","instTopEReal"],"value_dag_size":19,"value_refs":["EReal","EReal.coe_ne_top","Eq","Real","Real.toEReal","Top.top","eq_false","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_of_ne_bot_of_ne_top._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_of_ne_bot_of_ne_top","reducibility":null,"statement_dag_size":54,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","Bot.bot","EReal","Eq","HAdd.hAdd","Ne","Top.top","instAddCommMonoidEReal","instBotEReal","instHAdd","instTopEReal"],"value_dag_size":59,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","Bot.bot","EReal","EReal.add_ne_top_iff_ne_top₂","HAdd.hAdd","Ne","Top.top","instAddCommMonoidEReal","instBotEReal","instHAdd","instTopEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_sub_add_comm._proof_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.add_sub_add_comm","reducibility":null,"statement_dag_size":72,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","EReal","EReal.instNeg","EReal.instSubNegZeroMonoid","Eq","HAdd.hAdd","Neg.neg","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toSubNegMonoid","instAddCommMonoidEReal","instHAdd"],"value_dag_size":172,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toGrindNatModule","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","EReal","EReal.instNeg","EReal.instSubNegZeroMonoid","Eq","Eq.refl","False","HAdd.hAdd","Lean.Grind.Linarith.Expr.add","Lean.Grind.Linarith.Expr.var","Lean.Grind.Linarith.eq_normN","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toSubNegMonoid","eagerReduce","id","instAddCommMonoidEReal","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.bot_lt_add_iff._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.bot_lt_add_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Bot.bot","Eq","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":52,"value_refs":["Bot.bot","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","bot_lt_iff_ne_bot","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.exists_lt_add_left","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal","reducibility":null,"statement_dag_size":54,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","EReal","Exists","HAdd.hAdd","LT.lt","PartialOrder.toPreorder","Preorder.toLT","instAddCommMonoidEReal","instHAdd","instPartialOrderEReal"],"value_dag_size":332,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.casesOn","And.intro","Bot.bot","CoheytingAlgebra.toOrderTop","CompleteDistribLattice.toCoframe","CompleteDistribLattice.toFrame","CompleteLinearOrder.toCompletelyDistribLattice","CompletelyDistribLattice.toCompleteDistribLattice","EReal","EReal.add_bot","EReal.instSubNegZeroMonoid","EReal.sub_lt_iff","EReal.sub_lt_of_lt_add","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","HSub.hSub","HeytingAlgebra.toOrderBot","Iff.mp","LE.le","LT.lt","LT.lt.ne_top","LinearOrder.toPartialOrder","Mathlib.Tactic.Contrapose.contrapose₃","Ne","Not","Or.inl","Or.inr","Order.Coframe.toCoheytingAlgebra","Order.Frame.toHeytingAlgebra","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SubNegMonoid.toSub","SubNegZeroMonoid.toSubNegMonoid","Top.top","bot_le","exists_between","id","implies_congr","instAddCommMonoidEReal","instBotEReal","instCompleteLinearOrderEReal","instDenselyOrderedEReal","instHAdd","instHSub","instLinearOrderEReal","instPartialOrderEReal","instTopEReal","not_lt._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.exists_lt_add_right","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal","reducibility":null,"statement_dag_size":54,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","EReal","Exists","HAdd.hAdd","LT.lt","PartialOrder.toPreorder","Preorder.toLT","instAddCommMonoidEReal","instHAdd","instPartialOrderEReal"],"value_dag_size":133,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","EReal","Eq","Eq.mp","Eq.mpr","Exists","HAdd.hAdd","LT.lt","PartialOrder.toPreorder","Preorder.toLT","_private.Mathlib.Data.EReal.Operations.0.EReal.exists_lt_add_left","add_comm","congrArg","funext","id","instAddCommMonoidEReal","instHAdd","instPartialOrderEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.instNoZeroDivisors._simp_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.instNoZeroDivisors","reducibility":null,"statement_dag_size":34,"type_refs":["EReal","EReal.instMul","Eq","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"],"value_dag_size":38,"value_refs":["EReal","EReal.coe_mul","EReal.instMul","Eq.symm","HMul.hMul","Real","Real.instMul","Real.toEReal","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LE","LE.le","OrderTop","OrderTop.toTop","Top.top","True"],"value_dag_size":34,"value_refs":["LE","LE.le","OrderTop","OrderTop.toTop","Top.top","eq_true","le_top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.le_sub_iff_add_le","reducibility":null,"statement_dag_size":45,"type_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":49,"value_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_bot_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.left_distrib_of_nonneg_of_ne_top._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.left_distrib_of_nonneg_of_ne_top","reducibility":null,"statement_dag_size":43,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","EReal","Eq","HAdd.hAdd","Real","Real.instAdd","Real.toEReal","instAddCommMonoidEReal","instHAdd"],"value_dag_size":47,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","EReal","EReal.coe_add","Eq.symm","HAdd.hAdd","Real","Real.instAdd","Real.toEReal","instAddCommMonoidEReal","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_bot_of_neg.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_bot_of_neg","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":118,"value_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_bot_of_pos.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_bot_of_pos","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":111,"value_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top._proof_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top","reducibility":null,"statement_dag_size":102,"type_refs":["And","Bot.bot","EReal","EReal.instMul","Eq","HMul.hMul","Iff","LT.lt","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Top.top","Zero.toOfNat0","instBotEReal","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":2392,"value_refs":["And","And.casesOn","Bot.bot","Classical.byContradiction","EReal","EReal.instMul","EReal.mul_comm","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HMul.hMul","Iff","LT.lt","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Top.top","True","True.intro","Zero.toOfNat0","congr","congrArg","eq_false","eq_true","id","instBotEReal","instHMul","instPartialOrderEReal","instTopEReal","instZeroEReal","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top","reducibility":null,"statement_dag_size":19,"type_refs":["Bot.bot","EReal","Eq","False","Real","Real.toEReal","instBotEReal"],"value_dag_size":19,"value_refs":["Bot.bot","EReal","EReal.coe_ne_bot","Eq","Real","Real.toEReal","eq_false","instBotEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top","reducibility":null,"statement_dag_size":43,"type_refs":["EReal","Eq","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal"],"value_dag_size":44,"value_refs":["EReal","EReal.coe_neg'","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top._simp_1_4","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top","reducibility":null,"statement_dag_size":19,"type_refs":["EReal","Eq","False","Real","Real.toEReal","Top.top","instTopEReal"],"value_dag_size":19,"value_refs":["EReal","EReal.coe_ne_top","Eq","Real","Real.toEReal","Top.top","eq_false","instTopEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top._simp_1_5","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_eq_top","reducibility":null,"statement_dag_size":43,"type_refs":["EReal","Eq","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal"],"value_dag_size":44,"value_refs":["EReal","EReal.coe_pos","LT.lt","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Real.toEReal","Zero.toOfNat0","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_nonneg_iff._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_nonneg_iff","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","le_iff_lt_or_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_nonneg_iff._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_nonneg_iff","reducibility":null,"statement_dag_size":56,"type_refs":["And","EReal","EReal.instMul","Eq","HMul.hMul","LT.lt","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal"],"value_dag_size":58,"value_refs":["And","EReal","EReal.instMul","EReal.mul_pos_iff","HMul.hMul","LT.lt","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","True"],"value_dag_size":38,"value_refs":["LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","eq_true","le_of_lt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff._simp_1_3","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_pos_iff","reducibility":null,"statement_dag_size":205,"type_refs":["AddLeftReflectLT","AddLeftStrictMono","And","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","Eq","ExistsAddOfLE","HMul.hMul","LT.lt","Lattice.toSemilatticeInf","LinearOrder","MulPosStrictMono","MulZeroClass.toZero","OfNat.ofNat","Or","PartialOrder.toPreorder","PosMulStrictMono","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring"],"value_dag_size":215,"value_refs":["AddLeftReflectLT","AddLeftStrictMono","And","Distrib.toAdd","Distrib.toMul","DistribLattice.toLattice","ExistsAddOfLE","HMul.hMul","LT.lt","Lattice.toSemilatticeInf","LinearOrder","MulPosStrictMono","MulZeroClass.toZero","OfNat.ofNat","Or","PartialOrder.toPreorder","PosMulStrictMono","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","Semiring","Zero.toOfNat0","instDistribLatticeOfLinearOrder","instDistribOfSemiring","instHMul","instMulZeroClassOfSemiring","mul_pos_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_sub_of_nonneg_of_ne_top._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_sub_of_nonneg_of_ne_top","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul"],"value_dag_size":51,"value_refs":["Eq.symm","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul","neg_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_sub_of_nonneg_of_nonpos._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_sub_of_nonneg_of_nonpos","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul"],"value_dag_size":51,"value_refs":["Eq.symm","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul","neg_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_top_of_neg.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_top_of_neg","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":118,"value_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_top_of_pos.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.mul_top_of_pos","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"],"value_dag_size":111,"value_refs":["Bot.bot","EReal","LT.lt","OfNat.ofNat","Option.casesOn","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLT","Real","Real.toEReal","Top.top","WithTop","Zero.toOfNat0","instBotEReal","instPartialOrderEReal","instTopEReal","instZeroEReal"]}
+{"definition_height":12,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.recENNReal_neg_coe_ennreal","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal","reducibility":"regular","statement_dag_size":62,"type_refs":["ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.toEReal","EReal","EReal.instNeg","EReal.recENNReal","Eq","LT.lt","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","ProofWanted","Zero.toOfNat0"],"value_dag_size":62,"value_refs":["ENNReal","ENNReal.instPartialOrder","ENNReal.instZero","ENNReal.toEReal","EReal","EReal.instNeg","EReal.recENNReal","Eq","LT.lt","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","ProofWanted.mk","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.right_distrib_of_nonneg._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.right_distrib_of_nonneg","reducibility":null,"statement_dag_size":43,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","ENNReal","ENNReal.instAdd","ENNReal.toEReal","EReal","Eq","HAdd.hAdd","instAddCommMonoidEReal","instHAdd"],"value_dag_size":47,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","ENNReal","ENNReal.instAdd","ENNReal.toEReal","EReal","EReal.coe_ennreal_add","Eq.symm","HAdd.hAdd","instAddCommMonoidEReal","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.right_distrib_of_nonneg._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.right_distrib_of_nonneg","reducibility":null,"statement_dag_size":43,"type_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.toEReal","EReal","EReal.instMul","Eq","HMul.hMul","instDistribOfSemiring","instHMul"],"value_dag_size":47,"value_refs":["CommSemiring.toSemiring","Distrib.toMul","ENNReal","ENNReal.instCommSemiring","ENNReal.toEReal","EReal","EReal.coe_ennreal_mul","EReal.instMul","Eq.symm","HMul.hMul","instDistribOfSemiring","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_le_of_le_add._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_le_of_le_add","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_lt_sub_of_le_of_gt._proof_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_lt_sub_of_le_of_gt","reducibility":null,"statement_dag_size":35,"type_refs":["EReal","Eq","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","instPartialOrderEReal"],"value_dag_size":108,"value_refs":["Classical.byContradiction","EReal","Eq","Eq.mp","Eq.symm","Eq.trans","False","LE.le","LT.lt","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.Order.le_of_not_lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","eq_false","eq_true","id","instIsLinearOrder_mathlib","instIsPartialOrder_mathlib","instLawfulOrderLT_mathlib","instLinearOrderEReal","instPartialOrderEReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_mul_of_nonneg_of_ne_top._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.sub_mul_of_nonneg_of_ne_top","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul"],"value_dag_size":51,"value_refs":["Eq.symm","HMul.hMul","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","instHMul","neg_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.toENNReal_mul._simp_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.toENNReal_mul","reducibility":null,"statement_dag_size":57,"type_refs":["And","EReal","EReal.instMul","Eq","HMul.hMul","LE.le","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal"],"value_dag_size":59,"value_refs":["And","EReal","EReal.instMul","EReal.mul_nonpos_iff","HMul.hMul","LE.le","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","instHMul","instPartialOrderEReal","instZeroEReal","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.toENNReal_mul._simp_1_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.toENNReal_mul","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","True"],"value_dag_size":38,"value_refs":["LE.le","LT.lt","Preorder","Preorder.toLE","Preorder.toLT","eq_true","le_of_lt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.EReal.toReal_neg_eq.match_1_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.EReal.toReal_neg_eq","reducibility":"abbrev","statement_dag_size":32,"type_refs":["EReal","Option.none","Option.some","Real","Unit","WithTop"],"value_dag_size":56,"value_refs":["EReal","Option.casesOn","Option.none","Option.some","Real","Unit","Unit.unit","WithTop"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._proof_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._proof_2","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":null,"statement_dag_size":58,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":61,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_4","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":242,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":463,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_7","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd.match_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":193,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":235,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Nat.hasNotBit","OfNat.ofNat","Option","Option.ctorIdx","Option.some","Qq.Quoted","_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd.match_10","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd.match_4","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":201,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.positive","OfNat.ofNat","Option.some","Qq.Quoted"],"value_dag_size":615,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Option.some.noConfusion","Qq.Quoted","_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_4","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd.match_7","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._sparseCasesOn_7"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul._sparseCasesOn_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul","reducibility":"abbrev","statement_dag_size":282,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":497,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul.match_1","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul","reducibility":"abbrev","statement_dag_size":235,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","OfNat.ofNat","Option.some","Qq.Quoted"],"value_dag_size":704,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Option.some.noConfusion","Qq.Quoted","_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul._sparseCasesOn_1","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul.match_4","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul","reducibility":"abbrev","statement_dag_size":218,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":230,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.EReal.Operations","name":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul.match_6","namespace":"_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealMul","reducibility":"abbrev","statement_dag_size":156,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":168,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Erased","name":"_private.Mathlib.Data.Erased.0.Erased.mk_out.match_1_1","namespace":"_private.Mathlib.Data.Erased.0.Erased.mk_out","reducibility":"abbrev","statement_dag_size":54,"type_refs":["Eq","Erased","Exists","Subtype.mk"],"value_dag_size":79,"value_refs":["Eq","Erased","Exists","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Erased","name":"_private.Mathlib.Data.Erased.0.Erased.nonempty_iff.match_1_1","namespace":"_private.Mathlib.Data.Erased.0.Erased.nonempty_iff","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Erased","Nonempty","Nonempty.intro"],"value_dag_size":34,"value_refs":["Erased","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Erased","name":"_private.Mathlib.Data.Erased.0.Erased.nonempty_iff.match_1_3","namespace":"_private.Mathlib.Data.Erased.0.Erased.nonempty_iff","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FP.Basic","name":"_private.Mathlib.Data.FP.Basic.0.FP.Float.Zero.valid._proof_1_3","namespace":"_private.Mathlib.Data.FP.Basic.0.FP.Float.Zero.valid","reducibility":null,"statement_dag_size":110,"type_refs":["AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","FP.FloatCfg","FP.FloatCfg.emax","FP.prec","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instAddGroup","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","NatCast.natCast","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":422,"value_refs":["AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","FP.FloatCfg","FP.FloatCfg.emax","FP.prec","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instAddGroup","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","NegZeroClass.toZero","Not","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FP.Basic","name":"_private.Mathlib.Data.FP.Basic.0.FP.Float.Zero.valid._simp_1_4","namespace":"_private.Mathlib.Data.FP.Basic.0.FP.Float.Zero.valid","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","OfNat.ofNat","True","instNatCastInt","instOfNat"],"value_dag_size":27,"value_refs":["Int","Int.instLEInt","Int.natCast_nonneg","LE.le","Nat","Nat.cast","OfNat.ofNat","eq_true","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt","reducibility":null,"statement_dag_size":48,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNatNat"],"value_dag_size":422,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","OfNat.ofNat","Option.none","Option.some","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt","reducibility":null,"statement_dag_size":112,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instSub","LE.le","LT.lt","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","ite"],"value_dag_size":895,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLTInt","Int.ofNat_lt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.add_one_le_of_lt","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.castLT_sub_nezero._proof_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.castLT_sub_nezero","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Fin","Fin.val","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","Zero.ofOfNat0","Zero.toOfNat0","instHSub","instLTFin","instOfNatNat","instSubNat"],"value_dag_size":750,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","Zero.ofOfNat0","Zero.toOfNat0","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLTFin","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.castLT_sub_nezero._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.castLT_sub_nezero","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Fin","Fin.val","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","instHSub","instLTFin","instOfNatNat","instSubNat"],"value_dag_size":693,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLTFin","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.cast_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.cast_eq_zero","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.val","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instOfNatNat"],"value_dag_size":55,"value_refs":["Eq","Eq.symm","Fin","Fin.instOfNat","Fin.val","Fin.val_eq_zero_iff","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.cast_injective._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.cast_injective","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":36,"value_refs":["Eq","Eq.symm","Fin","Fin.val","Fin.val_eq_val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Int","Int.instAdd","Nat","NatCast.natCast","instAddNat","instHAdd","instNatCastInt"],"value_dag_size":117,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Fin","Fin.val","HAdd.hAdd","Int","Int.instAdd","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","NatCast.natCast","Not","True","congrArg","congrFun'","eq_self","instAddNat","instHAdd","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":44,"type_refs":["Fin","Fin.val","HAdd.hAdd","Int","Int.instLEInt","LE.le","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat"],"value_dag_size":350,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.not_le_eq","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Semiring.natCast_add","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":50,"type_refs":["Fin","Fin.val","HAdd.hAdd","Int","Int.instLTInt","LT.lt","Nat","NatCast.natCast","instAddNat","instHAdd","instLTNat","instNatCastInt"],"value_dag_size":521,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Int.lt_eq","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Nat","NatCast.natCast","instAddNat","instHAdd","instHSub","instNatCastInt"],"value_dag_size":142,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","NatCast.natCast","Not","True","congrArg","congrFun'","eq_self","instAddNat","instHAdd","instHSub","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_5","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":71,"type_refs":["Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","LT.lt","Nat","NatCast.natCast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":559,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite._proof_1_6","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_ite","reducibility":null,"statement_dag_size":49,"type_refs":["Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLTInt","Int.instSub","LT.lt","Nat","NatCast.natCast","instAddNat","instHAdd","instHSub","instNatCastInt"],"value_dag_size":590,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Int.lt_eq","Lean.Grind.IntInterval.co","Lean.Grind.Semiring.natCast_add","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_mod._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_add_eq_mod","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","False","Fin","Fin.instAdd","Fin.val","HAdd.hAdd","HMod.hMod","Int","Int.instAdd","Int.instMod","Nat","Nat.cast","Not","instHAdd","instHMod","instNatCastInt"],"value_dag_size":397,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instAdd","Fin.val","HAdd.hAdd","HMod.hMod","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Fin.ofNat_val_add","Lean.Omega.Int.add_congr","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instDecidableEqBool","instHAdd","instHMod","instHSub","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instSub","Nat","Nat.cast","Not","instAddNat","instHAdd","instHSub","instNatCastInt","instSubNat"],"value_dag_size":913,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":78,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLEFin","instNatCastInt","instOfNat","instSubNat"],"value_dag_size":825,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","Fin.val_le_of_le","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLEFin","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":62,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLTInt","Int.instSub","LT.lt","Nat","Nat.cast","Not","instAddNat","instHAdd","instHSub","instNatCastInt","instSubNat"],"value_dag_size":831,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Nat","Nat.cast","Not","instAddNat","instHAdd","instHSub","instNatCastInt","instSubNat"],"value_dag_size":916,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_5","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":59,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLEInt","LE.le","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instSubNat"],"value_dag_size":417,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite._proof_1_6","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_ite","reducibility":null,"statement_dag_size":64,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instLTInt","LE.le","LT.lt","Nat","Nat.cast","Not","instAddNat","instHAdd","instHSub","instLEFin","instNatCastInt","instSubNat"],"value_dag_size":802,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","Fin.val_add_one_le_of_lt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Fin.lt_of_not_le","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLEFin","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod","reducibility":null,"statement_dag_size":58,"type_refs":["False","Fin","Fin.val","HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","Not","OfNat.ofNat","instHSub","instLEFin","instNatCastInt","instOfNat"],"value_dag_size":372,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.val","Fin.val_le_of_le","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLEFin","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod","reducibility":null,"statement_dag_size":43,"type_refs":["False","Fin","Fin.val","HSub.hSub","Int","Int.instLTInt","Int.instSub","LT.lt","Nat","Nat.cast","Not","instHSub","instNatCastInt"],"value_dag_size":438,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod","reducibility":null,"statement_dag_size":61,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","Not","OfNat.ofNat","instHAdd","instHSub","instNatCastInt","instOfNat"],"value_dag_size":524,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod","reducibility":null,"statement_dag_size":65,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLTInt","Int.instSub","LE.le","LT.lt","Nat","Nat.cast","Not","instHAdd","instHSub","instLEFin","instNatCastInt"],"value_dag_size":482,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.val","Fin.val_add_one_le_of_lt","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Fin.lt_of_not_le","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLEFin","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.eq_one_of_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.eq_one_of_ne_zero","reducibility":null,"statement_dag_size":28,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":10,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.eq_one_of_ne_zero._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.eq_one_of_ne_zero","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":231,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","Fin","Fin.instOfNat","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper","Lean.Grind.ToInt.ofNat_eq","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.instOfNatFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_le","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":355,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Fin","Fin.val","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_le._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_le","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":88,"type_refs":["And","Eq","Exists","Fin","Fin.instAdd","Fin.instOfNat","HAdd.hAdd","LE.le","LT.lt","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTFin","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":270,"value_refs":["And","Bool","Bool.true","Eq","Eq.refl","Exists","False.elim","Fin","Fin.instAdd","Fin.instOfNat","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.toInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","Neg.neg","OfNat.ofNat","eagerReduce","instAddNat","instHAdd","instLEFin","instLTFin","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":459,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._proof_1_5","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":115,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instSub","LE.le","LT.lt","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","ite"],"value_dag_size":976,"value_refs":["And","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLTInt","Int.ofNat_lt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._simp_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt._simp_1_6","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_eq_add_of_lt","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","Zero.ofOfNat0","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dag_size":193,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Zero.ofOfNat0","Zero.toOfNat0","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt","reducibility":null,"statement_dag_size":24,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":251,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt","reducibility":null,"statement_dag_size":19,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":250,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt._proof_1_5","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Nat","Ne","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":389,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_unsat","Int.instNegInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","eagerReduce","id","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.exists_ne_and_ne_of_two_lt","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Fin","Fin.val","Nat","Ne"],"value_dag_size":36,"value_refs":["Eq.symm","Fin","Fin.val","Fin.val_ne_iff","Nat","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_ext_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_ext_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.val","Fin.val_eq_val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_fun_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_fun_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_fun₂_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.heq_fun₂_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.instNeZeroHAddNatOfNat_mathlib._simp_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.instNeZeroHAddNatOfNat_mathlib","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Ne","NeZero","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":33,"value_refs":["Ne","NeZero","OfNat.ofNat","Zero","Zero.toOfNat0","neZero_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.instNeZeroHAddNatOfNat_mathlib._simp_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.instNeZeroHAddNatOfNat_mathlib","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.decLe","Int.instAdd","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","Not","OfNat.ofNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","ite"],"value_dag_size":761,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.decLe","Int.instAdd","Int.instLEInt","Int.instSub","LE.le","Nat","Nat.cast","Not","instHAdd","instHSub","instNatCastInt","ite"],"value_dag_size":772,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLTInt","Int.ofNat_lt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.intCast_val_sub_eq_sub_add_ite","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.lt_last_iff_ne_last._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.lt_last_iff_ne_last","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","Fin","LE.le","LT.lt","Nat","Ne","instLEFin","instLTFin"],"value_dag_size":40,"value_refs":["And","Fin","Fin.lt_iff_le_and_ne","LE.le","LT.lt","Nat","Ne","instLEFin","instLTFin","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.lt_last_iff_ne_last._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.lt_last_iff_ne_last","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Fin","Fin.last","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","True","instAddNat","instHAdd","instLEFin","instOfNatNat"],"value_dag_size":43,"value_refs":["Fin","Fin.last","Fin.le_last","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","eq_true","instAddNat","instHAdd","instLEFin","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.natCast_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.natCast_eq_zero","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.natCast_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.natCast_eq_zero","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le","reducibility":null,"statement_dag_size":38,"type_refs":["Iff","LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instLENat","instOfNatNat"],"value_dag_size":110,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","True","congrArg","congrFun'","eq_self","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Nontrivial","Not","Subsingleton"],"value_dag_size":21,"value_refs":["Eq.symm","Nontrivial","Not","Subsingleton","not_subsingleton_iff_nontrivial","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.nontrivial_iff_two_le","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Fin","LE.le","Nat","OfNat.ofNat","Subsingleton","instLENat","instOfNatNat"],"value_dag_size":26,"value_refs":["Fin","Fin.subsingleton_iff_le_one","LE.le","Nat","OfNat.ofNat","Subsingleton","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.one_eq_mk._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.one_eq_mk","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.one_le_of_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.one_le_of_ne_zero","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Fin","Fin.instOfNat","LE.le","Nat","NeZero","OfNat.ofNat","True","Zero.ofOfNat0","instLEFin","instOfNatNat"],"value_dag_size":42,"value_refs":["Fin","Fin.instOfNat","Fin.zero_le","LE.le","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","eq_true","instLEFin","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.strong_induction_on.match_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.strong_induction_on","reducibility":"abbrev","statement_dag_size":70,"type_refs":["Fin","Fin.mk","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":98,"value_refs":["Fin","Fin.casesOn","Fin.mk","LT.lt","Nat","instLTFin","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le","reducibility":null,"statement_dag_size":132,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.decLe","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instSub","LE.le","LT.lt","Nat","Nat.cast","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat","ite"],"value_dag_size":1903,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLTInt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLTInt","Int.ofNat_lt","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.sub_succ_le_sub_of_le","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.instLEInt","LE.le","Nat","Nat.cast","instLENat","instNatCastInt"],"value_dag_size":36,"value_refs":["Eq.symm","Int","Int.instLEInt","Int.ofNat_le","LE.le","Nat","Nat.cast","instLENat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Basic","name":"_private.Mathlib.Data.Fin.Basic.0.Fin.val_add_one_of_lt'._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Basic.0.Fin.val_add_one_of_lt'","reducibility":null,"statement_dag_size":43,"type_refs":["Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":478,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.addNatEmb._simp_1","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.addNatEmb","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.equiv_iff_eq.match_1_1","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.equiv_iff_eq","reducibility":"abbrev","statement_dag_size":37,"type_refs":["Equiv","Fin","Nat","Nonempty","Nonempty.intro"],"value_dag_size":46,"value_refs":["Equiv","Fin","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.natAdd_castLEEmb._proof_1","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.natAdd_castLEEmb","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":631,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.pred","HAdd.hAdd","Nat","Nat.instNeZeroSucc","Ne","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":100,"value_refs":["Eq","Fin","Fin.instOfNat","Fin.pred","Fin.pred_inj","HAdd.hAdd","Nat","Nat.instNeZeroSucc","Ne","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff","reducibility":null,"statement_dag_size":50,"type_refs":["DFunLike.coe","EmbeddingLike","Eq","FunLike"],"value_dag_size":58,"value_refs":["DFunLike.coe","EmbeddingLike","EmbeddingLike.apply_eq_iff_eq","Eq","FunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.nonempty_embedding_iff","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Fin","Fin.succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq","Fin","Fin.succ","Fin.succ_inj","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb._proof_1_5","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Fin","Fin.natAdd_castLEEmb._proof_2","Function.Injective","HAdd.hAdd","HSub.hSub","LE.le","Nat","finCongr","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":50,"value_refs":["Equiv.injective","Fin","Fin.natAdd_castLEEmb._proof_2","HAdd.hAdd","HSub.hSub","LE.le","Nat","finCongr","instAddNat","instHAdd","instHSub","instLENat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb._proof_1_6","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb","reducibility":null,"statement_dag_size":46,"type_refs":["Fin","Fin.val","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":418,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","Fin","Fin.natAdd_castLEEmb._proof_2","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":45,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","Nat.sub_le_iff_le_add","instAddNat","instHAdd","instHSub","instLENat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Embedding","name":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb.match_1_3","namespace":"_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb","reducibility":"abbrev","statement_dag_size":227,"type_refs":["DFunLike.coe","Eq","Equiv.toEmbedding","Exists.intro","Fin","Fin.addNatEmb","Fin.natAdd_castLEEmb._proof_2","Function.Embedding","Function.Embedding.trans","Function.instFunLikeEmbedding","HAdd.hAdd","HSub.hSub","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.range","finCongr","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":284,"value_refs":["DFunLike.coe","Eq","Equiv.toEmbedding","Exists.casesOn","Exists.intro","Fin","Fin.addNatEmb","Fin.natAdd_castLEEmb._proof_2","Function.Embedding","Function.Embedding.trans","Function.instFunLikeEmbedding","HAdd.hAdd","HSub.hSub","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.range","finCongr","instAddNat","instHAdd","instHSub","instLENat","instSubNat"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2._aux_Mathlib_Data_Fin_Fin2___unexpand_Fin2_ofNat'_1","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":241,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Fin2.add.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Fin2.add.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Fin2.add.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Fin2.add.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.add.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Fin2.add.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Fin2","Fin2.fs","Fin2.fz","Fin2.toNat.match_1","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":64,"value_refs":["Eq.refl","Fin2","Fin2.fs","Fin2.fz","Fin2.toNat.match_1","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","Fin2","Fin2.fs","Fin2.fz","Fin2.toNat.match_1","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":67,"value_refs":["Eq.refl","Fin2","Fin2.fs","Fin2.fz","Fin2.toNat.match_1","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.toNat.match_1","reducibility":"abbrev","statement_dag_size":53,"type_refs":["Fin2","Fin2.fs","Fin2.fz","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["Fin2.toNat.match_1"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.«_aux_Mathlib_Data_Fin_Fin2___macroRules__private_Mathlib_Data_Fin_Fin2_0_Fin2_term&__1»","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":228,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Fin2","name":"_private.Mathlib.Data.Fin.Fin2.0.Fin2.«term&_»","namespace":"_private.Mathlib.Data.Fin.Fin2.0.Fin2","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":56,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.FlagRange","name":"_private.Mathlib.Data.Fin.FlagRange.0.IsMaxChain.range_fin_of_covBy._simp_1_1","namespace":"_private.Mathlib.Data.Fin.FlagRange.0.IsMaxChain.range_fin_of_covBy","reducibility":null,"statement_dag_size":48,"type_refs":["Bot.bot","Eq","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":52,"value_refs":["Bot.bot","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","bot_lt_iff_ne_bot","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Init","name":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_assoc._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_assoc","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Fin","Fin.instXorOp","HPow.hPow","HXor.hXor","Nat","OfNat.ofNat","instHPow","instHXorOfXorOp","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":749,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.ext","Fin.instXorOp","Fin.val","Fin.xor_val","HMod.hMod","HPow.hPow","HXor.hXor","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_aci","Lean.Grind.AC.diseq_simp_lhs_ac","Lean.Grind.AC.diseq_simp_lhs_exact","Lean.Grind.AC.diseq_simp_rhs_ac","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_aci","Lean.Grind.AC.eq_orient","Lean.Grind.AC.superpose_ac","Lean.Grind.imp_false_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.instAssociativeHXor","Nat.instCommutativeHXor","Nat.instLawfulCommIdentityHXorOfNat","Nat.instMod","Nat.instXorOp","Nat.mod_mod","Nat.xor_mod_two_pow","Not","OfNat.ofNat","PLift","PLift.up","Std.LawfulCommIdentity.toLawfulIdentity","congr","congrArg","eagerReduce","eq_false","id","instHMod","instHPow","instHXorOfXorOp","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Init","name":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_comm._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_comm","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Fin","Fin.instXorOp","HXor.hXor","Nat","instHXorOfXorOp"],"value_dag_size":541,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Fin","Fin.instXorOp","Fin.val","Fin.xor_val","HMod.hMod","HXor.hXor","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instMod","Int.instNegInt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_aci","Lean.Grind.AC.refl","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.mod_congr","Nat.ToInt.of_eq","Nat.cast","Nat.instAssociativeHXor","Nat.instCommutativeHXor","Nat.instLawfulCommIdentityHXorOfNat","Nat.instMod","Nat.instXorOp","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.LawfulCommIdentity.toLawfulIdentity","congrArg","eagerReduce","id","instHMod","instHXorOfXorOp","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Init","name":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_self._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_self","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instXorOp","HXor.hXor","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instHXorOfXorOp","instOfNatNat"],"value_dag_size":394,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.instOfNat","Fin.instXorOp","Fin.val","Fin.xor_val","HMod.hMod","HXor.hXor","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMod","Int.instNegInt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.cast","Nat.instMod","Nat.instXorOp","Nat.xor_self","Nat.zero_mod","NatCast.natCast","NeZero","Neg.neg","Not","OfNat.ofNat","Zero.ofOfNat0","congrArg","eagerReduce","id","instHMod","instHXorOfXorOp","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Init","name":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_zero._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Init.0.Fin.xor_zero","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.instXorOp","HXor.hXor","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instHXorOfXorOp","instOfNatNat"],"value_dag_size":732,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instOfNat","Fin.instXorOp","Fin.isLt","Fin.val","Fin.val_zero","Fin.xor_val","HAdd.hAdd","HMod.hMod","HXor.hXor","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.not_eq_norm_expr","Int.instMod","Int.instNegInt","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_aci","Lean.Grind.AC.eq_simp_rhs_ac","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_aci","Lean.Grind.AC.refl","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.mod_congr","Nat.ToInt.of_eq","Nat.cast","Nat.instAssociativeHXor","Nat.instCommutativeHXor","Nat.instLawfulCommIdentityHXorOfNat","Nat.instMod","Nat.instXorOp","Nat.mod_eq_of_lt","NatCast.natCast","NeZero","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.LawfulCommIdentity.toLawfulIdentity","True","Zero.ofOfNat0","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHMod","instHXorOfXorOp","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_add_one_iff_odd.match_1_1","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_add_one_iff_odd","reducibility":"abbrev","statement_dag_size":127,"type_refs":["Eq","Even","Exists.intro","Fin","Fin.instAdd","Fin.instOfNat","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","OfNat.ofNat","instHAdd"],"value_dag_size":162,"value_refs":["Eq","Even","Exists.casesOn","Exists.intro","Fin","Fin.instAdd","Fin.instOfNat","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","OfNat.ofNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_iff_of_even._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_iff_of_even","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Even","HSub.hSub","Iff","LE.le","Nat","instAddNat","instHSub","instLENat","instSubNat"],"value_dag_size":42,"value_refs":["Even","HSub.hSub","Iff","LE.le","Nat","Nat.even_sub","instAddNat","instHSub","instLENat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Iff"],"value_dag_size":17,"value_refs":["Iff","iff_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Even","Nat","Nat.instSemiring","Not","Odd","instAddNat"],"value_dag_size":27,"value_refs":["Eq.symm","Even","Nat","Nat.instSemiring","Nat.not_even_iff_odd","Not","Odd","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Iff","Not"],"value_dag_size":20,"value_refs":["Iff","Not","not_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove._simp_1_4","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.even_succAbove_add_predAbove","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Iff","Not"],"value_dag_size":20,"value_refs":["Iff","Not","not_iff_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.odd_add_one_iff_even.match_1_1","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.odd_add_one_iff_even","reducibility":"abbrev","statement_dag_size":238,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","CommRing.toCommSemiring","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Exists.intro","Fin","Fin.instAdd","Fin.instCommRing","Fin.instOfNat","HAdd.hAdd","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","NonAssocSemiring.toAddCommMonoidWithOne","Odd","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHAdd","instHMul","instOfNatAtLeastTwo"],"value_dag_size":314,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","CommRing.toCommSemiring","CommSemiring.toSemiring","Distrib.toAdd","Distrib.toMul","Eq","Exists.casesOn","Exists.intro","Fin","Fin.instAdd","Fin.instCommRing","Fin.instOfNat","HAdd.hAdd","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","NeZero","NonAssocSemiring.toAddCommMonoidWithOne","Odd","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHAdd","instHMul","instOfNatAtLeastTwo"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Parity","name":"_private.Mathlib.Data.Fin.Parity.0.Fin.odd_iff_of_even._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Parity.0.Fin.odd_iff_of_even","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HMod.hMod","Nat","Nat.instMod","Nat.instSemiring","Odd","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq","HMod.hMod","Nat","Nat.instMod","Nat.instSemiring","Nat.odd_iff","Odd","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castAdd_inj._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castAdd_inj","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castLE_inj._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castLE_inj","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj._simp_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj._simp_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj._simp_1_4","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_inj","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LE.le","Nat","instLEFin","instLENat"],"value_dag_size":41,"value_refs":["Eq.symm","Fin","Fin.le_def","Fin.val","LE.le","Nat","instLEFin","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_succAbove_castPred._simp_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castPred_succAbove_castPred","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Fin","Fin.castSucc","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":55,"value_refs":["Eq.symm","Fin","Fin.castSucc","Fin.castSucc_succAbove_castSucc","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_lt_or_lt_succ._proof_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_lt_or_lt_succ","reducibility":null,"statement_dag_size":48,"type_refs":["Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":463,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_lt_or_lt_succ._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_lt_or_lt_succ","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":35,"value_refs":["Fin","Fin.lt_def","Fin.val","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt","reducibility":null,"statement_dag_size":32,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":31,"value_refs":["HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt._proof_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt._proof_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_ne_zero_of_lt","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Fin","Fin.castSucc","Fin.instOfNat","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":409,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.castSucc","Fin.castSucc_ne_zero_iff","Fin.instOfNat","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.toInt","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","eq_true","id","instAddNat","instHAdd","instLTFin","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_pos_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_pos_iff","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.val","LT.lt","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instLTFin","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["Eq.symm","Fin","Fin.instOfNat","Fin.val","Fin.val_pos_iff","LT.lt","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instLTFin","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Fin","Nat"],"value_dag_size":36,"value_refs":["Eq","Eq.rec","Fin","Nat","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Fin","Nat"],"value_dag_size":24,"value_refs":["Eq","Eq.symm","Fin","Nat","_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_6","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Eq.rec","Fin","Fin.cast","Nat","cast","rfl"],"value_dag_size":793,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.cast","Fin.val","Fin.val.hcongr_2","Fin.val_cast","HEq.symm","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.not_eq_norm_expr","Int.instLEInt","Int.instLTInt","Int.instNegInt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.ToInt.toInt.hcongr_4","Lean.Grind.forall_imp_eq_or","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast.hcongr_1","Lean.Grind.nestedProof","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.of_eq","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_1","_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_eq_cast._proof_1_2","cast","cast_heq","congrArg","eagerReduce","eq_false","eq_of_heq","funext","id","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","or_false","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_inj._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.cast_inj","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":36,"value_refs":["Eq","Eq.symm","Fin","Fin.val","Fin.val_inj","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.coe_succ_lt_iff_lt._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.coe_succ_lt_iff_lt","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Fin","Fin.castSucc","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat"],"value_dag_size":54,"value_refs":["Fin","Fin.castSucc","Fin.castSucc_lt_castSucc_iff","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_fin_succ'.match_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_fin_succ'","reducibility":"abbrev","statement_dag_size":67,"type_refs":["Exists","Exists.intro","Fin","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":85,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_fin_succ'.match_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_fin_succ'","reducibility":"abbrev","statement_dag_size":70,"type_refs":["Exists","Exists.intro","Fin","Fin.castSucc","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":88,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Fin.castSucc","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_succ_eq.match_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.exists_succ_eq","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Eq","Exists","Exists.intro","Fin","Fin.succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":113,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Fin","Fin.succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.forall_fin_succ'.match_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.forall_fin_succ'","reducibility":"abbrev","statement_dag_size":80,"type_refs":["And","And.intro","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":98,"value_refs":["And","And.casesOn","And.intro","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.le_of_castSucc_lt_of_succ_lt._proof_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.le_of_castSucc_lt_of_succ_lt","reducibility":null,"statement_dag_size":67,"type_refs":["Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":477,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.le_of_castSucc_lt_of_succ_lt._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.le_of_castSucc_lt_of_succ_lt","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":35,"value_refs":["Fin","Fin.lt_def","Fin.val","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_last._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_last","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Fin","Fin.last","Fin.succ","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq.symm","Fin","Fin.last","Fin.succ","Fin.succ_last","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'._simp_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HSub.hSub","LE.le","Nat","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":40,"value_refs":["Eq","HSub.hSub","LE.le","Nat","Nat.sub_eq_zero_iff_le","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'._simp_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_one'","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","HMod.hMod","LE.le","Nat","Nat.instMod","True","instHMod","instLENat"],"value_dag_size":28,"value_refs":["HMod.hMod","LE.le","Nat","Nat.instMod","Nat.mod_le","eq_true","instHMod","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_succAbove_pred._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.pred_succAbove_pred","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Fin","Fin.succ","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":55,"value_refs":["Eq.symm","Fin","Fin.succ","Fin.succAbove","Fin.succ_succAbove_succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.range_castLE.match_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.range_castLE","reducibility":"abbrev","statement_dag_size":88,"type_refs":["Eq","Exists.intro","Fin","Fin.castLE","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.range","instLENat"],"value_dag_size":118,"value_refs":["Eq","Exists.casesOn","Exists.intro","Fin","Fin.castLE","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.range","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.range_castSucc._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.range_castSucc","reducibility":null,"statement_dag_size":27,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":102,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.sub_castAdd_eq_castAdd_sub_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.sub_castAdd_eq_castAdd_sub_of_le","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Fin","Fin.castAdd","Fin.instSub","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLEFin"],"value_dag_size":788,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.castAdd","Fin.ext","Fin.instSub","Fin.sub_val_of_le","Fin.val","Fin.val_castAdd","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.of_le","Lean.Grind.ToInt.of_not_le","Lean.Grind.ToInt.toInt","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.instLEFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.finVal","Nat.ToInt.of_eq","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLEFin","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_10","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":484,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_11","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1403,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_12","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":678,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_ge","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_13","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1088,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_ge","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_14","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":72,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Fin","Fin.val","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Not","OfNat.ofNat","True","congrArg","eq_self","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_15","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":662,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_16","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":700,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False.elim","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_17","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":582,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_18","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":106,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":717,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_le","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_19","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":474,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_le","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_20","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":476,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_ge","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_21","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":498,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_ge","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_5","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":52,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Fin","Fin.val","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Not","True","congrArg","eq_self"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_6","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":529,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.casesOn","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_7","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":70,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Fin","Fin.val","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Not","OfNat.ofNat","True","congrArg","eq_self","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_8","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1305,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_9","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":111,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1280,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._simp_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":35,"value_refs":["Fin","Fin.lt_def","Fin.val","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succ_injective._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succ_injective","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succ_ne_last_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.succ_ne_last_of_lt","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Fin","Fin.last","Fin.succ","HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat"],"value_dag_size":534,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","Fin","Fin.last","Fin.succ","Fin.val","Fin.val_last","Fin.val_succ","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.toInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","eagerReduce","id","instAddNat","instHAdd","instHMul","instLTFin","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_le","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LE.le","Nat","instLEFin","instLENat"],"value_dag_size":41,"value_refs":["Eq.symm","Fin","Fin.val","Fin.val_fin_le","LE.le","Nat","instLEFin","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt","reducibility":null,"statement_dag_size":63,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":831,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","Fin.val_add_one_le_of_lt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTFin","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt._proof_1_2","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt","reducibility":null,"statement_dag_size":56,"type_refs":["False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":814,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","Fin.val_add_one_le_of_lt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTFin","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt._proof_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_lt","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","False","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":2887,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.val","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.coordinate_eval_6","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_3","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge","reducibility":null,"statement_dag_size":47,"type_refs":["Fin","Fin.last","Fin.val","HAdd.hAdd","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":53,"value_refs":["Eq","Fin","Fin.last","Fin.val_lt_last","HAdd.hAdd","Lean.Grind.nestedProof","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_4","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge","reducibility":null,"statement_dag_size":64,"type_refs":["Fin","Fin.last","Fin.val","HAdd.hAdd","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTNat","instOfNatNat"],"value_dag_size":76,"value_refs":["Eq","Fin","Fin.last","Fin.ne_last_of_ne_last_of_le","Fin.val_lt_last","HAdd.hAdd","LE.le","Lean.Grind.nestedProof","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_5","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge","reducibility":null,"statement_dag_size":66,"type_refs":["Fin","Fin.last","Fin.val","HAdd.hAdd","LT.lt","Nat","Nat.instPreorder","Ne","OfNat.ofNat","Preorder.toLT","instAddNat","instHAdd","instLTFin","instOfNatNat"],"value_dag_size":80,"value_refs":["Fin","Fin.last","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","Nat","Nat.instPreorder","Ne","OfNat.ofNat","_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_3","instAddNat","instHAdd","instLTFin","instLTNat","instOfNatNat","lt_trans"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPred","name":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_6","namespace":"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","Fin","Fin.castPred","Fin.instSub","Fin.last","Fin.ne_last_of_ne_last_of_le","Fin.val","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLEFin","instLTFin","instOfNatNat","instSubNat"],"value_dag_size":1368,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.castLT","Fin.castPred","Fin.castPred.eq_1","Fin.instSub","Fin.last","Fin.ne_last_of_ne_last_of_le","Fin.val","Fin.val_lt_last","Fin.val_sub_castLT_of_lt","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.toInt","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.finVal","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.cast","Nat.instPreorder","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","True","_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_3","_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_4","_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castPred_of_ge._proof_1_5","congr","congrArg","congrFun'","eagerReduce","eq_of_heq","eq_true","forall_congr","id","instAddNat","instHAdd","instHMul","instHSub","instLEFin","instLTFin","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_congr","lt_trans","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPredOrder","name":"_private.Mathlib.Data.Fin.SuccPredOrder.0.Fin.instPredOrder._simp_1","namespace":"_private.Mathlib.Data.Fin.SuccPredOrder.0.Fin.instPredOrder","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin","Fin.castSucc","Fin.succ","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTFin","instOfNatNat"],"value_dag_size":59,"value_refs":["Fin","Fin.castSucc","Fin.le_castSucc_iff","Fin.succ","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.SuccPredOrder","name":"_private.Mathlib.Data.Fin.SuccPredOrder.0.Fin.instSuccOrder._simp_3","namespace":"_private.Mathlib.Data.Fin.SuccPredOrder.0.Fin.instSuccOrder","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin","Fin.castSucc","Fin.succ","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTFin","instOfNatNat"],"value_dag_size":59,"value_refs":["Fin","Fin.castSucc","Fin.castSucc_lt_iff_succ_le","Fin.succ","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLEFin","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.append_assoc._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.append_assoc","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Fin","Fin.cast","Fin.natAdd","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"],"value_dag_size":56,"value_refs":["Eq.symm","Fin","Fin.cast","Fin.natAdd","Fin.natAdd_natAdd","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.append_left'._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.append_left'","reducibility":null,"statement_dag_size":22,"type_refs":["HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":111,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_le_cons._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_le_cons","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","LE","LE.le","Pi.hasLe"],"value_dag_size":48,"value_refs":["LE","LE.le","Pi.hasLe","Pi.le_def","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_snoc_eq_snoc_cons._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_snoc_eq_snoc_cons","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Fin","Fin.castSucc","Fin.succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.symm","Fin","Fin.castSucc","Fin.castSucc_succ","Fin.succ","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_update._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.cons_update","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","Ne"],"value_dag_size":25,"value_refs":["Eq","Ne","Ne.symm","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.eq_insertNth_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.eq_insertNth_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_succ_pi.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_succ_pi","reducibility":"abbrev","statement_dag_size":82,"type_refs":["Exists","Exists.intro","Fin","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":99,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_succ_pi.match_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_succ_pi","reducibility":"abbrev","statement_dag_size":192,"type_refs":["Exists","Exists.intro","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":280,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_zero_pi.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.exists_fin_zero_pi","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists","Exists.intro","Fin","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":69,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find?_eq_dite._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find?_eq_dite","reducibility":null,"statement_dag_size":51,"type_refs":["Bool","Bool.true","Eq","Exists","Fin","Fin.find","Fin.findSome?","Nat","Option","Option.guard","Option.some","instDecidableEqBool"],"value_dag_size":299,"value_refs":["And","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.find","Fin.find?","Fin.find?_eq_some_iff","Fin.findSome?","Fin.find_min","Fin.find_spec","Iff","LT.lt","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Nat","Not","Option","Option.guard","Option.some","True","True.intro","eq_false","eq_true","id","implies_congr","instDecidableEqBool","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find?_eq_dite._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find?_eq_dite","reducibility":null,"statement_dag_size":39,"type_refs":["Bool","Bool.true","Eq","Exists","Fin","Fin.findSome?","Nat","Not","Option","Option.guard","Option.none"],"value_dag_size":148,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","False","Fin","Fin.find?","Fin.find?_eq_none_iff","Fin.findSome?","Iff","Lean.Grind.iff_eq","Lean.Grind.not_exists","Nat","Not","Option","Option.guard","Option.none","True","True.intro","eq_false","eq_true","forall_congr","id"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin","reducibility":"regular","statement_dag_size":48,"type_refs":["And","DecidablePred","Exists","Fin","LT.lt","Nat","Not","Subtype","instLTFin"],"value_dag_size":34,"value_refs":["DecidablePred","Exists","Fin","Nat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_8","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_11","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":53,"type_refs":["Exists","Fin","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":52,"value_refs":["Classical.choose","Exists","Fin","Fin.pos","HAdd.hAdd","Nat","Nat.sub_lt","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_12","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":62,"type_refs":["Exists","Fin","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":85,"value_refs":["Eq.mpr_prop","Exists","Fin","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_14","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":114,"type_refs":["Exists","Exists.choose","Fin","Fin.mk","Fin.pos","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.sub_lt","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1831,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","False","Fin","Fin.mk","Fin.mk.hcongr_3","Fin.pos","HAdd.hAdd","HEq","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.intro_with_eq'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.sub_lt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_11","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_12","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_9","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_15","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":50,"type_refs":["Exists","Fin","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Eq.substr","Eq.trans","Exists","Fin","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","Nat.sub_zero","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","congrArg","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_16","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":28,"type_refs":["Exists","Fin","LT.lt","Nat","instLTNat"],"value_dag_size":67,"value_refs":["Eq.mp","Exists","Fin","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_15","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_17","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":70,"type_refs":["Exists","False","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":358,"value_refs":["Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","Fin","Fin.mk","HAdd.hAdd","HEq","HEq.refl","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Nat","Nat.sub_zero","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_15","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_16","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","congrArg","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":40,"type_refs":["Exists","Fin","HSub.hSub","LT.lt","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":777,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_8","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":52,"type_refs":["Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTNat","instSubNat"],"value_dag_size":200,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_prop","Eq.refl","Eq.trans","Exists","False","False.casesOn","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq'","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.le_zero_eq","Nat.sub_self","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","congrArg","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_9","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":null,"statement_dag_size":64,"type_refs":["Exists","Fin","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":90,"value_refs":["Eq.substr","Exists","Fin","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":"regular","statement_dag_size":82,"type_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","Subtype","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":113,"value_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Nat.brecOn","Not","Subtype","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._f","instHSub","instLTFin","instLTNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._f","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":"abbrev","statement_dag_size":99,"type_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Nat.below","Not","Subtype","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":401,"value_refs":["And","And.intro","DecidablePred","Exists","Exists.choose","False","Fin","Fin.mk","Fin.pos","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.below","Nat.sub_lt","Nat.succ","Not","OfNat.ofNat","Subtype","Subtype.mk","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_14","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_17","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_3","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_6","absurd","dite","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":null,"statement_dag_size":58,"type_refs":["Exists","Fin","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":67,"value_refs":["Exists","Fin","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":null,"statement_dag_size":121,"type_refs":["And","Exists","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_11","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_1","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":144,"value_refs":["And.intro","Exists","Exists.choose","Fin","Fin.mk","Fin.pos","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.sub_lt","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_11","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_1","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":null,"statement_dag_size":46,"type_refs":["Exists","Fin","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":52,"value_refs":["Exists","Fin","HSub.hSub","LT.lt","Nat","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_4","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":null,"statement_dag_size":66,"type_refs":["Exists","False","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_3","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":97,"value_refs":["Exists","False","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_17","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_3","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_3","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._sunfold","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":"regular","statement_dag_size":82,"type_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","Subtype","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":268,"value_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","OfNat.ofNat","Subtype","Subtype.mk","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_11","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_14","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_1","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_2","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_3","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._proof_4","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_6","absurd","dite","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._unsafe_rec","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go","reducibility":"opaque","statement_dag_size":82,"type_refs":["And","DecidablePred","Exists","Fin","Fin.mk","HSub.hSub","LT.lt","Nat","Not","Subtype","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instHSub","instLTFin","instLTNat","instSubNat"],"value_dag_size":322,"value_refs":["And","And.intro","DecidablePred","Exists","Exists.choose","False","Fin","Fin.mk","Fin.pos","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.sub_lt","Not","OfNat.ofNat","Subtype","Subtype.mk","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_10","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_14","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_17","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.go._unsafe_rec","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_3","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_6","absurd","dite","instAddNat","instHAdd","instHSub","instLTFin","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists","Exists.intro","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":99,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Fin.casesOn","Fin.mk","LT.lt","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX.match_6","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX","reducibility":"abbrev","statement_dag_size":141,"type_refs":["Exists","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.succ","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":200,"value_refs":["Exists","Fin","Fin.mk","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.findX._proof_5","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_congr'.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_congr'","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Exists","Exists.intro","Fin","Nat"],"value_dag_size":57,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite","reducibility":null,"statement_dag_size":89,"type_refs":["DecidablePred","Eq","Exists","Fin","Fin.find","Fin.instOfNat","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":182,"value_refs":["Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","False","Fin","Fin.find","Fin.find_eq_zero","Fin.instOfNat","HAdd.hAdd","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","True","True.intro","eq_false","eq_true","id","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite","reducibility":null,"statement_dag_size":71,"type_refs":["Exists","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":104,"value_refs":["Exists","Fin","Fin.exists_fin_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Iff.mp","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Or","Or.resolve_left","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite","reducibility":null,"statement_dag_size":64,"type_refs":["Exists","Fin","Fin.cons._proof_1","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":107,"value_refs":["Exists","Fin","Fin.cons._proof_1","Fin.exists_fin_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Iff.mp","Lean.Grind.nestedProof","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Or","Or.resolve_left","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite","reducibility":null,"statement_dag_size":129,"type_refs":["DecidablePred","Eq","Exists","Fin","Fin.exists_fin_succ","Fin.find","Fin.instOfNat","Fin.succ","HAdd.hAdd","Iff.mp","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Or","Or.resolve_left","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":320,"value_refs":["Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Fin","Fin.exists_fin_succ","Fin.find","Fin.find_of_not_zero","Fin.instOfNat","Fin.succ","HAdd.hAdd","Iff.mp","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Nat","Nat.instNeZeroSucc","Not","OfNat.ofNat","Or","Or.resolve_left","True","True.intro","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_2","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_dite._proof_1_3","eq_false","eq_true","id","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff","reducibility":null,"statement_dag_size":62,"type_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","LT.lt","Lean.Grind.nestedProof","Nat","Not","instLTFin"],"value_dag_size":314,"value_refs":["And","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.find","Fin.find_min","Fin.find_spec","Fin.instLawfulOrderLT","Fin.instPartialOrder","HEq","HEq.refl","LT.lt","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.lt_le_trans","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Nat","Not","Or","PartialOrder.toPreorder","True","True.intro","eq_false","eq_of_heq","eq_true","id","instIsPreorder_mathlib","instLEFin","instLTFin","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff._proof_1_4","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff","reducibility":null,"statement_dag_size":69,"type_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","LE.le","LT.lt","Nat","Not","instLEFin","instLTFin"],"value_dag_size":412,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Exists","False","Fin","Fin.find","Fin.find_spec","Fin.instIsLinearOrder","Fin.instLawfulOrderLT","Fin.instPartialOrder","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.Order.le_of_not_lt","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.of_le","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.instLEFinCoOfNatIntCast","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","eagerReduce","eq_true","id","instIsPartialOrder_mathlib","instLEFin","instLTFin","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_iff","reducibility":"abbrev","statement_dag_size":83,"type_refs":["And","And.intro","Fin","LT.lt","Nat","Not","instLTFin"],"value_dag_size":97,"value_refs":["And","And.casesOn","And.intro","Fin","LT.lt","Nat","Not","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_eq_zero","reducibility":null,"statement_dag_size":57,"type_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","LT.lt","Nat","Not","instLTFin"],"value_dag_size":64,"value_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","Fin.find_eq_iff","LT.lt","Nat","Not","instLTFin","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_le_iff._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_le_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidablePred","Exists","Fin","Fin.find","LE.le","Lean.Grind.nestedProof","Nat","instLEFin"],"value_dag_size":233,"value_refs":["And","Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Fin","Fin.find","Fin.find_spec","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_exists","Nat","Not","Or","True","True.intro","eq_true","false_or","forall_congr","id","implies_congr","instLEFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_le_iff.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_le_iff","reducibility":"abbrev","statement_dag_size":91,"type_refs":["And","And.intro","Exists","Exists.intro","Fin","LE.le","Nat","instLEFin"],"value_dag_size":145,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Fin","LE.le","Nat","instLEFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_lt_iff._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_lt_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidablePred","Exists","Fin","Fin.find","LT.lt","Lean.Grind.nestedProof","Nat","instLTFin"],"value_dag_size":233,"value_refs":["And","Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Fin","Fin.find","Fin.find_spec","LT.lt","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_exists","Nat","Not","Or","True","True.intro","eq_true","false_or","forall_congr","id","implies_congr","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_lt_iff.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_lt_iff","reducibility":"abbrev","statement_dag_size":91,"type_refs":["And","And.intro","Exists","Exists.intro","Fin","LT.lt","Nat","instLTFin"],"value_dag_size":145,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Fin","LT.lt","Nat","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mem_find?_decide._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mem_find?_decide","reducibility":null,"statement_dag_size":28,"type_refs":["DecidablePred","Exists","Fin","Nat"],"value_dag_size":116,"value_refs":["Bool","Bool.true","Decidable","Decidable.decide","DecidablePred","Eq","Eq.mpr_prop","Eq.rec","Exists","Fin","Nat","congrArg","decide_eq_true_eq","funext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mem_find?_decide._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mem_find?_decide","reducibility":null,"statement_dag_size":51,"type_refs":["Decidable.decide","DecidablePred","Exists","Fin","Fin.find","Fin.findSome?","Membership.mem","Nat","Option","Option.guard","Option.instMembership"],"value_dag_size":445,"value_refs":["Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidablePred","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","False","Fin","Fin.find","Fin.find.congr_simp","Fin.find?","Fin.find?_eq_dite","Fin.findSome?","Iff","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Nat","Nat.decidableExistsFin","Not","Option","Option.guard","Option.instMembership","Option.mem_some","Option.none","Option.some","True","True.intro","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mem_find?_decide._proof_1_1","congrArg","decide_eq_true_eq","dite","dite_congr","eq_false","eq_self","eq_true","funext","id","instDecidableEqBool"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mono.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_mono","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Exists","Exists.intro","Fin","Nat"],"value_dag_size":57,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt","reducibility":null,"statement_dag_size":26,"type_refs":["And","Exists","LT.lt","Nat","instLTNat"],"value_dag_size":183,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_exists","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt","reducibility":null,"statement_dag_size":53,"type_refs":["And","Exists","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["And","Eq","Eq.rec","Exists","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","congrArg","congrFun'","funext","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt","reducibility":null,"statement_dag_size":50,"type_refs":["And","Classical.choose","Exists","Exists.choose","LT.lt","Nat","instLTNat"],"value_dag_size":291,"value_refs":["And","Classical.byContradiction","Classical.choose","Classical.choose.congr_simp","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","Exists","Exists.choose","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Nat","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1_1","congr","congrArg","congrFun'","eq_false","eq_true","funext","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt","reducibility":null,"statement_dag_size":77,"type_refs":["And","Classical.choose","Exists","Exists.choose","Fin.mk","Fin.val","Iff","LE.le","LT.lt","Nat","instLENat","instLTNat"],"value_dag_size":747,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Classical.choose","Classical.choose.congr_simp","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.choose","False","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","Iff","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.exists_prop","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_1_1","congr","congrArg","congrFun'","eagerReduce","eq_true","exists_prop_congr","funext","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt._proof_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_nat_lt","reducibility":null,"statement_dag_size":40,"type_refs":["And","Exists","Fin.mk","Fin.val","LT.lt","Nat","instLTNat"],"value_dag_size":591,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin.mk","Fin.val","HAdd.hAdd","HSub.hSub","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.exists_prop","Lean.Grind.forall_or_forall","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_true","exists_prop_congr","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","or_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_find_le._simp_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_find_le","reducibility":null,"statement_dag_size":34,"type_refs":["DecidablePred","Eq","Exists","Fin","Fin.find","Nat","True"],"value_dag_size":37,"value_refs":["DecidablePred","Exists","Fin","Fin.find","Fin.find_spec","Nat","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero","reducibility":null,"statement_dag_size":57,"type_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","LT.lt","Nat","Not","instLTFin"],"value_dag_size":64,"value_refs":["And","DecidablePred","Eq","Exists","Fin","Fin.find","Fin.find_eq_iff","LT.lt","Nat","Not","instLTFin","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":67,"value_refs":["And","Fin","Fin.forall_fin_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.find_of_not_zero","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","Fin","Fin.succ","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat"],"value_dag_size":54,"value_refs":["Fin","Fin.succ","Fin.succ_lt_succ_iff","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.forall_fin_add.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.forall_fin_add","reducibility":"abbrev","statement_dag_size":93,"type_refs":["And","And.intro","Fin","Fin.castAdd","Fin.natAdd","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":111,"value_refs":["And","And.casesOn","And.intro","Fin","Fin.castAdd","Fin.natAdd","HAdd.hAdd","Nat","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_snoc._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_snoc","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","True","instLTNat"],"value_dag_size":22,"value_refs":["Fin","Fin.is_lt","Fin.val","LT.lt","Nat","eq_true","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_update_castSucc._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_update_castSucc","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Fin","Fin.castSucc","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq","Fin","Fin.castSucc","Fin.castSucc_inj","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_update_last._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_update_last","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","False","Fin","LT.lt","Nat","instLTFin"],"value_dag_size":33,"value_refs":["Eq","Fin","Fin.ne_of_lt","LT.lt","Nat","eq_false","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_apply_succAbove._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_apply_succAbove","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Fin","Fin.castSucc","Fin.succAbove","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat"],"value_dag_size":55,"value_refs":["Fin","Fin.castSucc","Fin.succAbove","Fin.succAbove_lt_iff_castSucc_lt","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_eq_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_eq_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_le_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_le_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","LE","LE.le","Pi.hasLe"],"value_dag_size":48,"value_refs":["LE","LE.le","Pi.hasLe","Pi.le_def","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_removeNth._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_removeNth","reducibility":null,"statement_dag_size":94,"type_refs":["And","Eq","Fin","Fin.insertNth","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":100,"value_refs":["And","Eq","Fin","Fin.insertNth","Fin.insertNth_eq_iff","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_update._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.insertNth_update","reducibility":null,"statement_dag_size":94,"type_refs":["And","Eq","Fin","Fin.insertNth","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":100,"value_refs":["And","Eq","Fin","Fin.insertNth","Fin.insertNth_eq_iff","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_find_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_insertNth_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.le_insertNth_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","LE","LE.le","Pi.hasLe"],"value_dag_size":48,"value_refs":["LE","LE.le","Pi.hasLe","Pi.le_def","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_insertNth._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_insertNth","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Exists","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":57,"value_refs":["Exists","Fin","Fin.castSucc","Fin.exists_fin_succ'","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.range_snoc","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.removeNth_removeNth_heq_swap._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.removeNth_removeNth_heq_swap","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","HEq"],"value_dag_size":24,"value_refs":["Eq","HEq","heq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.sigma_eq_iff_eq_comp_cast.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.sigma_eq_iff_eq_comp_cast","reducibility":"abbrev","statement_dag_size":162,"type_refs":["Eq","Exists","Exists.intro","Fin","Fin.cast","Function.comp","Nat","Sigma","Sigma.fst","Sigma.snd"],"value_dag_size":195,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Fin","Fin.cast","Function.comp","Nat","Sigma","Sigma.fst","Sigma.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.sigma_eq_of_eq_comp_cast.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.sigma_eq_of_eq_comp_cast","reducibility":"abbrev","statement_dag_size":165,"type_refs":["Eq","Fin","Fin.cast","Function.comp","Nat","Sigma","Sigma.fst","Sigma.mk","Sigma.snd"],"value_dag_size":329,"value_refs":["Eq","Fin","Fin.cast","Function.comp","Nat","Sigma","Sigma.casesOn","Sigma.fst","Sigma.mk","Sigma.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_castSucc._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_castSucc","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","True","instLTNat"],"value_dag_size":22,"value_refs":["Fin","Fin.is_lt","Fin.val","LT.lt","Nat","eq_true","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_injective_of_injective._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_injective_of_injective","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Fin","Fin.castSucc","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq","Fin","Fin.castSucc","Fin.castSucc_inj","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_update._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.snoc_update","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","Ne"],"value_dag_size":25,"value_refs":["Eq","Ne","Ne.symm","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.update_insertNth._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.update_insertNth","reducibility":null,"statement_dag_size":94,"type_refs":["And","Eq","Fin","Fin.insertNth","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":100,"value_refs":["And","Eq","Fin","Fin.eq_insertNth_iff","Fin.insertNth","Fin.removeNth","Fin.succAbove","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Basic","name":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.val_find.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.val_find","reducibility":"abbrev","statement_dag_size":66,"type_refs":["Exists","Exists.intro","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":86,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","Fin.mk","LT.lt","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Embedding","name":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv._simp_4","namespace":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv","reducibility":null,"statement_dag_size":50,"type_refs":["DFunLike.coe","EmbeddingLike","Eq","FunLike"],"value_dag_size":58,"value_refs":["DFunLike.coe","EmbeddingLike","EmbeddingLike.apply_eq_iff_eq","Eq","FunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Embedding","name":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv._simp_5","namespace":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq","Fin","Fin.instOfNat","Fin.zero_eq_one_iff","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Embedding","name":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv._simp_6","namespace":"_private.Mathlib.Data.Fin.Tuple.Embedding.0.Function.Embedding.twoEmbeddingEquiv","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","False","Nat","Nat.succ"],"value_dag_size":14,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_ne_self","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.cons_mem_piFinset_cons._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.cons_mem_piFinset_cons","reducibility":null,"statement_dag_size":142,"type_refs":["And","Eq","Fin","Fin.fintype","Fin.instOfNat","Fin.succ","Fin.tail","Finset","Finset.instSetLike","Fintype.piFinset","HAdd.hAdd","Membership.mem","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SetLike.instMembership","instAddNat","instDecidableEqFin","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":146,"value_refs":["And","Fin","Fin.fintype","Fin.instOfNat","Fin.mem_piFinset_iff_zero_tail","Fin.succ","Fin.tail","Finset","Finset.instSetLike","Fintype.piFinset","HAdd.hAdd","Membership.mem","Nat","Nat.instNeZeroSucc","OfNat.ofNat","SetLike.instMembership","instAddNat","instDecidableEqFin","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Fintype","Fintype.piFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":72,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Fin","Fin.castSucc","Fin.forall_fin_succ'","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init._simp_1_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_last_init","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_pivot_removeNth._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_pivot_removeNth","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Fintype","Fintype.piFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":72,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_zero_tail._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_zero_tail","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Fintype","Fintype.piFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":72,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_zero_tail._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.mem_piFinset_iff_zero_tail","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":67,"value_refs":["And","Fin","Fin.forall_fin_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.snoc_mem_piFinset_snoc._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Fin.snoc_mem_piFinset_snoc","reducibility":null,"statement_dag_size":127,"type_refs":["And","Eq","Fin","Fin.castSucc","Fin.fintype","Fin.init","Fin.last","Finset","Finset.instSetLike","Fintype.piFinset","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"],"value_dag_size":131,"value_refs":["And","Fin","Fin.castSucc","Fin.fintype","Fin.init","Fin.last","Fin.mem_piFinset_iff_last_init","Finset","Finset.instSetLike","Fintype.piFinset","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_consEquiv._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_consEquiv","reducibility":null,"statement_dag_size":164,"type_refs":["DecidablePred","Eq","Equiv.symm","Equiv.toEmbedding","Fin","Fin.consEquiv","Fin.fintype","Fin.instOfNat","Fin.succ","Fin.tail","Finset","Finset.filter","Finset.instSProd","Finset.map","Fintype.piFinset","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":171,"value_refs":["DecidablePred","Eq.symm","Equiv.symm","Equiv.toEmbedding","Fin","Fin.consEquiv","Fin.fintype","Fin.instOfNat","Fin.succ","Fin.tail","Finset","Finset.filter","Finset.instSProd","Finset.map","Finset.map_consEquiv_filter_piFinset","Fintype.piFinset","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_insertNthEquiv._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_insertNthEquiv","reducibility":null,"statement_dag_size":157,"type_refs":["DecidablePred","Eq","Equiv.symm","Equiv.toEmbedding","Fin","Fin.fintype","Fin.insertNthEquiv","Fin.removeNth","Fin.succAbove","Finset","Finset.filter","Finset.instSProd","Finset.map","Fintype.piFinset","HAdd.hAdd","Nat","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"],"value_dag_size":165,"value_refs":["DecidablePred","Eq.symm","Equiv.symm","Equiv.toEmbedding","Fin","Fin.fintype","Fin.insertNthEquiv","Fin.removeNth","Fin.succAbove","Finset","Finset.filter","Finset.instSProd","Finset.map","Finset.map_insertNthEquiv_filter_piFinset","Fintype.piFinset","HAdd.hAdd","Nat","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_snocEquiv._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.filter_piFinset_eq_map_snocEquiv","reducibility":null,"statement_dag_size":149,"type_refs":["DecidablePred","Eq","Equiv.symm","Equiv.toEmbedding","Fin","Fin.castSucc","Fin.fintype","Fin.init","Fin.last","Fin.snocEquiv","Finset","Finset.filter","Finset.instSProd","Finset.map","Fintype.piFinset","HAdd.hAdd","Nat","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"],"value_dag_size":156,"value_refs":["DecidablePred","Eq.symm","Equiv.symm","Equiv.toEmbedding","Fin","Fin.castSucc","Fin.fintype","Fin.init","Fin.last","Fin.snocEquiv","Finset","Finset.filter","Finset.instSProd","Finset.map","Finset.map_snocEquiv_filter_piFinset","Fintype.piFinset","HAdd.hAdd","Nat","OfNat.ofNat","Prod","SProd.sprod","instAddNat","instDecidableEqFin","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_consEquiv_filter_piFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_consEquiv_filter_piFinset","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":67,"value_refs":["And","Fin","Fin.forall_iff_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_consEquiv_filter_piFinset._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_consEquiv_filter_piFinset","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_insertNthEquiv_filter_piFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_insertNthEquiv_filter_piFinset","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_snocEquiv_filter_piFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_snocEquiv_filter_piFinset","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Fin","Fin.castSucc","Fin.forall_iff_castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Finset","name":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_snocEquiv_filter_piFinset._simp_1_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Finset.0.Finset.map_snocEquiv_filter_piFinset","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq.refl","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1.eq_3","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq.refl","List.Nat.antidiagonalTuple.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple.match_1","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["List.Nat.antidiagonalTuple.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one._simp_1_5","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List","List.flatMap","List.instMembership","List.nil","Membership.mem"],"value_dag_size":53,"value_refs":["Eq","List","List.flatMap","List.flatMap_eq_nil_iff","List.instMembership","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one._simp_1_6","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","List","List.instMembership","List.range","Membership.mem","Nat","instLTNat"],"value_dag_size":30,"value_refs":["LT.lt","List","List.instMembership","List.mem_range","List.range","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one._simp_1_7","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.map","List.nil"],"value_dag_size":42,"value_refs":["Eq","List","List.map","List.map_eq_nil_iff","List.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._proof_1_17","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":272,"type_refs":["And","Eq","Fin","HAdd.hAdd","LT.lt","List","List.Nat.antidiagonal","List.Nat.antidiagonalTuple","List.Pairwise","List.instMembership","List.map","Membership.mem","Nat","Nat.succ","OfNat.ofNat","Or","Pi.Lex","Prod","Prod.fst","Prod.map","Prod.snd","id","instAddNat","instHAdd","instLTFin","instLTNat","instOfNatNat"],"value_dag_size":3885,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_or_forall","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_not","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nat.antidiagonal","List.Nat.antidiagonalTuple","List.Pairwise","List.Pairwise.map","List.instMembership","List.map","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Pi.Lex","Prod","Prod.casesOn","Prod.fst","Prod.map","Prod.map_fst","Prod.map_snd","Prod.mk","Prod.snd","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","forall_not_of_not_exists","funext","id","id.eq_1","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_10","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_11","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_12","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":37,"type_refs":["Eq"],"value_dag_size":43,"value_refs":["Eq","forall_apply_eq_imp_iff₂","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_13","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","HAdd.hAdd","List","List.Nat.antidiagonal","List.instMembership","Membership.mem","Nat","Prod","Prod.fst","Prod.snd","instAddNat","instHAdd"],"value_dag_size":50,"value_refs":["Eq","HAdd.hAdd","List","List.Nat.antidiagonal","List.Nat.mem_antidiagonal","List.instMembership","Membership.mem","Nat","Prod","Prod.fst","Prod.snd","instAddNat","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_14","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_15","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":174,"type_refs":["And","Eq","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","OfNat.ofNat","Or","Pi.Lex","instAddNat","instHAdd","instLTFin","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":182,"value_refs":["And","Eq","Fin","Fin.cons","Fin.instOfNat","Fin.pi_lex_lt_cons_cons","Fin.succ","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","OfNat.ofNat","Or","Pi.Lex","instAddNat","instHAdd","instLTFin","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_16","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_7","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":86,"type_refs":["And","Eq","List","List.Pairwise","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":92,"value_refs":["And","List","List.Pairwise","List.flatMap","List.instMembership","List.pairwise_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_8","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex._simp_1_9","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_pairwise_pi_lex","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":60,"value_refs":["Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_zero_right.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_zero_right","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_10","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_5","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_6","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_7","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","HAdd.hAdd","List","List.Nat.antidiagonal","List.instMembership","Membership.mem","Nat","Prod","Prod.fst","Prod.snd","instAddNat","instHAdd"],"value_dag_size":50,"value_refs":["Eq","HAdd.hAdd","List","List.Nat.antidiagonal","List.Nat.mem_antidiagonal","List.instMembership","Membership.mem","Nat","Prod","Prod.fst","Prod.snd","instAddNat","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_8","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":126,"type_refs":["And","Eq","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":132,"value_refs":["And","Eq","Fin","Fin.cons","Fin.cons_inj","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple._simp_1_9","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.mem_antidiagonalTuple","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.NatAntidiagonal","name":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.nodup_antidiagonalTuple._simp_1_5","namespace":"_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.nodup_antidiagonalTuple","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Function.onFun","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":63,"value_refs":["And","Function.onFun","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatMap","List.instMembership","List.nodup_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":null,"statement_dag_size":47,"type_refs":["Bool","Lean.Expr","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Prod","Prod.fst","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":47,"value_refs":["Bool","Lean.Expr","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Prod","Prod.fst","Qq.Quoted.unsafeMk","Qq.QuotedDefEq.unsafeIntro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat._sparseCasesOn_5","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":"abbrev","statement_dag_size":23,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.succ","Nat.hasNotBit"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat.match_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":"abbrev","statement_dag_size":276,"type_refs":["Lean.BinderInfo.default","Lean.Expr","Lean.Expr.app","Lean.Expr.bvar","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lam","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Impl.betaRev'","Qq.Quoted","Sigma","Sigma.mk","instOfNatNat"],"value_dag_size":327,"value_refs":["Lean.BinderInfo.default","Lean.Expr","Lean.Expr.app","Lean.Expr.bvar","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lam","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Impl.betaRev'","Qq.Quoted","Sigma","Sigma.casesOn","Sigma.mk","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat.match_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":"abbrev","statement_dag_size":23,"type_refs":["Nat","Option","Option.none","Option.some","Unit"],"value_dag_size":36,"value_refs":["Nat","Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat.match_5","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":"abbrev","statement_dag_size":80,"type_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Meta.Simp.SimpM","Lean.Meta.Simp.StepQ","Qq.Quoted"],"value_dag_size":132,"value_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.succ","Lean.Meta.Simp.SimpM","Lean.Meta.Simp.StepQ","Nat.hasNotBit","Qq.Quoted","_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat._sparseCasesOn_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat.match_8","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.prod_univ_ofNat","reducibility":"abbrev","statement_dag_size":106,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.up","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":115,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.casesOn","PLift.up","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.sum_univ_ofNat.match_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.Fin.sum_univ_ofNat","reducibility":"abbrev","statement_dag_size":276,"type_refs":["Lean.BinderInfo.default","Lean.Expr","Lean.Expr.app","Lean.Expr.bvar","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lam","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Impl.betaRev'","Qq.Quoted","Sigma","Sigma.mk","instOfNatNat"],"value_dag_size":327,"value_refs":["Lean.BinderInfo.default","Lean.Expr","Lean.Expr.app","Lean.Expr.bvar","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lam","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Impl.betaRev'","Qq.Quoted","Sigma","Sigma.casesOn","Sigma.mk","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Fin","FinVec.Forall.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":72,"value_refs":["Eq.refl","Fin","FinVec.Forall.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","Fin","FinVec.Forall.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":75,"value_refs":["Eq.refl","Fin","FinVec.Forall.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.Forall.match_1","reducibility":"abbrev","statement_dag_size":64,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["FinVec.Forall.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff._simp_1_6","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Exists","Fin","Nat","OfNat.ofNat","finZeroElim","instOfNatNat"],"value_dag_size":37,"value_refs":["Exists","Fin","Fin.exists_fin_zero_pi","Nat","OfNat.ofNat","finZeroElim","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff._simp_1_8","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","Exists","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":91,"value_refs":["Exists","Fin","Fin.cons","Fin.exists_fin_succ_pi","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Fin","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":72,"value_refs":["Fin","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff._simp_1_6","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Nat","OfNat.ofNat","finZeroElim","instOfNatNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_fin_zero_pi","Nat","OfNat.ofNat","finZeroElim","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff._simp_1_7","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Fin","Fin.cons","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":84,"value_refs":["Fin","Fin.cons","Fin.forall_fin_succ_pi","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.forall_iff","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Fin","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":72,"value_refs":["Fin","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ","reducibility":null,"statement_dag_size":215,"type_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":215,"value_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq.unsafeIntro","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ","reducibility":"regular","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":107,"value_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.brecOn","Qq.Quoted","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._f","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","reducibility":"abbrev","statement_dag_size":97,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.below","Qq.Quoted"],"value_dag_size":319,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Nat.below","Nat.succ","OfNat.ofNat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1","instOfNatNat"]}
+{"definition_height":14,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._sunfold","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","reducibility":"regular","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":299,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._unsafe_rec","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","reducibility":"opaque","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":295,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._unsafe_rec","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq","Eq.ndrec_symm","Nat","Nat.casesOn","Nat.succ","Not","OfNat.ofNat","Unit","Unit.unit","dite","instDecidableEqNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.match_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ","reducibility":"abbrev","statement_dag_size":96,"type_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Nat.succ","OfNat.ofNat","Qq.Quoted","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":127,"value_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Qq.Quoted","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ._proof_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ","reducibility":null,"statement_dag_size":235,"type_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":235,"value_refs":["HAdd.hAdd","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq.unsafeIntro","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":13,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ","reducibility":"regular","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":107,"value_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.brecOn","Qq.Quoted","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS._f","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS","reducibility":"abbrev","statement_dag_size":97,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.below","Qq.Quoted"],"value_dag_size":309,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Nat.below","Nat.succ","OfNat.ofNat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1","instOfNatNat"]}
+{"definition_height":14,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS._sunfold","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS","reducibility":"regular","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":289,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS._unsafe_rec","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS","reducibility":"opaque","statement_dag_size":92,"type_refs":["Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Qq.Quoted"],"value_dag_size":285,"value_refs":["Alternative.failure","Applicative.toPure","Bind.bind","IO.RealWorld","Lean.BinderInfo.default","Lean.Core.CoreM","Lean.Core.instMonadCoreM","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Meta.Context","Lean.Meta.MetaM","Lean.Meta.State","Lean.Meta.instAlternativeMetaM","Lean.Meta.instMonadMetaM","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","Lean.mkRawNatLit","List.cons","List.nil","Monad.toBind","Nat","Pure.pure","Qq.Impl.betaRev'","Qq.Quoted","Qq.Quoted.unsafeMk","ReaderT.instApplicativeOfMonad","StateRefT'","StateRefT'.instMonad","Unit","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS.match_1","_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkSumEqQ.makeRHS._unsafe_rec"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.prod_eq.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.prod_eq","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":115,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","Fin","FinVec.seq.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":91,"value_refs":["Eq.refl","Fin","FinVec.seq.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","Fin","FinVec.seq.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":96,"value_refs":["Eq.refl","Fin","FinVec.seq.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq.match_1","reducibility":"abbrev","statement_dag_size":83,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["FinVec.seq.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq_eq.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.seq_eq","reducibility":"abbrev","statement_dag_size":83,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":117,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1.eq_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":80,"value_refs":["Eq.refl","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1.eq_2","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":80,"value_refs":["Eq.refl","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1.eq_3","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":84,"value_refs":["Eq.refl","Fin","FinVec.sum.match_1","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1.splitter","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum.match_1","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["FinVec.sum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.Tuple.Reflection","name":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum_eq.match_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.sum_eq","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Fin","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":115,"value_refs":["Fin","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.graphEquiv₁._simp_6","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.graphEquiv₁","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_ge_iff_apply_ge_of_antitone._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_ge_iff_apply_ge_of_antitone","reducibility":null,"statement_dag_size":64,"type_refs":["Antitone","Fin","Fin.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLE","instLEFin"],"value_dag_size":241,"value_refs":["Antitone","Antitone.eq_1","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instPartialOrder","LE.le","Lean.Grind.Order.le_trans","Lean.Grind.imp_eq_of_eq_true_left","Nat","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","True","True.intro","eq_false","eq_true","id","instIsPreorder_mathlib","instLEFin","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_gt_iff_apply_gt_of_antitone._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_gt_iff_apply_gt_of_antitone","reducibility":null,"statement_dag_size":64,"type_refs":["Antitone","Fin","Fin.instPartialOrder","LE.le","LT.lt","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLT","instLEFin"],"value_dag_size":252,"value_refs":["Antitone","Antitone.eq_1","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instPartialOrder","LE.le","LT.lt","Lean.Grind.Order.lt_le_trans","Lean.Grind.imp_eq_of_eq_true_left","Nat","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","True","True.intro","eq_false","eq_true","id","instIsPreorder_mathlib","instLEFin","instLawfulOrderLT_mathlib","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_le_iff_apply_le_of_monotone._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_le_iff_apply_le_of_monotone","reducibility":null,"statement_dag_size":64,"type_refs":["Fin","Fin.instPartialOrder","LE.le","Monotone","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLE","instLEFin"],"value_dag_size":240,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instPartialOrder","LE.le","Lean.Grind.Order.le_trans","Lean.Grind.imp_eq_of_eq_true_left","Monotone","Monotone.eq_1","Nat","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","True","True.intro","eq_false","eq_true","id","instIsPreorder_mathlib","instLEFin","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_lt_iff_apply_lt_of_monotone._proof_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_lt_iff_apply_lt_of_monotone","reducibility":null,"statement_dag_size":64,"type_refs":["Fin","Fin.instPartialOrder","LE.le","LT.lt","Monotone","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLT","instLEFin"],"value_dag_size":252,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instPartialOrder","LE.le","LT.lt","Lean.Grind.Order.le_lt_trans","Lean.Grind.imp_eq_of_eq_true_left","Monotone","Monotone.eq_1","Nat","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","True","True.intro","eq_false","eq_true","id","instIsPreorder_mathlib","instLEFin","instLawfulOrderLT_mathlib","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.Tuple.Sort","name":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.sort_eq_refl_iff_monotone._simp_1_1","namespace":"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.sort_eq_refl_iff_monotone","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one._proof_1_3","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one","reducibility":null,"statement_dag_size":36,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":368,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one._proof_1_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Fin","Fin.mk","Fin.succ","HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one._proof_1_3","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":454,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","Fin","Fin.ext","Fin.mk","Fin.succ","Fin.val","Fin.val_succ","HAdd.hAdd","Int","Int.instNegInt","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.imp_false_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.succ","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one._proof_1_3","eagerReduce","eq_false","id","instAddNat","instHAdd","instLTNat","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one.match_1_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_cons_comp_swap_zero_one","reducibility":"abbrev","statement_dag_size":99,"type_refs":["Fin","Fin.mk","Fin.ofNat._proof_1","HAdd.hAdd","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":171,"value_refs":["Fin","Fin.casesOn","Fin.mk","Fin.ofNat._proof_1","HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.instNeZeroSucc","Nat.succ","Nat.zero","OfNat.ofNat","Unit","Unit.unit","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap","reducibility":null,"statement_dag_size":55,"type_refs":["Fin","Fin.instOfNat","Fin.val","HSub.hSub","LT.lt","Nat","Nat.instNeZeroSucc","Nat.succ","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":950,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instOfNat","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.finVal","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.instNeZeroSucc","Nat.not_le_eq","Nat.succ","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_2","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","Nat","NeZero","OfNat.ofNat","Zero.ofOfNat0","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":20,"value_refs":["Nat","Nat.instNeZeroSucc","OfNat.ofNat","instNeZeroNatHAdd_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_3","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","Fin.succ","Fin.val","HSub.hSub","Nat","Nat.instNeZeroSucc","Nat.succ","Ne","OfNat.ofNat","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_1","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1213,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instOfNat","Fin.mk","Fin.succ","Fin.val","Fin.val_succ","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.ofNat_FinZero","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.cast","Nat.instNeZeroSucc","Nat.succ","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instNeZeroNatHAdd_1","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Fin","Fin.instOfNat","Fin.mk","Fin.succ","Fin.val","HSub.hSub","Nat","Nat.instNeZeroSucc","Nat.succ","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_1","instHSub","instOfNatNat","instSubNat"],"value_dag_size":366,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.instOfNat","Fin.mk","Fin.succ","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.ToInt.of_diseq","Lean.Grind.ToInt.of_eq","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instNeZeroSucc","Nat.succ","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_1","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":24,"type_refs":["Lean.Expr","Lean.Expr.ctorIdx","Lean.Expr.lit","Lean.Literal","Nat.hasNotBit"],"value_dag_size":350,"value_refs":["Bool","Bool.false","Eq.refl","Lean.BinderInfo","Lean.Expr","Lean.Expr.app","Lean.Expr.bvar","Lean.Expr.const","Lean.Expr.ctorIdx","Lean.Expr.forallE","Lean.Expr.fvar","Lean.Expr.lam","Lean.Expr.letE","Lean.Expr.lit","Lean.Expr.mdata","Lean.Expr.mvar","Lean.Expr.proj","Lean.Expr.rec","Lean.Expr.sort","Lean.FVarId","Lean.Level","Lean.Literal","Lean.MData","Lean.MVarId","Lean.Name","List","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_5","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":24,"type_refs":["Lean.Literal","Lean.Literal.ctorIdx","Lean.Literal.natVal","Nat","Nat.hasNotBit"],"value_dag_size":74,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Literal","Lean.Literal.ctorIdx","Lean.Literal.natVal","Lean.Literal.rec","Lean.Literal.strVal","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","String","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val.match_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Lean.Expr","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List.nil","Nat","Option","Option.some","Prod","Prod.mk","Qq.Quoted"],"value_dag_size":74,"value_refs":["Lean.Expr","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List.nil","Nat","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","Prod","Prod.casesOn","Prod.mk","Qq.Quoted","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val.match_10","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Option","Option.some"],"value_dag_size":40,"value_refs":["Int","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val.match_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Literal.natVal","Lean.Name.mkStr1","List.nil","Nat","Qq.Quoted"],"value_dag_size":66,"value_refs":["Lean.Expr.const","Lean.Expr.ctorIdx","Lean.Expr.lit","Lean.Level","Lean.Literal","Lean.Literal.ctorIdx","Lean.Literal.natVal","Lean.Name.mkStr1","List.nil","Nat","Nat.hasNotBit","Qq.Quoted","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_4","_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val._sparseCasesOn_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val.match_8","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_val","reducibility":"abbrev","statement_dag_size":41,"type_refs":["Bool","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List.nil","Nat","Prod","Prod.mk","Qq.Quoted"],"value_dag_size":65,"value_refs":["Bool","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List.nil","Nat","Prod","Prod.casesOn","Prod.mk","Qq.Quoted"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt0._proof_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt0","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":255,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMul","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","NatCast.natCast","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt0._simp_1_3","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt0","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":32,"value_refs":["Eq.symm","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt1._simp_1_3","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAlt1","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":32,"value_refs":["Eq.symm","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAppend._proof_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAppend","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":219,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","NatCast.natCast","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAppend._simp_1_2","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_vecAppend","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HAdd.hAdd","LT.lt","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":36,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.add_lt_add_iff_right","instAddNat","instHAdd","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.empty_vecAlt0._simp_1_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.empty_vecAlt0","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.empty_vecAlt1._simp_1_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.empty_vecAlt1","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.matchVecConsPrefix.match_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.matchVecConsPrefix","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Lean.Expr","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List","List.nil","Prod","Prod.mk","Qq.Quoted"],"value_dag_size":66,"value_refs":["Lean.Expr","Lean.Expr.const","Lean.Level","Lean.Name.mkStr1","List","List.nil","Prod","Prod.casesOn","Prod.mk","Qq.Quoted"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.range_cons._simp_1_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.range_cons","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Exists","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":72,"value_refs":["Exists","Fin","Fin.exists_fin_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.range_cons._simp_1_2","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.range_cons","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt0._proof_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt0","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","LT.lt","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":503,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.finVal","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt0_vecAppend._proof_1_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt0_vecAppend","reducibility":null,"statement_dag_size":38,"type_refs":["Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":1181,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.finVal","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend._proof_1_5","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend._proof_1_6","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend","reducibility":null,"statement_dag_size":55,"type_refs":["Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1505,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toAdd","Lean.Grind.Semiring.toMul","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.Simproc.add_sub_add_le","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend._simp_1_4","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAlt1_vecAppend","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq","LT.lt","Nat","Nat.lt_one_iff","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAppend_eq_ite._proof_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.Matrix.vecAppend_eq_ite","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin","Fin.val","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":877,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ","reducibility":"regular","statement_dag_size":52,"type_refs":["Fin","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Qq.Quoted"],"value_dag_size":63,"value_refs":["Fin","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","PSigma.mk","Qq.Quoted","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","reducibility":"regular","statement_dag_size":54,"type_refs":["Fin","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","PSigma","Qq.Quoted"],"value_dag_size":307,"value_refs":["Fin","Fin.mk","Fin.rev","HAdd.hAdd","HSub.hSub","InvImage","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","Qq.Quoted","Qq.Quoted.unsafeMk","WellFounded.Nat.fix","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary._proof_1","dite","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary._proof_1","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary","reducibility":null,"statement_dag_size":161,"type_refs":["Fin","Fin.mk","Fin.rev","HAdd.hAdd","HSub.hSub","InvImage","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","Qq.Quoted","Qq.Quoted.unsafeMk","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1111,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.byContradiction","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.mk","Fin.rev","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","InvImage","LE.le","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.cast","Nat.decLt","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","PSigma","PSigma.casesOn","PSigma.mk","Qq.Quoted","Qq.Quoted.unsafeMk","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary.eq_def","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary","reducibility":null,"statement_dag_size":186,"type_refs":["Eq","Fin","Fin.mk","Fin.rev","HAdd.hAdd","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary","dite","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1082,"value_refs":["Eq","Eq.mpr","Eq.refl","Eq.trans","Fin","Fin.mk","Fin.rev","HAdd.hAdd","HSub.hSub","InvImage","LT.lt","Lean.BinderInfo.default","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","PSigma","PSigma.casesOn","PSigma.mk","PSigma.rec","Qq.Quoted","Qq.Quoted.unsafeMk","WellFounded.Nat.fix","WellFounded.Nat.fix_eq","_private.Mathlib.Data.Fin.VecNotation.0.PSigma.casesOn._arg_pusher","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary._proof_1","congrArg","congrFun'","dite","funext","have_body_congr'","id","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat","wfParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unsafe_rec","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","reducibility":"opaque","statement_dag_size":52,"type_refs":["Fin","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.ToExpr.toExpr","Lean.instToExprNat","List.nil","Nat","Qq.Quoted"],"value_dag_size":139,"value_refs":["Fin","Fin.mk","Fin.rev","HAdd.hAdd","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unsafe_rec","dite","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fin.VecNotation","name":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop.eq_def","namespace":"_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","reducibility":null,"statement_dag_size":149,"type_refs":["Eq","Fin","Fin.mk","Fin.rev","HAdd.hAdd","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","dite","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":167,"value_refs":["Eq","Fin","Fin.mk","Fin.rev","HAdd.hAdd","LT.lt","Lean.BinderInfo.default","Lean.Expr.app","Lean.Expr.const","Lean.Expr.forallE","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.ToExpr.toExpr","Lean.instToExprNat","List.cons","List.nil","Nat","Nat.decLt","Not","OfNat.ofNat","PSigma.mk","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop","_private.Mathlib.Data.Fin.VecNotation.0.PiFin.mkLiteralQ.loop._unary.eq_def","dite","id","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1.eq_1","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","FinEnum.Finset.enum.match_1","List","List.cons","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","FinEnum.Finset.enum.match_1","List","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1.eq_2","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","FinEnum.Finset.enum.match_1","List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","FinEnum.Finset.enum.match_1","List","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1.splitter","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.enum.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["FinEnum.Finset.enum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum._simp_1_4","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum._simp_1_5","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum._simp_1_6","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum._simp_1_7","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum._simp_1_9","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.Finset.mem_enum","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Classical.or_iff_not_imp_left","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.mem_toList._simp_1_2","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.mem_toList","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.mem_toList._simp_1_3","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.mem_toList","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","List","List.finRange","List.instMembership","Membership.mem","Nat","True"],"value_dag_size":26,"value_refs":["Fin","List","List.finRange","List.instMembership","List.mem_finRange","Membership.mem","Nat","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.FinEnum.ofInjective._simp_1","namespace":"_private.Mathlib.Data.FinEnum.0.FinEnum.ofInjective","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Exists","List","List.filterMap","List.instMembership","Membership.mem","Option","Option.some"],"value_dag_size":68,"value_refs":["And","Eq","Exists","List","List.filterMap","List.instMembership","List.mem_filterMap","Membership.mem","Option","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum","name":"_private.Mathlib.Data.FinEnum.0.List.pfunFinEnum._simp_2","namespace":"_private.Mathlib.Data.FinEnum.0.List.pfunFinEnum","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum.Option","name":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1.eq_1","namespace":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Eq.refl","FinEnum.recEmptyOption.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["Eq","Eq.refl","FinEnum.recEmptyOption.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum.Option","name":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1.eq_2","namespace":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Eq.refl","FinEnum.recEmptyOption.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":43,"value_refs":["Eq","Eq.refl","FinEnum.recEmptyOption.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.FinEnum.Option","name":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1.splitter","namespace":"_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["FinEnum.recEmptyOption.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FinEnum.Option","name":"_private.Mathlib.Data.FinEnum.Option.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.FinEnum.Option.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finite.Defs","name":"_private.Mathlib.Data.Finite.Defs.0.Equiv.set_finite_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finite.Defs.0.Equiv.set_finite_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Finite","Set","Set.Elem","Set.Finite"],"value_dag_size":28,"value_refs":["Eq.symm","Finite","Set","Set.Elem","Set.Finite","Set.finite_coe_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Defs","name":"_private.Mathlib.Data.Finite.Defs.0.Finite.nonempty_decidableEq.match_1_1","namespace":"_private.Mathlib.Data.Finite.Defs.0.Finite.nonempty_decidableEq","reducibility":"abbrev","statement_dag_size":51,"type_refs":["Equiv","Exists","Exists.intro","Fin","Nat","Nonempty","Nonempty.intro"],"value_dag_size":84,"value_refs":["Equiv","Exists","Exists.casesOn","Exists.intro","Fin","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Defs","name":"_private.Mathlib.Data.Finite.Defs.0.Finite.of_equiv.match_1_1","namespace":"_private.Mathlib.Data.Finite.Defs.0.Finite.of_equiv","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Equiv","Fin","Finite","Finite.intro","Nat"],"value_dag_size":42,"value_refs":["Equiv","Fin","Finite","Finite.casesOn","Finite.intro","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Defs","name":"_private.Mathlib.Data.Finite.Defs.0.finite_iff_exists_equiv_fin.match_1_1","namespace":"_private.Mathlib.Data.Finite.Defs.0.finite_iff_exists_equiv_fin","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Equiv","Fin","Finite","Finite.intro","Nat"],"value_dag_size":42,"value_refs":["Equiv","Fin","Finite","Finite.casesOn","Finite.intro","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Defs","name":"_private.Mathlib.Data.Finite.Defs.0.finite_iff_exists_equiv_fin.match_1_3","namespace":"_private.Mathlib.Data.Finite.Defs.0.finite_iff_exists_equiv_fin","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Equiv","Exists","Exists.intro","Fin","Nat","Nonempty","Nonempty.intro"],"value_dag_size":86,"value_refs":["Equiv","Exists","Exists.casesOn","Exists.intro","Fin","Nat","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finite.Perm","name":"_private.Mathlib.Data.Finite.Perm.0.Equiv.Perm.isMulCommutative_iff_card_le_two._simp_1_1","namespace":"_private.Mathlib.Data.Finite.Perm.0.Equiv.Perm.isMulCommutative_iff_card_le_two","reducibility":null,"statement_dag_size":46,"type_refs":["DFunLike.coe","Eq","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike"],"value_dag_size":49,"value_refs":["DFunLike.coe","Eq","Equiv.Perm","Equiv.Perm.ext_iff","Equiv.instEquivLike","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Prod","name":"_private.Mathlib.Data.Finite.Prod.0.Prod.finite_iff.match_1_1","namespace":"_private.Mathlib.Data.Finite.Prod.0.Prod.finite_iff","reducibility":"abbrev","statement_dag_size":39,"type_refs":["And","And.intro","Finite"],"value_dag_size":53,"value_refs":["And","And.casesOn","And.intro","Finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Prod","name":"_private.Mathlib.Data.Finite.Prod.0.Set.Finite.of_prod_left.match_1_1","namespace":"_private.Mathlib.Data.Finite.Prod.0.Set.Finite.of_prod_left","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership"],"value_dag_size":69,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finite.Prod","name":"_private.Mathlib.Data.Finite.Prod.0.Set.Finite.of_prod_right.match_1_1","namespace":"_private.Mathlib.Data.Finite.Prod.0.Set.Finite.of_prod_right","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership"],"value_dag_size":69,"value_refs":["Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Nonempty","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finite.Prod","name":"_private.Mathlib.Data.Finite.Prod.0.Set.finite_image2._proof_1_1","namespace":"_private.Mathlib.Data.Finite.Prod.0.Set.finite_image2","reducibility":null,"statement_dag_size":43,"type_refs":["And","Iff","Or","Set","Set.Infinite","Set.Nonempty"],"value_dag_size":922,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Not","Or","Or.casesOn","Set","Set.Infinite","Set.Infinite.nonempty","Set.Nonempty","True","True.intro","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finite.Prod","name":"_private.Mathlib.Data.Finite.Prod.0.Set.infinite_prod._simp_1_1","namespace":"_private.Mathlib.Data.Finite.Prod.0.Set.infinite_prod","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":24,"value_refs":["And","Classical.not_imp","Eq.symm","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.any._simp_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.any","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_empty.match_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_empty","reducibility":"abbrev","statement_dag_size":67,"type_refs":["EmptyCollection.emptyCollection","Finmap","Finmap.instEmptyCollection","Finmap.instMembership","Membership.mem"],"value_dag_size":283,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.refl","False","False.elim","Finmap","Finmap.instEmptyCollection","Finmap.instMembership","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.map","List.nil","Membership.mem","Sigma","Sigma.fst","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_union_left._simp_1_2","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_union_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_union_left._simp_1_3","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.disjoint_union_left","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.ext.match_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.ext","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Eq","Finmap","Finmap.entries","Finmap.mk","Multiset","Multiset.NodupKeys","Sigma"],"value_dag_size":197,"value_refs":["Eq","Finmap","Finmap.casesOn","Finmap.entries","Finmap.mk","Multiset","Multiset.NodupKeys","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.extract._simp_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.extract","reducibility":null,"statement_dag_size":45,"type_refs":["AList","AList.entries","AList.toFinmap","Eq","Finmap","List.Perm","Sigma"],"value_dag_size":49,"value_refs":["AList","AList.entries","AList.toFinmap","AList.toFinmap_eq","Eq","Finmap","List.Perm","Sigma","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.insert_insert_of_ne._simp_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.insert_insert_of_ne","reducibility":null,"statement_dag_size":45,"type_refs":["AList","AList.entries","AList.toFinmap","Eq","Finmap","List.Perm","Sigma"],"value_dag_size":49,"value_refs":["AList","AList.entries","AList.toFinmap","AList.toFinmap_eq","Eq","Finmap","List.Perm","Sigma","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv._simp_11","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv","reducibility":null,"statement_dag_size":33,"type_refs":["Bool","Bool.true","Eq","Exists","Option","Option.isSome","Option.some"],"value_dag_size":36,"value_refs":["Bool","Bool.true","Eq","Exists","Option","Option.isSome","Option.isSome_iff_exists","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv._simp_12","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finmap","Finmap.entries","Finmap.lookup","Membership.mem","Multiset","Multiset.instMembership","Option","Option.some","Sigma","Sigma.mk"],"value_dag_size":70,"value_refs":["DecidableEq","Eq","Finmap","Finmap.entries","Finmap.lookup","Finmap.lookup_eq_some_iff","Membership.mem","Multiset","Multiset.instMembership","Option","Option.some","Sigma","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv._simp_3","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv","reducibility":null,"statement_dag_size":91,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.fst","Sigma.snd"],"value_dag_size":96,"value_refs":["And","Finset","Finset.instSetLike","Finset.mem_sigma","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.fst","Sigma.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv._simp_4","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Option","Option.instMembership","Option.toFinset","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Membership.mem","Option","Option.instMembership","Option.mem_toFinset","Option.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv._simp_5","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.keysLookupEquiv","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":33,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finmap","Finmap.instEmptyCollection","Finmap.instMembership","Membership.mem"],"value_dag_size":34,"value_refs":["EmptyCollection.emptyCollection","Finmap","Finmap.instEmptyCollection","Finmap.instMembership","Finmap.notMem_empty","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_2","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_3","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":13,"type_refs":["Eq","Exists","False"],"value_dag_size":13,"value_refs":["Exists","False","eq_false","exists_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_4","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_5","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_6","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_7","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","HEq","Sigma","Sigma.mk"],"value_dag_size":56,"value_refs":["And","Eq","HEq","Sigma","Sigma.mk","Sigma.mk.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_8","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","True"],"value_dag_size":20,"value_refs":["Eq","Exists","eq_true","exists_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap._simp_1_9","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_list_toFinmap","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","HEq"],"value_dag_size":24,"value_refs":["Eq","HEq","heq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.mem_singleton._simp_1_2","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.mem_singleton","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Finmap","Finmap.entries","Finmap.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.keys"],"value_dag_size":52,"value_refs":["Finmap","Finmap.entries","Finmap.instMembership","Finmap.mem_def","Membership.mem","Multiset","Multiset.instMembership","Multiset.keys","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.sigma_keys_lookup._simp_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.sigma_keys_lookup","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finmap","Finmap.entries","Finmap.lookup","Membership.mem","Multiset","Multiset.instMembership","Option","Option.some","Sigma","Sigma.mk"],"value_dag_size":70,"value_refs":["DecidableEq","Eq","Finmap","Finmap.entries","Finmap.lookup","Finmap.lookup_eq_some_iff","Membership.mem","Multiset","Multiset.instMembership","Option","Option.some","Sigma","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.Finmap.union_assoc._simp_1_1","namespace":"_private.Mathlib.Data.Finmap.0.Finmap.union_assoc","reducibility":null,"statement_dag_size":58,"type_refs":["AList","AList.entries","AList.instUnion","DecidableEq","Eq","List.Perm","Sigma","True","Union.union"],"value_dag_size":62,"value_refs":["AList","AList.entries","AList.instUnion","AList.union_assoc","DecidableEq","List.Perm","Sigma","Union.union","eq_true"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0._aux_Mathlib_Data_Finmap___unexpand_AList_toFinmap_1","namespace":"_private.Mathlib.Data.Finmap.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":239,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.«_aux_Mathlib_Data_Finmap___macroRules__private_Mathlib_Data_Finmap_0_term⟦_⟧_1»","namespace":"_private.Mathlib.Data.Finmap.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":227,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finmap","name":"_private.Mathlib.Data.Finmap.0.«term⟦_⟧»","namespace":"_private.Mathlib.Data.Finmap.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":55,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finset.Attr","name":"_private.Mathlib.Data.Finset.Attr.0.initFn._@.Mathlib.Data.Finset.Attr.3237354494._hygCtx._hyg.3","namespace":"_private.Mathlib.Data.Finset.Attr.0.initFn._@.Mathlib.Data.Finset.Attr.3237354494._hygCtx._hyg","reducibility":"regular","statement_dag_size":3,"type_refs":["IO","Unit"],"value_dag_size":37,"value_refs":["Aesop.Frontend.declareRuleSetUnchecked","Aesop.RuleSetName","Array.forM","Array.mkArray1","Array.size","Bool.true","IO","IO.Error","Lean.Name","Lean.Name.mkStr1","Nat","OfNat.ofNat","instMonadEIO","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.disjUnionEquiv_symm_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.disjUnionEquiv_symm_left","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_eq","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.disjUnionEquiv_symm_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.disjUnionEquiv_symm_right","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_eq","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.union_symm_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.union_symm_left","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_eq","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.union_symm_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.union_symm_right","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_eq","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.attach_eq_empty_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.attach_eq_empty_iff","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjUnion_eq_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjUnion_eq_union","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instUnion","Union.union"],"value_dag_size":329,"value_refs":["Classical.byContradiction","DecidableEq","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.disjUnion","Finset.ext","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.instUnion","Finset.mem_disjUnion","Finset.mem_union","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SetLike.instMembership","Union.union","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":60,"value_refs":["Disjoint","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjUnion","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_left","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":60,"value_refs":["Disjoint","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjUnion","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_disjUnion_right","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_erase_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_erase_comm","reducibility":null,"statement_dag_size":51,"type_refs":["Disjoint","Eq","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedBooleanAlgebra.toSDiff","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder"],"value_dag_size":56,"value_refs":["Disjoint","GeneralizedBooleanAlgebra","GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedBooleanAlgebra.toOrderBot","GeneralizedBooleanAlgebra.toSDiff","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","SDiff.sdiff","SemilatticeInf.toPartialOrder","disjoint_sdiff_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter_filter'._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter_filter'","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter_filter'._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_filter_filter'","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_left","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.disjoint_union_right","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Finset","Finset.cons","Finset.erase","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":555,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.cons","Finset.erase","Finset.ext","Finset.instSetLike","Finset.mem_cons","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons_of_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons_of_ne","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","False","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":57,"value_refs":["DecidableEq","Finset","Finset.erase","Finset.erase_subset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons_of_ne._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons_of_ne","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.cons","Finset.erase","Finset.erase_subset","Finset.instSetLike","Membership.mem","Ne","Not","SetLike.instMembership"],"value_dag_size":943,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.cons","Finset.erase","Finset.erase_subset","Finset.ext","Finset.instSetLike","Finset.mem_cons","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Basic.0.Finset.erase_cons_of_ne._proof_1_1","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":538,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert_eq_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert_eq_erase","reducibility":null,"statement_dag_size":34,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Insert.insert"],"value_dag_size":573,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert_of_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_insert_of_ne","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Insert.insert","Ne"],"value_dag_size":824,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_inter","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInter","Inter.inter"],"value_dag_size":639,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_inter_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_inter_comm","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInter","Inter.inter"],"value_dag_size":642,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_nonempty","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_sdiff_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_sdiff_comm","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSDiff","SDiff.sdiff"],"value_dag_size":641,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSDiff","Finset.instSetLike","Finset.mem_erase","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_sdiff_distrib._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_sdiff_distrib","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSDiff","SDiff.sdiff"],"value_dag_size":712,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSDiff","Finset.instSetLike","Finset.mem_erase","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.erase","Finset.instEmptyCollection","Finset.instSingleton","Singleton.singleton"],"value_dag_size":348,"value_refs":["And","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.ext","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_erase","Finset.mem_singleton","Finset.notMem_empty","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Ne","Not","Or","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_ssubset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_ssubset","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","LT.lt","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":448,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.not_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_and","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_distrib._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_distrib","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instUnion","Union.union"],"value_dag_size":949,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_erase","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_eq","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Membership.mem","SetLike.instMembership","Singleton.singleton","Union.union"],"value_dag_size":595,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_erase","Finset.mem_singleton","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.erase_union_of_mem","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.instUnion","Membership.mem","SetLike.instMembership","Union.union"],"value_dag_size":600,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_erase","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_and._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_and","reducibility":null,"statement_dag_size":65,"type_refs":["And","DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instInter","Inter.inter","instDecidableAnd"],"value_dag_size":690,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.mem_filter","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableAnd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_and_not._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_and_not","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instSDiff","Not","SDiff.sdiff","instDecidableAnd","instDecidableNot"],"value_dag_size":751,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSDiff","Finset.instSetLike","Finset.mem_filter","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableAnd","instDecidableNot","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_cons._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_cons","reducibility":null,"statement_dag_size":51,"type_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":63,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_of_mem_filter","Function.mt","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_cons._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_cons","reducibility":null,"statement_dag_size":83,"type_refs":["DecidablePred","Eq","Finset","Finset.cons","Finset.filter","Finset.instSetLike","Finset.mem_of_mem_filter","Function.mt","Membership.mem","Not","SetLike.instMembership","ite"],"value_dag_size":1266,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.cons","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_cons","Finset.mem_filter","Finset.mem_of_mem_filter","Function.mt","HEq","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Basic.0.Finset.filter_cons._proof_1_1","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_eq'._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_eq'","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","ite"],"value_dag_size":811,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter","Finset.mem_singleton","Finset.notMem_empty","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_eq","reducibility":null,"statement_dag_size":61,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","ite"],"value_dag_size":815,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter","Finset.mem_singleton","Finset.notMem_empty","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_erase","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.erase","Finset.filter"],"value_dag_size":627,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_erase","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_insert","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instInsert","Insert.insert","ite"],"value_dag_size":1151,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instInsert","Finset.instSetLike","Finset.mem_filter","Finset.mem_insert","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_inter","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instInter","Inter.inter"],"value_dag_size":644,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.mem_filter","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_inter_distrib._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_inter_distrib","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instInter","Inter.inter"],"value_dag_size":678,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.mem_filter","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_mem_eq_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_mem_eq_inter","reducibility":null,"statement_dag_size":61,"type_refs":["Decidable","DecidableEq","Eq","Finset","Finset.filter","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":317,"value_refs":["And","Classical.byContradiction","Decidable","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.mem_filter","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SetLike.instMembership","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_ne","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.filter","Not","instDecidableNot"],"value_dag_size":576,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_erase","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableNot","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_not._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_not","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instSDiff","Not","SDiff.sdiff","instDecidableNot"],"value_dag_size":610,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSDiff","Finset.instSetLike","Finset.mem_filter","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableNot","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_notMem_eq_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_notMem_eq_sdiff","reducibility":null,"statement_dag_size":64,"type_refs":["Decidable","DecidableEq","Eq","Finset","Finset.filter","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":330,"value_refs":["And","Classical.byContradiction","Decidable","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.instSDiff","Finset.instSetLike","Finset.mem_filter","Finset.mem_sdiff","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SDiff.sdiff","SetLike.instMembership","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_or._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_or","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instUnion","Or","Union.union","instDecidableOr"],"value_dag_size":1105,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableOr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_singleton","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSingleton","Singleton.singleton","ite"],"value_dag_size":823,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter","Finset.mem_singleton","Finset.notMem_empty","HEq","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_union","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instUnion","Union.union"],"value_dag_size":881,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_union_right._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.filter_union_right","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instUnion","Or","Union.union","instDecidableOr"],"value_dag_size":1164,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableOr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.insert_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.insert_erase","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":540,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.insert_inter_distrib._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.insert_inter_distrib","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instInter","Insert.insert","Inter.inter"],"value_dag_size":934,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.mem_insert","Finset.mem_inter","Iff","Insert.insert","Inter.inter","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.inter_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.inter_erase","reducibility":null,"statement_dag_size":37,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInter","Inter.inter"],"value_dag_size":623,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_erase","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.inter_filter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.inter_filter","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.instInter","Inter.inter"],"value_dag_size":633,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instInter","Finset.instSetLike","Finset.mem_filter","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.pairwiseDisjoint_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.pairwiseDisjoint_iff","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Disjoint","Eq","Finset","Finset.Nonempty","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Inter.inter","Not"],"value_dag_size":47,"value_refs":["DecidableEq","Disjoint","Finset","Finset.Nonempty","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Finset.not_disjoint_iff_nonempty_inter","Inter.inter","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.range_filter_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.range_filter_eq","reducibility":null,"statement_dag_size":53,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSingleton","Finset.range","LT.lt","Nat","Nat.decLt","Singleton.singleton","instDecidableEqNat","instLTNat","ite"],"value_dag_size":1224,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_filter","Finset.mem_range","Finset.mem_singleton","Finset.notMem_empty","Finset.range","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Singleton.singleton","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_eq_filter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_eq_filter","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","instDecidableNot"],"value_dag_size":338,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.instSDiff","Finset.instSetLike","Finset.mem_filter","Finset.mem_sdiff","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SDiff.sdiff","SetLike.instMembership","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","instDecidableNot","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_erase","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Insert.insert","Membership.mem","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":895,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_erase_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_erase_self","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Membership.mem","SDiff.sdiff","SetLike.instMembership","Singleton.singleton"],"value_dag_size":594,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_erase","Finset.mem_sdiff","Finset.mem_singleton","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_insert","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSDiff","Insert.insert","SDiff.sdiff"],"value_dag_size":673,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_insert_insert_of_mem_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_insert_insert_of_mem_of_notMem","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Insert.insert","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":854,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_singleton_eq_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_singleton_eq_erase","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSDiff","Finset.instSingleton","SDiff.sdiff","Singleton.singleton"],"value_dag_size":569,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_erase","Finset.mem_sdiff","Finset.mem_singleton","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_union_erase_cancel._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_union_erase_cancel","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","Union.union"],"value_dag_size":1032,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_erase","Finset.mem_sdiff","Finset.mem_union","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.ssubset_iff_exists_subset_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.ssubset_iff_exists_subset_erase","reducibility":null,"statement_dag_size":68,"type_refs":["And","DecidableEq","Exists","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","LT.lt","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":1631,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_and","false_or","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_insert_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_insert_iff","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Iff","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":731,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finset.subset_iff","Iff","Insert.insert","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim","reducibility":null,"statement_dag_size":57,"type_refs":["Classical.propDecidable","DecidableEq","Eq","Finset","Finset.filter","Finset.instUnion","Membership.mem","Not","Set","Set.instMembership","Union.union","instDecidableNot"],"value_dag_size":659,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set","Set.instMembership","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableNot","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim","reducibility":null,"statement_dag_size":46,"type_refs":["Classical.propDecidable","Finset","Finset.filter","Finset.instSetLike","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","SetLike.coe"],"value_dag_size":280,"value_refs":["And","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.filter","Finset.instSetLike","Finset.mem_coe","Finset.mem_filter","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Set","Set.instLE","Set.instMembership","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.subset_union_elim","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Finset.union_erase_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Finset.union_erase_of_mem","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Finset.instUnion","Membership.mem","SetLike.instMembership","Union.union"],"value_dag_size":610,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_erase","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.List.toFinset_filter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.List.toFinset_filter","reducibility":null,"statement_dag_size":41,"type_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","List.mem_filter","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_nonempty","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.Nonempty","Finset.instEmptyCollection","Ne"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.nonempty_iff_ne_empty","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_replicate._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_replicate","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Basic","name":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_replicate._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Basic.0.Multiset.toFinset_replicate","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.replicate","Nat","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":51,"value_refs":["And","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_replicate","Multiset.replicate","Nat","Ne","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left","reducibility":null,"statement_dag_size":61,"type_refs":["Codisjoint","Eq","Max.max","OrderTop","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Top.top"],"value_dag_size":66,"value_refs":["Codisjoint","Eq","Max.max","OrderTop","OrderTop.toTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","Top.top","codisjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":42,"value_refs":["Eq","Finset","Finset.eq_univ_iff_forall","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left._simp_1_3","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.codisjoint_left","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Classical.or_iff_not_imp_left","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Classical.or_iff_not_imp_left","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase._simp_1_2","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase._simp_1_3","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase._simp_1_4","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_erase","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert._simp_1_3","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_insert","reducibility":null,"statement_dag_size":47,"type_refs":["And","DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_ne_univ_iff_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.compl_ne_univ_iff_nonempty","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":42,"value_refs":["Eq","Finset","Finset.eq_univ_iff_forall","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.mem_bihimp_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.mem_bihimp_iff","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq","Iff"],"value_dag_size":21,"value_refs":["And","Iff","iff_def'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.mem_himp_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.mem_himp_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Not","Or","imp_iff_or_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.subtype_eq_univ._simp_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.subtype_eq_univ","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.BooleanAlgebra","name":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.univ_filter_mem_range._proof_1_1","namespace":"_private.Mathlib.Data.Finset.BooleanAlgebra.0.Finset.univ_filter_mem_range","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.image","Finset.univ","Fintype","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":1009,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.image","Finset.instSetLike","Finset.mem_filter","Finset.mem_image","Finset.mem_univ","Finset.univ","Fintype","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.instMembership","Set.mem_range","Set.range","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.Nonempty.strong_induction.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.Nonempty.strong_induction","reducibility":"abbrev","statement_dag_size":31,"type_refs":["Finset","Finset.Nonempty"],"value_dag_size":31,"value_refs":["Finset","Finset.Nonempty"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_bij.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_bij","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk"],"value_dag_size":101,"value_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_four._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_four","reducibility":null,"statement_dag_size":135,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","Singleton.singleton","instOfNatNat"],"value_dag_size":1631,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_eq_three","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.exists_and_left","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_four._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_four","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Not","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":1838,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_singleton","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_singleton","HAdd.hAdd","Iff","Insert.insert","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_and_left","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Finset","Finset.attach","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","True"],"value_dag_size":60,"value_refs":["Finset","Finset.attach","Finset.instSetLike","Finset.mem_attach","Membership.mem","SetLike.instMembership","Subtype","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective.match_1_4","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_of_bijective","reducibility":"abbrev","statement_dag_size":53,"type_refs":["Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","SetLike.instMembership","Subtype","Subtype.mk"],"value_dag_size":70,"value_refs":["Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Multiset","Multiset.card","Multiset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Multiset","Multiset.card","Multiset.card_eq_one","Multiset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Finset","Finset.val","Multiset"],"value_dag_size":38,"value_refs":["Eq","Eq.symm","Finset","Finset.val","Finset.val_inj","Multiset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one_iff_existsUnique._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one_iff_existsUnique","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Finset","Finset.card","Finset.card_eq_one","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one_iff_existsUnique._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_one_iff_existsUnique","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Exists","ExistsUnique","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":47,"value_refs":["Eq","Exists","ExistsUnique","Finset","Finset.instSetLike","Finset.instSingleton","Finset.singleton_iff_unique_mem","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ.match_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ","reducibility":"abbrev","statement_dag_size":255,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Not","SetLike.instMembership"],"value_dag_size":547,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Nat","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ_iff_cons.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_succ_iff_cons","reducibility":"abbrev","statement_dag_size":250,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.cons","Finset.instSetLike","Membership.mem","Nat","Not","SetLike.instMembership"],"value_dag_size":540,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.cons","Finset.instSetLike","Membership.mem","Nat","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_three._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_three","reducibility":null,"statement_dag_size":116,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","Singleton.singleton","instOfNatNat"],"value_dag_size":1035,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_eq_two","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.exists_and_left","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_three._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_three","reducibility":null,"statement_dag_size":80,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Not","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":1151,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_singleton","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_singleton","HAdd.hAdd","Iff","Insert.insert","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_and_left","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_two._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_two","reducibility":null,"statement_dag_size":101,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","Singleton.singleton","instOfNatNat"],"value_dag_size":695,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_eq_one","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.Grind.not_not","Membership.mem","Nat","Not","OfNat.ofNat","Or","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","id","implies_congr","instOfNatNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_two._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_eq_two","reducibility":null,"statement_dag_size":65,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Not","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":680,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_singleton","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","HAdd.hAdd","Iff","Insert.insert","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_eq_ite._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_eq_ite","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.decidableMem","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat","ite"],"value_dag_size":741,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_le_card","Finset.decidableMem","Finset.insert_eq_of_mem","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_le","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instInsert","HAdd.hAdd","Insert.insert","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":746,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_le_card","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.subset_iff","HAdd.hAdd","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_of_notMem","reducibility":null,"statement_dag_size":37,"type_refs":["Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":46,"value_refs":["Finset","Finset.instSetLike","Lean.Grind.not_eq_of_eq_false","Membership.mem","Not","SetLike.instMembership","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_of_notMem._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_of_notMem","reducibility":null,"statement_dag_size":67,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":367,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_cons","Finset.cons","Finset.cons_eq_insert","Finset.instInsert","Finset.instSetLike","HAdd.hAdd","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SetLike.instMembership","True","_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_of_notMem._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instUnion","HAdd.hAdd","HSub.hSub","Inter.inter","Nat","Union.union","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":1200,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Union.union","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter_add_card_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter_add_card_sdiff","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instSDiff","HAdd.hAdd","Inter.inter","Nat","SDiff.sdiff","instAddNat","instHAdd"],"value_dag_size":311,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","False","Finset","Finset.card","Finset.card_sdiff_add_card_inter","Finset.instInter","Finset.instSDiff","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Inter.inter","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SDiff.sdiff","eagerReduce","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter_add_card_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_inter_add_card_union","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instUnion","HAdd.hAdd","Inter.inter","Nat","Union.union","instAddNat","instHAdd"],"value_dag_size":349,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","False","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instUnion","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Inter.inter","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Union.union","eagerReduce","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_card_of_injective._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_card_of_injective","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":51,"value_refs":["Eq","Eq.symm","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_card_sdiff_add_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_card_sdiff_add_card","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instSDiff","HAdd.hAdd","LE.le","Nat","SDiff.sdiff","instAddNat","instHAdd","instLENat"],"value_dag_size":1483,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_le_card","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.le_card_sdiff","Finset.mem_inter","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Exists","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":274,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Iff","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Membership.mem","Not","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":488,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_le_one_iff","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","Finset","Finset.card","Finset.instSetLike","Iff","LE.le","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instLENat","instOfNatNat"],"value_dag_size":909,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_le_one","Finset.instSetLike","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_pair_eq_one_or_two._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_pair_eq_one_or_two","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","OfNat.ofNat","Or","Singleton.singleton","instOfNatNat"],"value_dag_size":978,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_le_card","Finset.card_singleton","Finset.insert_eq_of_mem","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","HAdd.hAdd","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.not_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","Singleton.singleton","True","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instSDiff","Inter.inter","Nat","SDiff.sdiff"],"value_dag_size":2551,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff_of_subset","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_inter","Finset.mem_sdiff","Finset.subset_iff","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instHSub","instIsPartialOrder_mathlib","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff","reducibility":null,"statement_dag_size":36,"type_refs":["DecidableEq","Finset","Finset.instInter","Finset.instPartialOrder","Inter.inter","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":227,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInter","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_inter","Finset.subset_iff","Iff","Inter.inter","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_add_card_eq_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_add_card_eq_card","reducibility":null,"statement_dag_size":60,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","HAdd.hAdd","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","instAddNat","instHAdd"],"value_dag_size":760,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff_of_subset","Finset.instPartialOrder","Finset.instSDiff","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_eq_card_sdiff_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_eq_card_sdiff_iff","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instSDiff","Iff","Nat","SDiff.sdiff"],"value_dag_size":5203,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff","Finset.card_sdiff_add_card_inter","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","Union.union","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_le_card_sdiff_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_le_card_sdiff_iff","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instSDiff","Iff","LE.le","Nat","SDiff.sdiff","instLENat"],"value_dag_size":1969,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","Finset","Finset.card","Finset.card_sdiff_add_card_inter","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instSDiff","Finset.instUnion","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","SDiff.sdiff","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","Union.union","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_lt_card_sdiff_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sdiff_lt_card_sdiff_iff","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instSDiff","Iff","LT.lt","Nat","SDiff.sdiff","instLTNat"],"value_dag_size":1814,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","Finset","Finset.card","Finset.card_sdiff_add_card_inter","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instSDiff","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","SDiff.sdiff","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","Union.union","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_singleton_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_singleton_inter","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instInter","Finset.instSingleton","Inter.inter","LE.le","Nat","OfNat.ofNat","Singleton.singleton","instLENat","instOfNatNat"],"value_dag_size":414,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.trans","False","Finset","Finset.card","Finset.card_empty","Finset.card_singleton","Finset.decidableMem","Finset.instEmptyCollection","Finset.instInter","Finset.instSetLike","Finset.instSingleton","Finset.singleton_inter","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","congrArg","eagerReduce","eq_false","eq_true","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq","reducibility":null,"statement_dag_size":56,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instSDiff","HSub.hSub","Inter.inter","Nat","SDiff.sdiff","instHSub","instSubNat"],"value_dag_size":5770,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Union.union","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instSDiff","HSub.hSub","Inter.inter","Nat","SDiff.sdiff","instHSub","instSubNat"],"value_dag_size":8968,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff","Finset.card_sdiff_of_subset","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Union.union","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_sub_card_eq","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instSDiff","HSub.hSub","Inter.inter","Nat","SDiff.sdiff","instHSub","instSubNat"],"value_dag_size":16485,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff","Finset.card_sdiff_of_subset","Finset.card_union_add_card_inter","Finset.instAssociativeUnion","Finset.instCommutativeUnion","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.mem_sdiff","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ac","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","Union.union","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instUnion","HAdd.hAdd","HSub.hSub","Inter.inter","Nat","Union.union","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":1198,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Union.union","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_add_card_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_add_card_inter","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInsert","Finset.instInter","Finset.instSetLike","Finset.instUnion","HAdd.hAdd","Insert.insert","Inter.inter","Membership.mem","Nat","Not","SetLike.instMembership","Union.union","instAddNat","instHAdd"],"value_dag_size":2109,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.card_le_card","Finset.decidableMem","Finset.insert_eq_of_mem","Finset.insert_inter","Finset.instInsert","Finset.instInter","Finset.instPartialOrder","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.mem_union","Finset.subset_iff","Finset.union_insert","HAdd.hAdd","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","Union.union","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_eq_card_add_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_eq_card_add_card","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Disjoint","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Inter.inter"],"value_dag_size":51,"value_refs":["DecidableEq","Disjoint","EmptyCollection.emptyCollection","Eq","Finset","Finset.disjoint_iff_inter_eq_empty","Finset.instEmptyCollection","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Inter.inter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.card_union_le","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instUnion","HAdd.hAdd","LE.le","Nat","Union.union","instAddNat","instHAdd","instLENat"],"value_dag_size":402,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","False","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instUnion","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","Inter.inter","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Union.union","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.existsUnique_notMem_image_of_injOn_of_card_eq_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.existsUnique_notMem_image_of_injOn_of_card_eq_add_one","reducibility":null,"statement_dag_size":107,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","Finset.instSDiff","Finset.instSetLike","HAdd.hAdd","Nat","OfNat.ofNat","SDiff.sdiff","Set.InjOn","Set.MapsTo","SetLike.coe","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":818,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_image_of_injOn","Finset.card_sdiff_of_subset","Finset.image","Finset.instSDiff","Finset.instSetLike","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set.InjOn","Set.MapsTo","Set.MapsTo.finsetImage_subset","SetLike.coe","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.existsUnique_notMem_image_of_injOn_of_card_eq_add_one._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.existsUnique_notMem_image_of_injOn_of_card_eq_add_one","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","ExistsUnique","Finset","Finset.card","Finset.instSetLike","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq","ExistsUnique","Finset","Finset.card","Finset.card_eq_one_iff_existsUnique","Finset.instSetLike","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","HAdd.hAdd","Insert.insert","LE.le","Membership.mem","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":537,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.subset_iff","HAdd.hAdd","Iff","Insert.insert","LE.le","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Nat","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff","reducibility":null,"statement_dag_size":72,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instPartialOrder","Finset.instSDiff","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":748,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_sdiff_of_subset","Finset.instPartialOrder","Finset.instSDiff","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_eq_insert_iff","reducibility":null,"statement_dag_size":118,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","HAdd.hAdd","Insert.insert","LE.le","Membership.mem","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1115,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.eq_of_subset_of_card_le","Finset.instInsert","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_sdiff","Finset.mem_singleton","Finset.subset_iff","HAdd.hAdd","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_or_forall","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_self","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_of_one_lt_card_pi._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_of_one_lt_card_pi","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["And","Exists","Finset","Finset.card","Finset.instSetLike","Finset.one_lt_card_iff","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_of_one_lt_card_pi._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_of_one_lt_card_pi","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Exists","Ne"],"value_dag_size":38,"value_refs":["Exists","Function.ne_iff","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subset_or_subset_of_two_mul_lt_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subset_or_subset_of_two_mul_lt_card","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instUnion","HMul.hMul","LE.le","LT.lt","Nat","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Union.union","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":801,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instPartialOrder","Finset.instUnion","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","Inter.inter","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.le_eq_true","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","True","Union.union","congr","congrArg","congrFun'","eagerReduce","eq_true","forall_congr","id","instAddNat","instHAdd","instHMul","instHSub","instIsPreorder_mathlib","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq","reducibility":null,"statement_dag_size":76,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.Nonempty","Finset.card","Finset.instSDiff","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","SDiff.sdiff","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":524,"value_refs":["Bool","Bool.true","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Nonempty","Finset.card","Finset.card_le_card","Finset.instPartialOrder","Finset.instSDiff","Finset.sdiff_nonempty","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq","reducibility":null,"statement_dag_size":163,"type_refs":["And","Classical.propDecidable","Eq","Finset","Finset.card","Finset.erase","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","HAdd.hAdd","LE.le","LT.lt","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":3853,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_erase_of_mem","Finset.card_le_card","Finset.erase","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_erase","Finset.mem_sdiff","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq","reducibility":"abbrev","statement_dag_size":190,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":327,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","HAdd.hAdd","LE.le","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_eq_iff_bijOn_of_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_eq_iff_bijOn_of_card","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","Finset.instSetLike","Iff","LE.le","Nat","Set.BijOn","SetLike.coe","instLENat"],"value_dag_size":572,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.card","Finset.image","Finset.image_eq_iff_surjOn_mapsTo","Finset.injOn_of_surjOn_of_card_le","Finset.instSetLike","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Nat","Not","Or","Or.casesOn","Set.BijOn","Set.BijOn.eq_1","Set.InjOn","Set.MapsTo","Set.SurjOn","SetLike.coe","True","True.intro","congrArg","eq_false","eq_true","id","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":112,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","HSub.hSub","Iff","LE.le","Nat","Nat.iterate","Not","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":632,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.image","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.eq_congr'","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.iterate","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","eagerReduce","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":108,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","HSub.hSub","LE.le","LT.lt","Nat","Nat.iterate","OfNat.ofNat","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1133,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.image","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.iterate","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","congrArg","congrFun'","eagerReduce","eq_true","forall_congr","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","HSub.hSub","Nat","Nat.iterate","OfNat.ofNat","instHSub","instOfNatNat","instSubNat"],"value_dag_size":283,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.refl","Eq.symm","False","Finset","Finset.card","Finset.image","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.iterate","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._proof_1_5","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":155,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.image","HAdd.hAdd","HSub.hSub","Iff","LT.lt","Nat","Nat.iterate","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2197,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_le_card","Finset.image","Finset.image_image","Finset.instPartialOrder","Function.comp","Function.iterate_succ'","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.iterate","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._proof_1_6","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":156,"type_refs":["And","DecidableEq","Eq","Finset","Finset.card","Finset.image","HSub.hSub","Iff","LE.le","LT.lt","Nat","Nat.iterate","OfNat.ofNat","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1209,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_image_le","Finset.image","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.iterate","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.image_iterate_stabilises_lt_card","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Function.comp"],"value_dag_size":67,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.image","Finset.image_image","Function.comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.injOn_of_card_image_eq._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.injOn_of_card_image_eq","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.injOn_of_surjOn_of_card_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.injOn_of_surjOn_of_card_le","reducibility":null,"statement_dag_size":92,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.card","Finset.image","LE.le","Nat","instLENat"],"value_dag_size":344,"value_refs":["Bool","Bool.true","Classical.byContradiction","Classical.propDecidable","Eq","Eq.refl","Eq.symm","False","Finset","Finset.card","Finset.image","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.inter_nonempty_of_card_lt_card_add_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.inter_nonempty_of_card_lt_card_add_card","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instInter","Finset.instUnion","HAdd.hAdd","Inter.inter","Nat","Union.union","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.card","Finset.card_union_add_card_inter","Finset.instInter","Finset.instUnion","HAdd.hAdd","Inter.inter","Nat","Union.union","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_iff_exists_subset_card.match_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_iff_exists_subset_card","reducibility":"abbrev","statement_dag_size":129,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":201,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_of_inj_on_range._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_of_inj_on_range","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.le_card_sdiff","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Finset","Finset.card","Finset.instSDiff","HSub.hSub","LE.le","Nat","SDiff.sdiff","instHSub","instLENat","instSubNat"],"value_dag_size":4258,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_le_card","Finset.card_sdiff","Finset.card_sdiff_of_subset","Finset.instInter","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_inter","Finset.mem_sdiff","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.one_lt_card_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.one_lt_card_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.pred_card_le_card_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.pred_card_le_card_erase","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Finset","Finset.card","Finset.erase","HSub.hSub","LE.le","Nat","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1220,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_erase_of_mem","Finset.card_le_card","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.subset_iff","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.sdiff_nonempty_of_card_lt_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.sdiff_nonempty_of_card_lt_card","reducibility":null,"statement_dag_size":39,"type_refs":["DecidableEq","Finset","Finset.Nonempty","Finset.card","Finset.instSDiff","LT.lt","Nat","SDiff.sdiff","instLTNat"],"value_dag_size":386,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Nonempty","Finset.card","Finset.card_le_card","Finset.instPartialOrder","Finset.instSDiff","Finset.sdiff_nonempty","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.toPartialOrder","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.strongDownwardInduction._proof_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.strongDownwardInduction","reducibility":null,"statement_dag_size":52,"type_refs":["Finset","Finset.card","HSub.hSub","LE.le","LT.lt","Nat","instHSub","instLENat","instLTNat","instSubNat"],"value_dag_size":947,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card","reducibility":null,"statement_dag_size":92,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat"],"value_dag_size":94,"value_refs":["And","Exists","Finset","Finset.card","Finset.instSetLike","Finset.three_lt_card_iff","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.lt_iff_add_one_le","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":56,"value_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.le_card_iff_exists_subset_card","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff","reducibility":null,"statement_dag_size":96,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":100,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.card_eq_four","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.three_lt_card_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","DecidableEq","Finset","Finset.insert_subset_iff","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card","reducibility":null,"statement_dag_size":75,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["And","Exists","Finset","Finset.card","Finset.instSetLike","Finset.two_lt_card_iff","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.lt_iff_add_one_le","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":56,"value_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.le_card_iff_exists_subset_card","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff","reducibility":null,"statement_dag_size":80,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":84,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.card","Finset.card_eq_three","Finset.instInsert","Finset.instSingleton","Insert.insert","Nat","Ne","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Card","name":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":66,"value_refs":["And","DecidableEq","Finset","Finset.insert_subset_iff","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.Finset.perm_toList._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.Finset.perm_toList","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.toList","List","List.instMembership","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_toList","Finset.toList","List","List.instMembership","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset.ext_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset.ext_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset_eq_iff_perm_dedup._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset_eq_iff_perm_dedup","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset_surjective.match_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.List.toFinset_surjective","reducibility":"abbrev","statement_dag_size":152,"type_refs":["And","And.intro","DecidableEq","Eq","Exists.intro","Finset","List","List.Nodup","List.toFinset","Membership.mem","Set","Set.image","Set.instMembership","Set.ofPred"],"value_dag_size":244,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists.casesOn","Exists.intro","Finset","List","List.Nodup","List.toFinset","Membership.mem","Set","Set.image","Set.instMembership","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_ssubset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_ssubset","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":47,"value_refs":["And","Finset","Finset.instPartialOrder","Finset.ssubset_def","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_subset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Dedup","name":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_subset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Dedup.0.Multiset.toFinset_subset","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.eq_of_veq.match_1_1","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.eq_of_veq","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Eq","Finset","Finset.mk","Finset.val","Multiset","Multiset.Nodup"],"value_dag_size":152,"value_refs":["Eq","Finset","Finset.casesOn","Finset.mk","Finset.val","Multiset","Multiset.Nodup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.forall_mem_not_eq'._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.forall_mem_not_eq'","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":366,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.forall_mem_not_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.forall_mem_not_eq","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":371,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.not_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.not_subset","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.not_subset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.not_subset","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Exists","LE.le","Membership.mem","Not","Set","Set.instLE","Set.instMembership"],"value_dag_size":48,"value_refs":["And","Exists","LE.le","Membership.mem","Not","Set","Set.instLE","Set.instMembership","Set.not_subset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.subset_iff_notMem._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.subset_iff_notMem","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Defs","name":"_private.Mathlib.Data.Finset.Defs.0.Finset.subset_iff_notMem._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Defs.0.Finset.subset_iff_notMem","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.DenselyOrdered","name":"_private.Mathlib.Data.Finset.DenselyOrdered.0.Finset.exists_between'.match_1_1","namespace":"_private.Mathlib.Data.Finset.DenselyOrdered.0.Finset.exists_between'","reducibility":"abbrev","statement_dag_size":131,"type_refs":["DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.Nonempty","Finset.max'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":165,"value_refs":["DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.max'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.DenselyOrdered","name":"_private.Mathlib.Data.Finset.DenselyOrdered.0.Finset.exists_between'.match_1_3","namespace":"_private.Mathlib.Data.Finset.DenselyOrdered.0.Finset.exists_between'","reducibility":"abbrev","statement_dag_size":131,"type_refs":["DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.Nonempty","Finset.min'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":165,"value_refs":["DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.min'","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_one._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_one","reducibility":null,"statement_dag_size":83,"type_refs":["DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","InvOneClass.toOne","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","instHDiv"],"value_dag_size":88,"value_refs":["DivInvMonoid.toDiv","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","InvOneClass.toOne","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","One.toOfNat1","Zero.toOfNat0","div_eq_one_iff_eq","instHDiv","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_one._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_one","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Finset","Finset.card","Finset.univ","Fintype","Fintype.card","Nat"],"value_dag_size":38,"value_refs":["Eq","Finset","Finset.card","Finset.card_eq_iff_eq_univ","Finset.univ","Fintype","Fintype.card","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_eq_zero","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Fintype","Fintype.card","IsEmpty","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":31,"value_refs":["Eq","Fintype","Fintype.card","Fintype.card_eq_zero_iff","IsEmpty","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_sdiff_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_sdiff_comm","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Distrib.toAdd","DivisionSemiring.toSemiring","Eq","Finset","Finset.dens","Finset.instSDiff","Finset.instUnion","Fintype","HAdd.hAdd","NNRat","NNRat.instSemifield","SDiff.sdiff","Semifield.toDivisionSemiring","Union.union","instDistribOfSemiring","instHAdd"],"value_dag_size":76,"value_refs":["DecidableEq","Distrib.toAdd","DivisionSemiring.toSemiring","Eq.symm","Finset","Finset.dens","Finset.dens_sdiff_add_dens","Finset.instSDiff","Finset.instUnion","Fintype","HAdd.hAdd","NNRat","NNRat.instSemifield","SDiff.sdiff","Semifield.toDivisionSemiring","Union.union","instDistribOfSemiring","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_union_add_dens_inter._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_union_add_dens_inter","reducibility":null,"statement_dag_size":61,"type_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","instDistribOfSemiring","instHAdd","instHDiv"],"value_dag_size":68,"value_refs":["Distrib.toAdd","DivInvMonoid.toDiv","DivisionSemiring","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq.symm","GroupWithZero.toDivInvMonoid","HAdd.hAdd","HDiv.hDiv","add_div","instDistribOfSemiring","instHAdd","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Density","name":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_union_add_dens_inter._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Density.0.Finset.dens_union_add_dens_inter","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_left","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Finset","Finset.val","Multiset"],"value_dag_size":38,"value_refs":["Eq","Eq.symm","Finset","Finset.val","Finset.val_inj","Multiset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_left","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Multiset","Multiset.instAdd","instHAdd"],"value_dag_size":43,"value_refs":["Eq","HAdd.hAdd","Multiset","Multiset.add_left_inj","Multiset.instAdd","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_right","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Finset","Finset.val","Multiset"],"value_dag_size":38,"value_refs":["Eq","Eq.symm","Finset","Finset.val","Finset.val_inj","Multiset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_right._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjUnion_inj_right","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HAdd.hAdd","Multiset","Multiset.instAdd","instHAdd"],"value_dag_size":42,"value_refs":["Eq","HAdd.hAdd","Multiset","Multiset.add_right_inj","Multiset.instAdd","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe","reducibility":null,"statement_dag_size":67,"type_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership"],"value_dag_size":70,"value_refs":["BoundedOrder.toOrderBot","Disjoint","DistribLattice.toLattice","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.disjoint_left","Set.instBoundedOrder","Set.instDistribLattice","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not"],"value_dag_size":18,"value_refs":["Not","imp_not_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_iff_ne","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_insert_left","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.pairwiseDisjoint_singleton_iff_injOn._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Finset.pairwiseDisjoint_singleton_iff_injOn","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Multiset.disjoint_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Multiset.disjoint_toFinset","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Disjoint","name":"_private.Mathlib.Data.Finset.Disjoint.0.Multiset.disjoint_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Disjoint.0.Multiset.disjoint_toFinset","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.Nonempty.forall_const.match_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.Nonempty.forall_const","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.Nonempty.to_type.match_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.Nonempty.to_type","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.coe_empty._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.coe_empty","reducibility":null,"statement_dag_size":27,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Set","Set.instEmptyCollection","SetLike.coe"],"value_dag_size":304,"value_refs":["Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.mem_coe","Finset.notMem_empty","Iff","Lean.Grind.eq_false_eq","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.coe_eq_empty._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.coe_eq_empty","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Iff","Set","Set.instEmptyCollection","SetLike.coe"],"value_dag_size":654,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instSetLike","Finset.mem_coe","Finset.notMem_empty","Iff","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.ext","Set.instEmptyCollection","Set.instMembership","Set.mem_empty_iff_false","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.eq_empty_iff_forall_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.eq_empty_iff_forall_notMem","reducibility":null,"statement_dag_size":37,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Iff","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":541,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.exists_mem_empty_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.exists_mem_empty_iff","reducibility":null,"statement_dag_size":39,"type_refs":["And","EmptyCollection.emptyCollection","Exists","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":246,"value_refs":["And","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Iff","Lean.Grind.eq_false_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_exists","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","congrArg","eq_false","false_or","forall_congr","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.forall_mem_empty_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.forall_mem_empty_iff","reducibility":null,"statement_dag_size":34,"type_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","True"],"value_dag_size":164,"value_refs":["Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Iff","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","SetLike.instMembership","True","True.intro","congrArg","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Finset.mem_def","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","Membership.mem","Multiset","Multiset.instMembership","Multiset.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":31,"value_refs":["Membership.mem","Multiset","Multiset.instMembership","Multiset.instZero","Multiset.notMem_zero","OfNat.ofNat","Zero.toOfNat0","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.notMem_empty","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.not_nonempty_empty.match_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.not_nonempty_empty","reducibility":"abbrev","statement_dag_size":68,"type_refs":["EmptyCollection.emptyCollection","Exists.intro","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":95,"value_refs":["EmptyCollection.emptyCollection","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Finset.not_ssubset_empty._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Finset.not_ssubset_empty","reducibility":null,"statement_dag_size":28,"type_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":454,"value_refs":["And","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSetLike","Finset.notMem_empty","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Membership.mem","Ne","Not","Or","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Empty","name":"_private.Mathlib.Data.Finset.Empty.0.Mathlib.Meta.proveFinsetNonempty.match_1","namespace":"_private.Mathlib.Data.Finset.Empty.0.Mathlib.Meta.proveFinsetNonempty","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Aesop.Stats","Array","Lean.MVarId","Prod","Prod.mk"],"value_dag_size":36,"value_refs":["Aesop.Stats","Array","Lean.MVarId","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Erase","name":"_private.Mathlib.Data.Finset.Erase.0.Finset.coe_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Erase.0.Finset.coe_erase","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","SDiff.sdiff","Set","Set.instSDiff","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":651,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.instSetLike","Finset.mem_coe","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","Set","Set.ext","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Set.mem_sdiff","Set.mem_singleton_iff","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Erase","name":"_private.Mathlib.Data.Finset.Erase.0.Finset.eq_of_mem_of_notMem_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Erase.0.Finset.eq_of_mem_of_notMem_erase","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":162,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Membership.mem","Ne","Not","SetLike.instMembership","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Erase","name":"_private.Mathlib.Data.Finset.Erase.0.Finset.erase_inj._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Erase.0.Finset.erase_inj","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":428,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_and","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Erase","name":"_private.Mathlib.Data.Finset.Erase.0.Finset.erase_right_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Erase.0.Finset.erase_right_comm","reducibility":null,"statement_dag_size":30,"type_refs":["DecidableEq","Eq","Finset","Finset.erase"],"value_dag_size":598,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Erase","name":"_private.Mathlib.Data.Finset.Erase.0.Finset.subset_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Erase.0.Finset.subset_erase","reducibility":null,"statement_dag_size":56,"type_refs":["And","DecidableEq","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1038,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_and","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.disjoint_filter_and_not_filter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.disjoint_filter_and_not_filter","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_comm","reducibility":null,"statement_dag_size":38,"type_refs":["DecidablePred","Eq","Finset","Finset.filter"],"value_dag_size":619,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_eq_empty_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_eq_empty_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_eq_self._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_eq_self","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_filter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_filter","reducibility":null,"statement_dag_size":53,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","instDecidableAnd"],"value_dag_size":613,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableAnd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_inj'._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_inj'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_inj._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_inj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_mem_eq_of_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_mem_eq_of_subset","reducibility":null,"statement_dag_size":66,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":544,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_filter","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.Nonempty","Finset.instEmptyCollection","Ne"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.nonempty_iff_ne_empty","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_ssubset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.filter_ssubset","reducibility":null,"statement_dag_size":62,"type_refs":["And","DecidablePred","Exists","Finset","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Iff","LT.lt","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":1091,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_filter","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Finset.monotone_filter_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Finset.monotone_filter_right","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Filter","name":"_private.Mathlib.Data.Finset.Filter.0.Mathlib.Meta.knownToBeFinsetNotSet.match_1","namespace":"_private.Mathlib.Data.Finset.Filter.0.Mathlib.Meta.knownToBeFinsetNotSet","reducibility":"abbrev","statement_dag_size":23,"type_refs":["Lean.Expr","Option","Option.none","Option.some","Unit"],"value_dag_size":35,"value_refs":["Lean.Expr","Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Fin","name":"_private.Mathlib.Data.Finset.Fin.0.Finset.mem_attachFin.match_1_1","namespace":"_private.Mathlib.Data.Finset.Fin.0.Finset.mem_attachFin","reducibility":"abbrev","statement_dag_size":150,"type_refs":["Eq","Exists","Exists.intro","Fin","Fin.mk","Finset","Finset.instSetLike","Finset.val","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":219,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Fin","Fin.mk","Finset","Finset.instSetLike","Finset.val","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Nat","SetLike.instMembership","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Fold","name":"_private.Mathlib.Data.Finset.Fold.0.Finset.fold_const._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Fold.0.Finset.fold_const","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instInsert","Insert.insert"],"value_dag_size":40,"value_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.insert_ne_empty","Finset.instEmptyCollection","Finset.instInsert","Insert.insert","eq_false"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finset.Fold","name":"_private.Mathlib.Data.Finset.Fold.0.Finset.«_aux_Mathlib_Data_Finset_Fold___macroRules__private_Mathlib_Data_Finset_Fold_0_Finset_term_*__1»","namespace":"_private.Mathlib.Data.Finset.Fold.0.Finset","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":261,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Finset.Fold","name":"_private.Mathlib.Data.Finset.Fold.0.Finset.«term_*_»","namespace":"_private.Mathlib.Data.Finset.Fold.0.Finset","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":57,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Functor","name":"_private.Mathlib.Data.Finset.Functor.0.Finset.image₂_def._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Functor.0.Finset.image₂_def","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_sup","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Functor","name":"_private.Mathlib.Data.Finset.Functor.0.Finset.lawfulApplicative._simp_1","namespace":"_private.Mathlib.Data.Finset.Functor.0.Finset.lawfulApplicative","reducibility":null,"statement_dag_size":86,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","DecidableEq","Exists","Finset","Finset.instLattice","Finset.instOrderBot","Finset.instSetLike","Finset.mem_sup","Finset.sup","Lattice.toSemilatticeSup","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Functor","name":"_private.Mathlib.Data.Finset.Functor.0.Finset.lawfulApplicative._simp_2","namespace":"_private.Mathlib.Data.Finset.Functor.0.Finset.lawfulApplicative","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Functor","name":"_private.Mathlib.Data.Finset.Functor.0.Finset.map_traverse._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Functor.0.Finset.map_traverse","reducibility":null,"statement_dag_size":74,"type_refs":["Applicative","Applicative.toFunctor","CommApplicative","Eq","Function.comp","Functor.map","Multiset","Multiset.functor","Multiset.traverse"],"value_dag_size":85,"value_refs":["Applicative","Applicative.toFunctor","CommApplicative","Eq.symm","Function.comp","Functor.map","Multiset","Multiset.functor","Multiset.map_traverse","Multiset.traverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.CovBy.exists_finset_cons.match_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.CovBy.exists_finset_cons","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Exists","Exists.intro","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":281,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.CovBy.exists_finset_erase._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.CovBy.exists_finset_erase","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_cons._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_cons","reducibility":null,"statement_dag_size":45,"type_refs":["CovBy","Eq","Finset","Finset.instPartialOrder","Finset.val","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":54,"value_refs":["CovBy","Eq.symm","Finset","Finset.instPartialOrder","Finset.val","Finset.val_covBy_val","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_card_sdiff_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_card_sdiff_eq_one","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Finset","Finset.card","Finset.card_eq_one","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase","reducibility":null,"statement_dag_size":67,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","CovBy","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","CovBy","Eq.symm","Finset","Finset.coe_covBy_coe","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase","reducibility":null,"statement_dag_size":82,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CovBy","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":85,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CovBy","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeInf","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SDiff.sdiff","SemilatticeInf.toPartialOrder","Set","Set.covBy_iff_exists_sdiff_singleton","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","Set.instSingletonSet","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_erase","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert","reducibility":null,"statement_dag_size":67,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","CovBy","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","CovBy","Eq.symm","Finset","Finset.coe_covBy_coe","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Preorder.toLT","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert","reducibility":null,"statement_dag_size":78,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CovBy","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","Insert.insert","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instInsert","Set.instMembership"],"value_dag_size":81,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CovBy","Eq","Exists","GeneralizedCoheytingAlgebra.toLattice","Insert.insert","Lattice.toSemilatticeInf","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.covBy_iff_exists_insert","Set.instBooleanAlgebra","Set.instInsert","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.covBy_iff_exists_insert","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.erase_wcovBy._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.erase_wcovBy","reducibility":null,"statement_dag_size":62,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","WCovBy"],"value_dag_size":71,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq.symm","Finset","Finset.coe_wcovBy_coe","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","WCovBy","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff","reducibility":null,"statement_dag_size":49,"type_refs":["Bot.bot","CovBy","Eq","IsAtom","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":59,"value_refs":["Bot.bot","CovBy","Eq.symm","IsAtom","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","bot_covBy_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff","reducibility":null,"statement_dag_size":64,"type_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":67,"value_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.covBy_iff_exists_cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isAtom_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff","reducibility":null,"statement_dag_size":61,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","Compl.compl","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","IsAtom","IsCoatom","Lattice.toSemilatticeInf","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder"],"value_dag_size":70,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","CoheytingAlgebra.toOrderTop","Compl.compl","Eq.symm","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","IsAtom","IsCoatom","Lattice.toSemilatticeInf","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","isAtom_compl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Exists","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSingleton","IsAtom","PartialOrder.toPreorder","Singleton.singleton"],"value_dag_size":44,"value_refs":["Eq","Exists","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSingleton","Finset.isAtom_iff","IsAtom","PartialOrder.toPreorder","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff","reducibility":null,"statement_dag_size":54,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Eq","GeneralizedCoheytingAlgebra.toLattice","IsCompl","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder"],"value_dag_size":58,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Eq","GeneralizedCoheytingAlgebra.toLattice","IsCompl","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","compl_eq_iff_isCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.isCoatom_iff","reducibility":null,"statement_dag_size":54,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Eq","GeneralizedCoheytingAlgebra.toLattice","IsCompl","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder"],"value_dag_size":58,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra","BooleanAlgebra.toBiheytingAlgebra","BooleanAlgebra.toBoundedOrder","BooleanAlgebra.toCompl","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Compl.compl","Eq","GeneralizedCoheytingAlgebra.toLattice","IsCompl","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","eq_compl_iff_isCompl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Finset.wcovBy_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Finset.wcovBy_insert","reducibility":null,"statement_dag_size":62,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","WCovBy"],"value_dag_size":71,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteLattice","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq.symm","Finset","Finset.coe_wcovBy_coe","Finset.instPartialOrder","Finset.instSetLike","PartialOrder.toPreorder","Set","Set.instCompleteAtomicBooleanAlgebra","SetLike.coe","WCovBy","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff","reducibility":null,"statement_dag_size":49,"type_refs":["Bot.bot","CovBy","Eq","IsAtom","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":59,"value_refs":["Bot.bot","CovBy","Eq.symm","IsAtom","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","bot_covBy_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff","reducibility":null,"statement_dag_size":43,"type_refs":["CovBy","Eq","Exists","Multiset","Multiset.cons","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":46,"value_refs":["CovBy","Eq","Exists","Multiset","Multiset.cons","Multiset.covBy_iff","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Grade","name":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Grade.0.Multiset.isAtom_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_10","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":58,"type_refs":["Finset","Finset.instSetLike","Finset.map","Function.Embedding.mk","Membership.mem","SetLike.instMembership","Subtype","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9"],"value_dag_size":251,"value_refs":["And","DFunLike.coe","Eq","Eq.rec","Equiv.finsetSubtypeComm.match_1","Exists","Finset","Finset.instSetLike","Finset.map","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mp","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","SetLike.instMembership","Subtype","Subtype.property","Subtype.val","Subtype.val_injective"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_11","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":83,"type_refs":["Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding.mk","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9"],"value_dag_size":299,"value_refs":["And","DFunLike.coe","Eq","Eq.refl","Eq.trans","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Function.Embedding","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mpr","Iff.of_eq","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","Subtype.val_injective","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","exists_prop_congr","funext","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_12","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":131,"type_refs":["Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding.mk","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_10","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_11","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9"],"value_dag_size":586,"value_refs":["And","DFunLike.coe","Eq","Eq.rec","Eq.refl","Eq.trans","Equiv.finsetSubtypeComm.match_1","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mp","Iff.mpr","Iff.of_eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","Subtype.val_injective","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","exists_prop_congr","funext","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_13","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":87,"type_refs":["Finset","Finset.instSetLike","Finset.map","Function.Embedding.mk","Lean.Grind.nestedProof","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9"],"value_dag_size":86,"value_refs":["Exists.intro","Finset","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_11","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_14","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":133,"type_refs":["Finset","Finset.instSetLike","Finset.map","Function.Embedding.mk","Lean.Grind.nestedProof","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_10","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_13","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9"],"value_dag_size":86,"value_refs":["Exists.intro","Finset","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_12","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_15","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":618,"type_refs":["And","DFunLike.coe","Eq","Eq.rec","Eq.refl","Eq.trans","Equiv.finsetSubtypeComm.match_1","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mp","Iff.mpr","Iff.of_eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","Subtype.val_injective","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","exists_prop_congr","funext","propext"],"value_dag_size":1345,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv.finsetSubtypeComm.match_1","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","HEq.refl","Iff.mp","Iff.mpr","Iff.of_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","Not","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.property","Subtype.val","Subtype.val_injective","True","True.intro","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_12","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_14","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","eq_false","eq_of_heq","eq_true","exists_prop_congr","funext","heq_of_eq","id","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_16","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":25,"type_refs":["Subtype","Subtype.val"],"value_dag_size":29,"value_refs":["Subtype","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_17","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":19,"type_refs":["Subtype","Subtype.val"],"value_dag_size":25,"value_refs":["Subtype","Subtype.property","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_16"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_18","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":567,"type_refs":["And","DFunLike.coe","Eq","Eq.rec","Eq.refl","Eq.trans","Equiv.finsetSubtypeComm.match_1","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mp","Iff.mpr","Iff.of_eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","Subtype.val_injective","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","exists_prop_congr","funext","propext"],"value_dag_size":866,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Equiv.finsetSubtypeComm.match_1","Exists","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_map._simp_1","Finset.val","Function.Embedding","Function.Embedding.coeFn_mk","Function.Embedding.mk","Function.instFunLikeEmbedding","Iff.mp","Iff.mpr","Iff.of_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","Not","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","Subtype.val_injective","True","True.intro","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_12","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_16","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_17","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","congrArg","eq_of_heq","eq_true","exists_prop_congr","forall_congr","funext","id","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_20","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":84,"type_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":97,"value_refs":["Eq.refl","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","SetLike.instMembership","Subtype","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_21","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":93,"type_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_20"],"value_dag_size":133,"value_refs":["Eq.refl","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_22","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":208,"type_refs":["And","Eq","Eq.refl","Exists","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","True"],"value_dag_size":818,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","HEq","Iff.mpr","Iff.of_eq","Lean.Grind.exists_and_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.mk.noConfusion","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_21","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","congrArg","congrFun'","eq_false","eq_true","exists_prop_congr","funext","heq_eq_eq","id","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_23","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":209,"type_refs":["And","Eq","Eq.refl","Exists","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Membership.mem","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","True"],"value_dag_size":813,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Finset","Finset.instSetLike","Iff.mpr","Iff.of_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.exists_and_right","Lean.Grind.forall_forall_or","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Membership.mem","Not","Or","SetLike.instMembership","Subtype","Subtype.impEmbedding._proof_2","Subtype.mk","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_21","_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","congrArg","congrFun'","eq_true","exists_prop_congr","false_or","forall_congr","funext","id","implies_congr","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_8","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":12,"type_refs":[],"value_dag_size":24,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._proof_9","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":19,"type_refs":["Function.Injective","Subtype","Subtype.val"],"value_dag_size":12,"value_refs":["Subtype.val_injective"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_3","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Finset","Finset.attach","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype","True"],"value_dag_size":60,"value_refs":["Finset","Finset.attach","Finset.instSetLike","Finset.mem_attach","Membership.mem","SetLike.instMembership","Subtype","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_4","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_5","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm._simp_6","namespace":"_private.Mathlib.Data.Finset.Image.0.Equiv.finsetSubtypeComm","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_filterMap._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_filterMap","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_image._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_image","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_image._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_image","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_map._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_map","reducibility":null,"statement_dag_size":60,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Set","Set.image","SetLike.coe"],"value_dag_size":1151,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_coe","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.ext","Set.image","Set.instMembership","Set.mem_image","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_map_subset_range._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.coe_map_subset_range","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Set","Set.instLE","Set.range","SetLike.coe"],"value_dag_size":507,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_coe","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Set","Set.instLE","Set.instMembership","Set.mem_range","Set.range","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","eq_false","eq_true","forall_not_of_not_exists","id","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.erase_image_subset_image_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.erase_image_subset_image_erase","reducibility":null,"statement_dag_size":56,"type_refs":["DecidableEq","Finset","Finset.erase","Finset.image","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":790,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.mem_image","Finset.subset_iff","HEq","HEq.refl","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.filterMap_mono._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.filterMap_mono","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","Finset","Finset.filterMap","Finset.instPartialOrder","LE.le","Membership.mem","Option","Option.instMembership","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":807,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.filterMap","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_filterMap","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Option","Option.instMembership","Option.some","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.filterMap_some._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.filterMap_some","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.filter_image._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.filter_image","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.filter","Finset.image"],"value_dag_size":1278,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.image","Finset.instSetLike","Finset.mem_filter","Finset.mem_image","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.forall_mem_map._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.forall_mem_map","reducibility":null,"statement_dag_size":99,"type_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finset.map","Finset.mem_map_of_mem","Function.Embedding","Function.instFunLikeEmbedding","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":1141,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Finset.mem_map_of_mem","Function.Embedding","Function.instFunLikeEmbedding","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_congr._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_congr","reducibility":null,"statement_dag_size":30,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq.symm","Exists","bex_def","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_eq_iff_surjOn_mapsTo._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_eq_iff_surjOn_mapsTo","reducibility":null,"statement_dag_size":65,"type_refs":["And","DecidableEq","Eq","Finset","Finset.image","Finset.instSetLike","Iff","Set.MapsTo","Set.SurjOn","SetLike.coe"],"value_dag_size":527,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mapsTo_iff_image_subset","Finset.surjOn_iff_subset_image","Iff","LE.le","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set.MapsTo","Set.SurjOn","SetLike.coe","True","True.intro","congr","congrArg","eq_false","eq_true","id","instIsPartialOrder_mathlib","instIsPreorder_mathlib","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_erase","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.image","Function.Injective"],"value_dag_size":1349,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.erase","Finset.ext","Finset.image","Finset.instSetLike","Finset.mem_erase","Finset.mem_image","Function.Injective","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Nonempty","Nonempty.intro","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_id._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_id","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_insert","reducibility":null,"statement_dag_size":56,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instInsert","Insert.insert"],"value_dag_size":2538,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.image","Finset.instInsert","Finset.instSetLike","Finset.mem_image","Finset.mem_insert","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_singleton","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instSingleton","Singleton.singleton"],"value_dag_size":925,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.image","Finset.instSetLike","Finset.instSingleton","Finset.mem_image","Finset.mem_singleton","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.val","HasSubset.Subset","LE.le","Multiset","Multiset.instHasSubset","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":45,"value_refs":["Finset","Finset.instPartialOrder","Finset.subset_def","Finset.val","HasSubset.Subset","LE.le","Multiset","Multiset.instHasSubset","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image","reducibility":null,"statement_dag_size":32,"type_refs":["DecidableEq","Eq","HasSubset.Subset","Multiset","Multiset.dedup","Multiset.instHasSubset"],"value_dag_size":36,"value_refs":["DecidableEq","HasSubset.Subset","Multiset","Multiset.dedup","Multiset.instHasSubset","Multiset.subset_dedup'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_subset_image","reducibility":null,"statement_dag_size":33,"type_refs":["DecidableEq","Eq","HasSubset.Subset","Multiset","Multiset.dedup","Multiset.instHasSubset"],"value_dag_size":37,"value_refs":["DecidableEq","HasSubset.Subset","Multiset","Multiset.dedup","Multiset.dedup_subset'","Multiset.instHasSubset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_toFinset","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.image_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.image_toFinset","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.map_refl._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.map_refl","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.map_subset_map._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.map_subset_map","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.val","HasSubset.Subset","LE.le","Multiset","Multiset.instHasSubset","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":45,"value_refs":["Finset","Finset.instPartialOrder","Finset.subset_def","Finset.val","HasSubset.Subset","LE.le","Multiset","Multiset.instHasSubset","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.map_symm_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.map_symm_subset","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","Equiv","Equiv.symm","Equiv.toEmbedding","Finset","Finset.instPartialOrder","Finset.map","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":85,"value_refs":["Eq.symm","Equiv","Equiv.symm","Equiv.toEmbedding","Finset","Finset.instPartialOrder","Finset.map","Finset.subset_map_symm","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.map_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.map_toFinset","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.map_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.map_toFinset","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mapsTo_iff_image_subset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mapsTo_iff_image_subset","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Finset.mem_def","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image","reducibility":null,"statement_dag_size":33,"type_refs":["DecidableEq","Eq","Membership.mem","Multiset","Multiset.dedup","Multiset.instMembership"],"value_dag_size":37,"value_refs":["DecidableEq","Membership.mem","Multiset","Multiset.dedup","Multiset.instMembership","Multiset.mem_dedup","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image_const._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_image_const","reducibility":null,"statement_dag_size":55,"type_refs":["And","DecidableEq","Eq","Finset","Finset.Nonempty","Finset.image","Finset.instSetLike","Function.const","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":564,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","False","False.elim","Finset","Finset.Nonempty","Finset.image","Finset.instSetLike","Finset.mem_image","Finset.nonempty_def","Function.const","Function.const_apply","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_and_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","funext","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_map_equiv._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_map_equiv","reducibility":null,"statement_dag_size":96,"type_refs":["And","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Exists","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":834,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.apply_symm_apply","Equiv.instEquivLike","Equiv.symm","Equiv.symm_apply_apply","EquivLike.toFunLike","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","FunLike","HEq.refl","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","eq_false","eq_of_heq","eq_true","false_or","forall_congr","heq_of_eq","id","implies_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq'._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq'","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq'._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq.match_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Eq","Exists","Exists.intro","HMod.hMod","Int","Int.instMod","Nat","Nat.cast","instHMod","instNatCastInt"],"value_dag_size":96,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HMod.hMod","Int","Int.instMod","Nat","Nat.cast","instHMod","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq.match_1_3","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_range_iff_mem_finset_range_of_mod_eq","reducibility":"abbrev","statement_dag_size":91,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Int","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Int","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_subtype.match_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.mem_subtype","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Subtype","Subtype.mk"],"value_dag_size":43,"value_refs":["Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_image_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_image_iff","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_image_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_image_iff","reducibility":null,"statement_dag_size":85,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","LE.le","Set","Set.image","Set.instLE","SetLike.coe"],"value_dag_size":91,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.subset_set_image_iff","LE.le","Set","Set.image","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_set_image_iff._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_set_image_iff","reducibility":null,"statement_dag_size":80,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","LE.le","Set","Set.image","Set.instLE","SetLike.coe"],"value_dag_size":795,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instSetLike","Finset.mem_coe","Finset.mem_image","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Set","Set.image","Set.instLE","Set.instMembership","Set.mem_image","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_set_image_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_set_image_iff","reducibility":"abbrev","statement_dag_size":107,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":181,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_univ_image_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subset_univ_image_iff","reducibility":null,"statement_dag_size":79,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":85,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instPartialOrder","Finset.subset_image_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subtype_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subtype_eq_empty","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Finset.subtype_eq_empty._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Image.0.Finset.subtype_eq_empty","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.mk"],"value_dag_size":39,"value_refs":["Subtype","Subtype.forall","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.Function.Injective.mem_finset_image._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.Function.Injective.mem_finset_image","reducibility":null,"statement_dag_size":62,"type_refs":["DecidableEq","Finset","Finset.image","Finset.instSetLike","Function.Injective","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":604,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Function.Injective","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Nonempty","Nonempty.intro","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Image","name":"_private.Mathlib.Data.Finset.Image.0.List.toFinset_filterMap._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Image.0.List.toFinset_filterMap","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.Nonempty.exists_eq_singleton_or_nontrivial.match_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.Nonempty.exists_eq_singleton_or_nontrivial","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_eq_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_eq_singleton","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Iff","Set","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":668,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_singleton","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.ext","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_insert","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Set","Set.instInsert","SetLike.coe"],"value_dag_size":359,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_coe","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instInsert","Set.instMembership","Set.mem_insert_iff","SetLike.coe","SetLike.instMembership","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_pair._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_pair","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Insert.insert","Set","Set.instInsert","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":408,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_insert","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_singleton_iff","SetLike.coe","SetLike.instMembership","Singleton.singleton","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Set","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":307,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_singleton","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","Set","Set.ext","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","SetLike.coe","SetLike.instMembership","Singleton.singleton","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_subset_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_subset_singleton","reducibility":null,"statement_dag_size":53,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":741,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_singleton","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Set.subset_def","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_10","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":13,"type_refs":["Eq"],"value_dag_size":25,"value_refs":["Eq","Finset.prodPiCons._proof_1","eq_self","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_11","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":92,"type_refs":["DecidableEq","Eq","Finset","Finset.consPiProd","Finset.instSetLike","Finset.prodPiCons","Membership.mem","Not","Prod","Prod.fst","SetLike.instMembership"],"value_dag_size":469,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.cons","Finset.consPiProd","Finset.consPiProd.eq_1","Finset.instSetLike","Finset.mem_cons_of_mem","Finset.mem_cons_self","Finset.mem_of_mem_cons_of_ne","Finset.prodPiCons","Finset.prodPiCons._proof_1","Finset.prodPiCons.eq_1","HEq.trans","Lean.Grind.nestedProof","Membership.mem","Not","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_10","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_4","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5","cast","cast_heq","congrArg","dite","dite_cond_eq_true","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_12","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":85,"value_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Finset.mem_of_mem_cons_of_ne","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_13","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":111,"type_refs":["DecidableEq","Eq","Finset","Finset.consPiProd","Finset.instSetLike","Finset.prodPiCons","Membership.mem","Not","Prod","Prod.snd","SetLike.instMembership"],"value_dag_size":764,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.cons","Finset.consPiProd","Finset.consPiProd.eq_1","Finset.instSetLike","Finset.mem_cons_of_mem","Finset.mem_cons_self","Finset.mem_of_mem_cons_of_ne","Finset.prodPiCons","Finset.prodPiCons._proof_1","Finset.prodPiCons.eq_1","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_12","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_4","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5","cast","congrArg","dite","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_4","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":47,"type_refs":["Finset","Finset.cons","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":45,"value_refs":["Finset","Finset.instSetLike","Finset.mem_cons_self","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":61,"type_refs":["Finset","Finset.cons","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":61,"value_refs":["Finset","Finset.instSetLike","Finset.mem_cons_of_mem","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_6","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":87,"value_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Finset.mem_of_mem_cons_of_ne","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_7","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":85,"value_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_6"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_8","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv","reducibility":null,"statement_dag_size":91,"type_refs":["DecidableEq","Eq","Finset","Finset.cons","Finset.consPiProd","Finset.instSetLike","Finset.prodPiCons","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":1096,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.cons","Finset.consPiProd","Finset.consPiProd.eq_1","Finset.instSetLike","Finset.mem_cons_of_mem","Finset.mem_cons_self","Finset.mem_of_mem_cons_of_ne","Finset.prodPiCons","Finset.prodPiCons._proof_1","Finset.prodPiCons.eq_1","HEq","HEq.refl","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_4","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_5","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_6","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_7","cast","cast_heq","congrArg","dite","eq_false","eq_of_heq","eq_true","funext","heq_of_eq","id","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.cons_induction.match_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.cons_induction","reducibility":"abbrev","statement_dag_size":28,"type_refs":["Finset","Finset.mk","Multiset","Multiset.Nodup"],"value_dag_size":42,"value_refs":["Finset","Finset.casesOn","Finset.mk","Multiset","Multiset.Nodup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.eq_singleton_iff_nonempty_unique_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.eq_singleton_iff_nonempty_unique_mem","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.instSingleton","Iff","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":1116,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.Nonempty","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.nonempty_def","Finset.singleton_nonempty","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.eq_singleton_iff_unique_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.eq_singleton_iff_unique_mem","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.instSingleton","Iff","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":978,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.exists_mem_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.exists_mem_insert","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidableEq","Exists","Finset","Finset.instInsert","Finset.instSetLike","Iff","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":952,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.forall_mem_cons._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.forall_mem_cons","reducibility":null,"statement_dag_size":60,"type_refs":["And","Finset","Finset.cons","Finset.instSetLike","Iff","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":872,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.cons","Finset.instSetLike","Finset.mem_cons","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.forall_mem_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.forall_mem_insert","reducibility":null,"statement_dag_size":54,"type_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Iff","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":864,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","HEq","HEq.refl","Iff","Insert.insert","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.induction_on'.match_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.induction_on'","reducibility":"abbrev","statement_dag_size":119,"type_refs":["And","And.intro","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":141,"value_refs":["And","And.casesOn","And.intro","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_10","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":75,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_of_mem_insert_of_ne","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_11","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":110,"type_refs":["DecidableEq","Eq","Finset","Finset.insertPiProd","Finset.instSetLike","Finset.prodPiInsert","Membership.mem","Not","Prod","Prod.snd","SetLike.instMembership"],"value_dag_size":737,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.insertPiProd","Finset.insertPiProd.eq_1","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_of_mem","Finset.mem_insert_self","Finset.mem_of_mem_insert_of_ne","Finset.prodPiCons._proof_1","Finset.prodPiInsert","Finset.prodPiInsert.eq_1","HEq","HEq.refl","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_10","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_9","cast","congrArg","dite","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_4","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":75,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_of_mem_insert_of_ne","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_5","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":75,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_of_mem","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_6","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":83,"type_refs":["DecidableEq","Eq","Finset","Finset.insertPiProd","Finset.instInsert","Finset.instSetLike","Finset.prodPiInsert","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":1026,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.insertPiProd","Finset.insertPiProd.eq_1","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_of_mem","Finset.mem_insert_self","Finset.mem_of_mem_insert_of_ne","Finset.prodPiCons._proof_1","Finset.prodPiInsert","Finset.prodPiInsert.eq_1","HEq","HEq.refl","HEq.trans","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_4","_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_5","cast","cast_heq","congrArg","dite","eq_false","eq_of_heq","eq_true","funext","heq_of_eq","id","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_8","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","Finset","Finset.insertPiProd","Finset.instSetLike","Finset.prodPiInsert","Membership.mem","Prod","Prod.fst","SetLike.instMembership"],"value_dag_size":421,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.insertPiProd","Finset.insertPiProd.eq_1","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_of_mem","Finset.mem_insert_self","Finset.mem_of_mem_insert_of_ne","Finset.prodPiCons._proof_1","Finset.prodPiInsert","Finset.prodPiInsert.eq_1","HEq.trans","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.consPiProdEquiv._proof_10","cast","cast_heq","congrArg","dite","dite_cond_eq_true","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv._proof_9","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insertPiProdEquiv","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":50,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.mem_insert_of_mem","Lean.Grind.nestedProof","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_comm","reducibility":null,"statement_dag_size":33,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Insert.insert"],"value_dag_size":602,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_eq_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_eq_self","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Iff","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":408,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.insert_eq_of_mem","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","id","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_idem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_idem","reducibility":null,"statement_dag_size":28,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Insert.insert"],"value_dag_size":196,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.insert_eq_of_mem","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff","Insert.insert","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","id","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_iff","reducibility":null,"statement_dag_size":59,"type_refs":["And","DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Iff","Insert.insert","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1036,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.subset_iff","Iff","Insert.insert","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_insert","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":383,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.subset_iff","Iff","Insert.insert","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_insert_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.insert_subset_insert_iff","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.nonempty_iff_eq_singleton_default._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.nonempty_iff_eq_singleton_default","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":55,"value_refs":["And","Eq","Finset","Finset.Nonempty","Finset.eq_singleton_iff_nonempty_unique_mem","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.nonempty_iff_eq_singleton_default._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.nonempty_iff_eq_singleton_default","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'","reducibility":null,"statement_dag_size":109,"type_refs":["And","Eq","Finset","Finset.instSetLike","Iff","Membership.mem","Not","Set","Set.Pairwise","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":1463,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_and","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","Set","Set.Pairwise","Set.instMembership","SetLike.coe","SetLike.instMembership","True","True.intro","congr","congrArg","eq_false","eq_true","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Function.onFun","Membership.mem","Pairwise","Set.Pairwise","SetLike.coe","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":89,"value_refs":["Finset","Finset.instSetLike","Finset.pairwise_subtype_iff_pairwise_finset'","Function.onFun","Membership.mem","Pairwise","Set.Pairwise","SetLike.coe","SetLike.instMembership","Subtype","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'","reducibility":null,"statement_dag_size":60,"type_refs":["And","Eq","Insert.insert","Membership.mem","Ne","Set","Set.Pairwise","Set.instInsert","Set.instMembership"],"value_dag_size":65,"value_refs":["And","Insert.insert","Membership.mem","Ne","Set","Set.Pairwise","Set.instInsert","Set.instMembership","Set.pairwise_insert","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_iff_unique_mem._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_iff_unique_mem","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":61,"value_refs":["And","Eq","Finset","Finset.eq_singleton_iff_unique_mem","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_subset_coe._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_subset_coe","reducibility":null,"statement_dag_size":53,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","Set.instSingletonSet","SetLike.coe","Singleton.singleton"],"value_dag_size":730,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_singleton","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","Set.instMembership","Set.instSingletonSet","Set.singleton_subset_iff","Set.subset_def","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_self","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_subset_set_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.singleton_subset_set_iff","reducibility":null,"statement_dag_size":44,"type_refs":["Finset","Finset.instSetLike","Finset.instSingleton","Iff","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","SetLike.coe","Singleton.singleton"],"value_dag_size":588,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_coe","Finset.mem_singleton","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Set","Set.instLE","Set.instMembership","Set.subset_def","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_self","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_iff_exists_cons_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_iff_exists_cons_subset","reducibility":null,"statement_dag_size":37,"type_refs":["Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":46,"value_refs":["Finset","Finset.instSetLike","Lean.Grind.not_eq_of_eq_false","Membership.mem","Not","SetLike.instMembership","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_iff_exists_cons_subset._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_iff_exists_cons_subset","reducibility":null,"statement_dag_size":69,"type_refs":["Exists","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","LT.lt","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":1740,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.cons","Finset.ext","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_cons","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_iff_exists_cons_subset._proof_1_1","congrArg","congrFun'","eq_false","eq_self","eq_true","exists_prop_congr","forall_congr","funext","id","implies_congr","of_eq_true","or_false","propext","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_singleton_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.ssubset_singleton_iff","reducibility":null,"statement_dag_size":42,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","Iff","LT.lt","PartialOrder.toPreorder","Preorder.toLT","Singleton.singleton"],"value_dag_size":1273,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.notMem_empty","Finset.singleton_subset_iff","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.Order.le_eq_true","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instIsPreorder_mathlib","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subset_singleton_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subset_singleton_iff","reducibility":null,"statement_dag_size":46,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSingleton","Iff","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton"],"value_dag_size":1263,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.notMem_empty","Finset.subset_iff","Iff","LE.le","Lean.Grind.Order.le_of_eq_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instIsPreorder_mathlib","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":95,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Not","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":122,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Iff.mp","Insert.insert","Membership.mem","Not","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.property","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":59,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.mem_insert_of_mem","Membership.mem","SetLike.instMembership","Subtype","Subtype.property","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_3","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":104,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_1"],"value_dag_size":95,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Lean.Grind.nestedProof","Membership.mem","Not","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_1","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_4","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":186,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Not","Option","Option.elim","Option.none","Option.some","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","dite"],"value_dag_size":760,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","HEq.refl","Iff.mp","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Option","Option.elim","Option.elim_none","Option.elim_some","Option.none","Option.some","Or","Or.casesOn","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_1","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_3","congrArg","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_6","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":162,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_self","Insert.insert","Membership.mem","Not","Option.elim","Option.none","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2"],"value_dag_size":194,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Not","Option.elim","Option.none","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_7","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":216,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Not","Option","Option.elim","Option.none","Option.some","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","dite"],"value_dag_size":490,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Lean.Grind.dite_cond_eq_true'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","Option","Option.elim","Option.elim_none","Option.none","Option.some","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.mk.inj","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_6","dite","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_8","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":179,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert_self","Insert.insert","Membership.mem","Not","Option.elim","Option.some","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2"],"value_dag_size":211,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Not","Option.elim","Option.some","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_9","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption","reducibility":null,"statement_dag_size":246,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","Iff.mp","Insert.insert","Membership.mem","Not","Option","Option.elim","Option.none","Option.some","Or","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.mk","Subtype.property","Subtype.val","dite"],"value_dag_size":852,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_insert_of_mem","Finset.mem_insert_self","HEq.refl","Iff.mp","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","Option","Option.elim","Option.elim_some","Option.none","Option.some","Or","Or.casesOn","Or.resolve_left","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.mk.inj","Subtype.property","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_2","_private.Mathlib.Data.Finset.Insert.0.Finset.subtypeInsertEquivOption._proof_8","congrArg","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.toList_cons._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.toList_cons","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.Finset.toList_cons._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Insert.0.Finset.toList_cons","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.toList","List","List.instMembership","Membership.mem","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Finset.mem_toList","Finset.toList","List","List.instMembership","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.List.toFinset_nonempty_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.List.toFinset_nonempty_iff","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.Nonempty","Finset.instEmptyCollection","Ne"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.nonempty_iff_ne_empty","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Insert","name":"_private.Mathlib.Data.Finset.Insert.0.List.toFinset_replicate_of_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Insert.0.List.toFinset_replicate_of_ne_zero","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","List","List.instMembership","List.replicate","Membership.mem","Nat","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":51,"value_refs":["And","Eq","List","List.instMembership","List.mem_replicate","List.replicate","Membership.mem","Nat","Ne","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Icc_eq_filter_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Icc_eq_filter_powerset","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_filter_ssubsets._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_filter_ssubsets","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ico_eq_image_ssubsets","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.ssubsets","LT.lt","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_ssubsets","Finset.ssubsets","LT.lt","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ioc_eq_filter_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ioc_eq_filter_powerset","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ioo_eq_filter_ssubsets._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.Ioo_eq_filter_ssubsets","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder._simp_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":56,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.instOrderBot","Finset.instPartialOrder"],"value_dag_size":62,"value_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.disjUnion_inj_left","Finset.instOrderBot","Finset.instPartialOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder._simp_2","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder._simp_4","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":56,"type_refs":["And","DecidableEq","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff"],"value_dag_size":61,"value_refs":["And","DecidableEq","Disjoint","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","Finset.subset_sdiff","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder._simp_5","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_cons._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_cons","reducibility":null,"statement_dag_size":63,"type_refs":["CovBy","Eq","LE.le","LocallyFiniteOrder","Monotone","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":69,"value_refs":["CovBy","LE.le","LocallyFiniteOrder","Monotone","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","monotone_iff_forall_covBy","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_cons._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_cons","reducibility":null,"statement_dag_size":64,"type_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":67,"value_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.covBy_iff_exists_cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.monotone_iff_forall_le_insert","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","Monotone","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":72,"value_refs":["Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Finset.monotone_iff_forall_le_cons","LE.le","Membership.mem","Monotone","Not","PartialOrder.toPreorder","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_cons._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_cons","reducibility":null,"statement_dag_size":56,"type_refs":["CovBy","Eq","LT.lt","LocallyFiniteOrder","Preorder","Preorder.toLT","StrictMono"],"value_dag_size":62,"value_refs":["CovBy","LT.lt","LocallyFiniteOrder","Preorder","Preorder.toLT","StrictMono","propext","strictMono_iff_forall_covBy"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_cons._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_cons","reducibility":null,"statement_dag_size":64,"type_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":67,"value_refs":["CovBy","Eq","Exists","Finset","Finset.cons","Finset.covBy_iff_exists_cons","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Interval","name":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Interval.0.Finset.strictMono_iff_forall_lt_insert","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","LT.lt","Membership.mem","Not","PartialOrder.toPreorder","Preorder","Preorder.toLT","SetLike.instMembership","StrictMono"],"value_dag_size":72,"value_refs":["Finset","Finset.cons","Finset.instPartialOrder","Finset.instSetLike","Finset.strictMono_iff_forall_lt_cons","LT.lt","Membership.mem","Not","PartialOrder.toPreorder","Preorder","Preorder.toLT","SetLike.instMembership","StrictMono","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.forall_mem_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.forall_mem_union","reducibility":null,"statement_dag_size":57,"type_refs":["And","DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Iff","Membership.mem","SetLike.instMembership","Union.union"],"value_dag_size":747,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice._simp_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice._simp_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice._simp_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice._simp_4","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.instDistribLattice","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_assoc._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_assoc","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Inter.inter"],"value_dag_size":613,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_comm","reducibility":null,"statement_dag_size":29,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Inter.inter"],"value_dag_size":487,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_left_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_left_comm","reducibility":null,"statement_dag_size":34,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Inter.inter"],"value_dag_size":593,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_right_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_right_comm","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Inter.inter"],"value_dag_size":624,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.subset_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.subset_inter","reducibility":null,"statement_dag_size":63,"type_refs":["DecidableEq","Finset","Finset.instInter","Finset.instPartialOrder","Inter.inter","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":396,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInter","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_inter","Finset.subset_iff","Iff","Inter.inter","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_inter_cancel_left._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_inter_cancel_left","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instUnion","Inter.inter","Union.union"],"value_dag_size":501,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.mem_union","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_inter_cancel_right._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_inter_cancel_right","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instUnion","Inter.inter","Union.union"],"value_dag_size":479,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.mem_union","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_left_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_left_comm","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Or"],"value_dag_size":22,"value_refs":["Or","or_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Basic","name":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_right_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.union_right_comm","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","or_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.disjoint_sup_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.disjoint_sup_left","reducibility":null,"statement_dag_size":61,"type_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder"],"value_dag_size":66,"value_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.disjoint_sup_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.disjoint_sup_right","reducibility":null,"statement_dag_size":61,"type_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder"],"value_dag_size":66,"value_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.exists_inf_eq_iInf.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.exists_inf_eq_iInf","reducibility":"abbrev","statement_dag_size":163,"type_refs":["BoundedOrder.toOrderTop","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toLattice","Exists","Exists.intro","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"],"value_dag_size":204,"value_refs":["BoundedOrder.toOrderTop","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.exists_sup_eq_iSup.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.exists_sup_eq_iSup","reducibility":"abbrev","statement_dag_size":163,"type_refs":["BoundedOrder.toOrderBot","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toLattice","Exists","Exists.intro","Finset","Finset.sup","LE.le","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder"],"value_dag_size":204,"value_refs":["BoundedOrder.toOrderBot","CompleteLattice","CompleteLattice.toBoundedOrder","CompleteLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.sup","LE.le","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf'_induction.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf'_induction","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Option.none","Option.some","Top.top","True","WithTop","WithTop.recTopCoe","WithTop.some","WithTop.top"],"value_dag_size":198,"value_refs":["Option.casesOn","Option.none","Option.some","Top.top","True","WithTop","WithTop.recTopCoe","WithTop.some","WithTop.top"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_dite_neg_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_dite_neg_le","reducibility":null,"statement_dag_size":106,"type_refs":["DecidablePred","Finset","Finset.inf","Finset.instSetLike","LE.le","Membership.mem","Not","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership","dite"],"value_dag_size":366,"value_refs":["Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.inf","Finset.inf_le_of_le","Finset.instSetLike","LE.le","Lean.Grind.Order.le_of_eq_1","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","dite","eq_false","eq_true","id","instIsPreorder_mathlib"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_dite_pos_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_dite_pos_le","reducibility":null,"statement_dag_size":105,"type_refs":["DecidablePred","Finset","Finset.inf","Finset.instSetLike","LE.le","Membership.mem","Not","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership","dite"],"value_dag_size":363,"value_refs":["Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.inf","Finset.inf_le_of_le","Finset.instSetLike","LE.le","Lean.Grind.Order.le_of_eq_1","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","dite","eq_false","eq_true","id","instIsPreorder_mathlib"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":288,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff.match_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff","reducibility":"abbrev","statement_dag_size":207,"type_refs":["DistribLattice.toLattice","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.inl","Or.inr","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":221,"value_refs":["DistribLattice.toLattice","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.casesOn","Or.inl","Or.inr","OrderTop","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff.match_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_le_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":288,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":288,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff.match_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff","reducibility":"abbrev","statement_dag_size":208,"type_refs":["DistribLattice.toLattice","Finset","Finset.inf","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.inl","Or.inr","OrderTop","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":222,"value_refs":["DistribLattice.toLattice","Finset","Finset.inf","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.casesOn","Or.inl","Or.inr","OrderTop","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff.match_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.inf_lt_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":288,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeSup","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeSup.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.isLUB_sup._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.isLUB_sup","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","True"],"value_dag_size":79,"value_refs":["Finset","Finset.instSetLike","Finset.le_sup","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_dite_neg._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_dite_neg","reducibility":null,"statement_dag_size":106,"type_refs":["DecidablePred","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","Not","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","dite"],"value_dag_size":364,"value_refs":["Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.le_sup_of_le","Finset.sup","LE.le","Lean.Grind.Order.le_of_eq_2","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","True","True.intro","dite","eq_false","eq_true","id","instIsPreorder_mathlib"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_dite_pos._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_dite_pos","reducibility":null,"statement_dag_size":105,"type_refs":["DecidablePred","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","Not","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","dite"],"value_dag_size":361,"value_refs":["Classical.byContradiction","DecidablePred","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.le_sup_of_le","Finset.sup","LE.le","Lean.Grind.Order.le_of_eq_2","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","True","True.intro","dite","eq_false","eq_true","id","instIsPreorder_mathlib"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":285,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff.match_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff","reducibility":"abbrev","statement_dag_size":203,"type_refs":["DistribLattice.toLattice","Finset","Finset.sup","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.inl","Or.inr","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":217,"value_refs":["DistribLattice.toLattice","Finset","Finset.sup","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.casesOn","Or.inl","Or.inr","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff.match_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.le_sup_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":285,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LE.le","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":285,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff.match_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff","reducibility":"abbrev","statement_dag_size":204,"type_refs":["DistribLattice.toLattice","Finset","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.inl","Or.inr","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":218,"value_refs":["DistribLattice.toLattice","Finset","Finset.sup","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Or","Or.casesOn","Or.inl","Or.inr","OrderBot","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff.match_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.lt_sup_iff","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":285,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_induction.match_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_induction","reducibility":"abbrev","statement_dag_size":143,"type_refs":["Bot.bot","Option.none","Option.some","True","WithBot","WithBot.bot","WithBot.recBotCoe","WithBot.some"],"value_dag_size":198,"value_refs":["Bot.bot","Option.casesOn","Option.none","Option.some","True","WithBot","WithBot.bot","WithBot.recBotCoe","WithBot.some"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_union._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_union","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_union._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup'_union","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_eq_one","reducibility":null,"statement_dag_size":55,"type_refs":["Bot.bot","Eq","IsBotOneClass","OfNat.ofNat","One","One.toOfNat1","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":62,"value_refs":["Bot.bot","Eq.symm","IsBotOneClass","OfNat.ofNat","One","One.toOfNat1","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","bot_eq_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_eq_top_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_eq_top_iff","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top"],"value_dag_size":55,"value_refs":["Eq","Eq.symm","LE.le","OrderTop","OrderTop.toTop","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Top.top","propext","top_le_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_induction._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_induction","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Finset","Finset.cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":67,"value_refs":["And","Finset","Finset.cons","Finset.forall_mem_cons","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_iff","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":15,"type_refs":["Eq"],"value_dag_size":19,"value_refs":["forall_prop_of_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Not","True"],"value_dag_size":21,"value_refs":["Not","True","forall_prop_of_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","forall_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed._simp_1_6","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_le_of_le_directed","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Max.max","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax"],"value_dag_size":61,"value_refs":["And","LT.lt","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toLattice","Max.max","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","propext","sup_lt_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Membership.mem","Not","Or","SetLike.instMembership"],"value_dag_size":62,"value_refs":["Eq","Finset","Finset.cons","Finset.instSetLike","Finset.mem_cons","Membership.mem","Not","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_lt_iff","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_mem_of_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_mem_of_nonempty","reducibility":null,"statement_dag_size":19,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.Nonempty","Finset.instEmptyCollection"],"value_dag_size":18,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.not_nonempty_empty","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_singleton_apply._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_singleton_apply","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_singleton_apply._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_singleton_apply","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_union._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_union","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Fold","name":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_union._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Fold.0.Finset.sup_union","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_mem","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":25,"value_refs":["And","Or","or_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.insert_inter_of_notMem","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.singleton_inter_of_notMem._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.singleton_inter_of_notMem","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Lemmas","name":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.singleton_inter_of_notMem._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.singleton_inter_of_notMem","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Pi","name":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Pi","name":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Pi","name":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup","reducibility":null,"statement_dag_size":96,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.pi","Membership.mem","SetLike.instMembership"],"value_dag_size":102,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.mem_pi","Finset.pi","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Pi","name":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Pi","name":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup._simp_1_6","namespace":"_private.Mathlib.Data.Finset.Lattice.Pi.0.Finset.inf_sup","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.instSetLike","Finset.sup'","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":84,"value_refs":["Finset","Finset.Nonempty","Finset.instSetLike","Finset.sup'","Finset.sup'_le_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","LE","LE.le","Prod","Prod.fst","Prod.instLE_mathlib","Prod.snd"],"value_dag_size":69,"value_refs":["And","LE","LE.le","Prod","Prod.fst","Prod.instLE_mathlib","Prod.le_def","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Lattice.Prod","name":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.sup_prodMap","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","LE","LE.le","Prod","Prod.fst","Prod.instLE_mathlib","Prod.snd"],"value_dag_size":69,"value_refs":["And","LE","LE.le","Prod","Prod.fst","Prod.instLE_mathlib","Prod.le_def","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.card_le_sdiff_of_interleaved.match_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.card_le_sdiff_of_interleaved","reducibility":"abbrev","statement_dag_size":234,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":389,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","LT.lt","Lattice.toSemilatticeInf","LinearOrder","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.induction_on_max_value._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.induction_on_max_value","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.image","Finset.instEmptyCollection"],"value_dag_size":54,"value_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.image","Finset.image_eq_empty","Finset.instEmptyCollection","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.induction_on_max_value._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.induction_on_max_value","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.max_of_mem.match_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.max_of_mem","reducibility":"abbrev","statement_dag_size":239,"type_refs":["And","And.intro","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.sup","LE.le","Lattice.toSemilatticeSup","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","WithBot","WithBot.instOrderBot","WithBot.semilatticeSup","WithBot.some","instDistribLatticeOfLinearOrder"],"value_dag_size":329,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.sup","LE.le","Lattice.toSemilatticeSup","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","WithBot","WithBot.instOrderBot","WithBot.semilatticeSup","WithBot.some","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.max_of_nonempty.match_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.max_of_nonempty","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.mem_of_max._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.mem_of_max","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.max","Insert.insert","LinearOrder","LinearOrder.toDecidableEq","Membership.mem","SetLike.instMembership","WithBot","WithBot.some"],"value_dag_size":516,"value_refs":["Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInsert","Finset.instSetLike","Finset.max","Finset.max_insert","Finset.mem_insert","Iff","Insert.insert","LE.le","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toDecidableEq","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","SetLike.instMembership","True","True.intro","WithBot","WithBot.coe_eq_coe","WithBot.decidableLE","WithBot.instPreorder","WithBot.linearOrder","WithBot.semilatticeSup","WithBot.some","eq_false","eq_true","id","instDistribLatticeOfLinearOrder","ite","ite_cond_eq_false","ite_cond_eq_true","max_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.min'_lt_max'_of_card._proof_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.min'_lt_max'_of_card","reducibility":null,"statement_dag_size":34,"type_refs":["Finset","Finset.card","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":273,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Finset","Finset.card","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.min_eq_top._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.min_eq_top","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":41,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.eq_empty_iff_forall_notMem","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.min_of_mem.match_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.min_of_mem","reducibility":"abbrev","statement_dag_size":239,"type_refs":["And","And.intro","DistribLattice.toLattice","Eq","Exists","Exists.intro","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","WithTop","WithTop.instOrderTop","WithTop.semilatticeInf","WithTop.some","instDistribLatticeOfLinearOrder"],"value_dag_size":332,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.inf","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","WithTop","WithTop.instOrderTop","WithTop.semilatticeInf","WithTop.some","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Max","name":"_private.Mathlib.Data.Finset.Max.0.Finset.min_of_nonempty.match_1_1","namespace":"_private.Mathlib.Data.Finset.Max.0.Finset.min_of_nonempty","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mem_mulAntidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mem_mulAntidiagonal","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.mem_toFinset","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mem_mulAntidiagonal._simp_1_2","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mem_mulAntidiagonal","reducibility":null,"statement_dag_size":79,"type_refs":["And","Eq","HMul.hMul","Membership.mem","Mul","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","Set.mulAntidiagonal","instHMul"],"value_dag_size":85,"value_refs":["And","Eq","HMul.hMul","Membership.mem","Mul","Prod","Prod.fst","Prod.snd","Set","Set.instMembership","Set.mem_mulAntidiagonal","Set.mulAntidiagonal","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mulAntidiagonal_min_mul_min._simp_1_1","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mulAntidiagonal_min_mul_min","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mulAntidiagonal_min_mul_min._simp_1_2","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.mulAntidiagonal_min_mul_min","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.support_antidiagonal_subset_add.match_1_1","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.support_antidiagonal_subset_add","reducibility":"abbrev","statement_dag_size":163,"type_refs":["AddCommMonoid","Exists.intro","Finset","Finset.Nonempty","Finset.antidiagonal","Finset.instSetLike","IsOrderedCancelAddMonoid","Membership.mem","PartialOrder","PartialOrder.toPreorder","Prod","Set","Set.IsPWO","Set.instMembership","Set.ofPred","SetLike.instMembership"],"value_dag_size":207,"value_refs":["AddCommMonoid","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.antidiagonal","Finset.instSetLike","IsOrderedCancelAddMonoid","Membership.mem","PartialOrder","PartialOrder.toPreorder","Prod","Set","Set.IsPWO","Set.instMembership","Set.ofPred","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.MulAntidiagonal","name":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.support_mulAntidiagonal_subset_mul.match_1_1","namespace":"_private.Mathlib.Data.Finset.MulAntidiagonal.0.Finset.support_mulAntidiagonal_subset_mul","reducibility":"abbrev","statement_dag_size":163,"type_refs":["CommMonoid","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Finset.mulAntidiagonal","IsOrderedCancelMonoid","Membership.mem","PartialOrder","PartialOrder.toPreorder","Prod","Set","Set.IsPWO","Set.instMembership","Set.ofPred","SetLike.instMembership"],"value_dag_size":207,"value_refs":["CommMonoid","Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Finset.mulAntidiagonal","IsOrderedCancelMonoid","Membership.mem","PartialOrder","PartialOrder.toPreorder","Prod","Set","Set.IsPWO","Set.instMembership","Set.ofPred","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.image","Finset.image₂"],"value_dag_size":62,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.biUnion","Finset.biUnion_image_left","Finset.image","Finset.image₂"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right","reducibility":null,"statement_dag_size":68,"type_refs":["DecidableEq","Disjoint","Eq","Finset","Finset.biUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":74,"value_refs":["DecidableEq","Disjoint","Finset","Finset.biUnion","Finset.disjoint_biUnion_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right._simp_1_3","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.card_dvd_card_image₂_right","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.exists_mem_image₂._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.exists_mem_image₂","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":49,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.exists_mem_image₂._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.exists_mem_image₂","reducibility":null,"statement_dag_size":88,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image2","Set.instMembership"],"value_dag_size":96,"value_refs":["And","Exists","Membership.mem","Set","Set.exists_mem_image2","Set.image2","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.forall_mem_image₂._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.forall_mem_image₂","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":49,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.forall_mem_image₂._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.forall_mem_image₂","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","Membership.mem","Set","Set.image2","Set.instMembership"],"value_dag_size":84,"value_refs":["Membership.mem","Set","Set.forall_mem_image2","Set.image2","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_mk_eq_product._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_mk_eq_product","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_subset_iff_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_subset_iff_left","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_subset_iff_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.image₂_subset_iff_right","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.mem_image₂._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.mem_image₂","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.subset_set_image₂._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.subset_set_image₂","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","LE.le","Set","Set.image","Set.instLE","Set.preimage"],"value_dag_size":53,"value_refs":["LE.le","Set","Set.image","Set.image_subset_iff","Set.instLE","Set.preimage","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Finset.subset_set_image₂._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Finset.subset_set_image₂","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Fintype","Fintype.piFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":72,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Exists"],"value_dag_size":37,"value_refs":["Classical.skolem","Exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂._simp_1_3","namespace":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NAry","name":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂._simp_1_4","namespace":"_private.Mathlib.Data.Finset.NAry.0.Fintype.piFinset_image₂","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatAntidiagonal","name":"_private.Mathlib.Data.Finset.NatAntidiagonal.0.Finset.Nat.antidiagonal_filter_fst_le_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NatAntidiagonal.0.Finset.Nat.antidiagonal_filter_fst_le_of_le","reducibility":null,"statement_dag_size":105,"type_refs":["DFunLike.coe","DecidablePred","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.filter","Finset.map","Function.comp","instDecidablePredComp_batteries"],"value_dag_size":113,"value_refs":["DFunLike.coe","DecidablePred","Eq.symm","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.filter","Finset.map","Finset.map_filter","Function.comp","instDecidablePredComp_batteries"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatAntidiagonal","name":"_private.Mathlib.Data.Finset.NatAntidiagonal.0.Finset.Nat.antidiagonal_filter_le_snd_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NatAntidiagonal.0.Finset.Nat.antidiagonal_filter_le_snd_of_le","reducibility":null,"statement_dag_size":105,"type_refs":["DFunLike.coe","DecidablePred","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.filter","Finset.map","Function.comp","instDecidablePredComp_batteries"],"value_dag_size":113,"value_refs":["DFunLike.coe","DecidablePred","Eq.symm","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.filter","Finset.map","Finset.map_filter","Function.comp","instDecidablePredComp_batteries"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors._simp_1_3","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.Coprime.mul_injOn_divisors","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Nat.mem_divisors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":98,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instSetLike","Finset.mul","HMul.hMul","Membership.mem","Mul","SetLike.instMembership","instHMul"],"value_dag_size":104,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.instSetLike","Finset.mem_mul","Finset.mul","HMul.hMul","Membership.mem","Mul","SetLike.instMembership","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Nat.mem_divisors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_3","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":49,"type_refs":["And","Dvd.dvd","Eq","Exists","HMul.hMul","Nat","Nat.instDvd","instHMul","instMulNat"],"value_dag_size":53,"value_refs":["And","Dvd.dvd","Eq","Exists","HMul.hMul","Nat","Nat.dvd_mul","Nat.instDvd","instHMul","instMulNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_4","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","Ne","NoZeroDivisors","OfNat.ofNat","Zero.toOfNat0","instHMul"],"value_dag_size":66,"value_refs":["And","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","Ne","NoZeroDivisors","OfNat.ofNat","Zero.toOfNat0","instHMul","mul_ne_zero_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_5","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_6","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_7","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_8","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NatDivisors","name":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_9","namespace":"_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Finset.noncommProd_union_of_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Finset.noncommProd_union_of_disjoint","reducibility":null,"statement_dag_size":41,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.val","Multiset","Multiset.instOrderBot","Multiset.instPartialOrder"],"value_dag_size":50,"value_refs":["Disjoint","Eq.symm","Finset","Finset.disjoint_val","Finset.instOrderBot","Finset.instPartialOrder","Finset.val","Multiset","Multiset.instOrderBot","Multiset.instPartialOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.map_noncommProd_aux._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.map_noncommProd_aux","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.mul_noncommProd_erase._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.mul_noncommProd_erase","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_cons'._simp_1_2","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_cons'","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_cons'._simp_1_3","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_cons'","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_eq_pow_card._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_eq_pow_card","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.NoncommProd","name":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_induction._simp_1_1","namespace":"_private.Mathlib.Data.Finset.NoncommProd.0.Multiset.noncommProd_induction","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Option","name":"_private.Mathlib.Data.Finset.Option.0.Finset.forall_mem_insertNone._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Option.0.Finset.forall_mem_insertNone","reducibility":null,"statement_dag_size":28,"type_refs":["And","Eq","Option","Option.none","Option.some"],"value_dag_size":31,"value_refs":["And","Option","Option.forall","Option.none","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Option","name":"_private.Mathlib.Data.Finset.Option.0.Finset.mem_insertNone.match_1_1","namespace":"_private.Mathlib.Data.Finset.Option.0.Finset.mem_insertNone","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":39,"value_refs":["Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Option","name":"_private.Mathlib.Data.Finset.Option.0.Option.mem_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Option.0.Option.mem_toFinset","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Order","name":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le.match_1_1","namespace":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Order","name":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le.match_1_3","namespace":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le","reducibility":"abbrev","statement_dag_size":93,"type_refs":["And","And.intro","Exists","Exists.intro"],"value_dag_size":145,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Order","name":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le.match_1_5","namespace":"_private.Mathlib.Data.Finset.Order.0.Directed.finset_le","reducibility":"abbrev","statement_dag_size":98,"type_refs":["Exists","Exists.intro","Membership.mem","Multiset","Multiset.instMembership"],"value_dag_size":126,"value_refs":["Exists","Exists.casesOn","Exists.intro","Membership.mem","Multiset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PImage","name":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_inter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_inter","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PImage","name":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_inter._simp_1_2","namespace":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_inter","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Inter.inter","LE.le","PFun","PFun.image","Set","Set.instInter","Set.instLE","True"],"value_dag_size":58,"value_refs":["Inter.inter","LE.le","PFun","PFun.image","PFun.image_inter","Set","Set.instInter","Set.instLE","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PImage","name":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_some._simp_1_1","namespace":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_some","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PImage","name":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_subset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PImage","name":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_union._simp_1_1","namespace":"_private.Mathlib.Data.Finset.PImage.0.Finset.pimage_union","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","PFun","PFun.image","Set","Set.instUnion","Union.union"],"value_dag_size":53,"value_refs":["Eq.symm","PFun","PFun.image","PFun.image_union","Set","Set.instUnion","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pairwise","name":"_private.Mathlib.Data.Finset.Pairwise.0.Set.PairwiseDisjoint.biUnion_finset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Pairwise.0.Set.PairwiseDisjoint.biUnion_finset","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.Pi.cons_injective._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.Pi.cons_injective","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Or"],"value_dag_size":42,"value_refs":["Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.Pi.cons_injective._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.Pi.cons_injective","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.domRestrict_preimage._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.domRestrict_preimage","reducibility":null,"statement_dag_size":153,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.image","Finset.instSetLike","Membership.mem","Not","Set","Set.Elem","Set.domRestrict","Set.instMembership","Set.pi","Set.preimage","Set.univ","SetLike.coe","Subtype","Subtype.mk","Subtype.val","dite"],"value_dag_size":2464,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.coe_injective","Finset.image","Finset.instSetLike","Finset.mem_coe","Finset.mem_image","Function.Injective","HEq.refl","HEq.trans","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Set","Set.Elem","Set.domRestrict","Set.domRestrict_apply","Set.ext","Set.instMembership","Set.mem_pi","Set.mem_preimage","Set.mem_univ","Set.pi","Set.preimage","Set.univ","SetLike.coe","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.val","True","True.intro","congr","congrArg","congrFun'","dite","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","heq_of_eq","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.pi_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.pi_nonempty","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Exists"],"value_dag_size":37,"value_refs":["Classical.skolem","Exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.pi_singletons._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.pi_singletons","reducibility":null,"statement_dag_size":67,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.pi","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":1174,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_pi","Finset.mem_singleton","Finset.pi","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage","reducibility":null,"statement_dag_size":59,"type_refs":["Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype.mk","Subtype.val"],"value_dag_size":69,"value_refs":["Eq.mpr_prop","Eq.refl","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Subtype.mk","Subtype.val"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage","reducibility":null,"statement_dag_size":98,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_2"],"value_dag_size":97,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.restrict₂._proof_1","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage","reducibility":null,"statement_dag_size":79,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk","Subtype.val"],"value_dag_size":78,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.restrict₂._proof_1","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_5","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage","reducibility":null,"statement_dag_size":86,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_4"],"value_dag_size":96,"value_refs":["Eq.mpr_prop","Eq.refl","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Lean.Grind.nestedProof","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype.mk","Subtype.val","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Pi","name":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_6","namespace":"_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage","reducibility":null,"statement_dag_size":186,"type_refs":["DecidablePred","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.restrict₂","LE.le","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","Set","Set.pi","Set.preimage","Set.univ","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","dite"],"value_dag_size":2620,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.restrict₂","Finset.restrict₂._proof_1","Finset.restrict₂.eq_1","HEq","HEq.refl","HEq.trans","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.ext","Set.instMembership","Set.mem_pi","Set.mem_preimage","Set.mem_univ","Set.pi","Set.preimage","Set.univ","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_2","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_3","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_4","_private.Mathlib.Data.Finset.Pi.0.Finset.restrict₂_preimage._proof_1_5","congr","congrArg","congrFun'","dite","dite_congr","eq_false","eq_of_heq","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.PiInduction","name":"_private.Mathlib.Data.Finset.PiInduction.0.Finset.induction_on_pi.match_1_1","namespace":"_private.Mathlib.Data.Finset.PiInduction.0.Finset.induction_on_pi","reducibility":"abbrev","statement_dag_size":66,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.PiInduction","name":"_private.Mathlib.Data.Finset.PiInduction.0.Finset.induction_on_pi_of_choice._simp_1_1","namespace":"_private.Mathlib.Data.Finset.PiInduction.0.Finset.induction_on_pi_of_choice","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Piecewise","name":"_private.Mathlib.Data.Finset.Piecewise.0.Finset.piecewise_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Piecewise.0.Finset.piecewise_insert","reducibility":null,"statement_dag_size":62,"type_refs":["Decidable","Eq","Finset","Finset.instSetLike","Finset.piecewise","Membership.mem","Set.piecewise","SetLike.coe","SetLike.instMembership"],"value_dag_size":70,"value_refs":["Decidable","Eq.symm","Finset","Finset.instSetLike","Finset.piecewise","Finset.piecewise_coe","Membership.mem","Set.piecewise","SetLike.coe","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Piecewise","name":"_private.Mathlib.Data.Finset.Piecewise.0.Finset.piecewise_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Piecewise.0.Finset.piecewise_insert","reducibility":null,"statement_dag_size":83,"type_refs":["Decidable","DecidableEq","Eq","Function.update","Insert.insert","Membership.mem","Set","Set.instInsert","Set.instMembership","Set.piecewise"],"value_dag_size":94,"value_refs":["Decidable","DecidableEq","Eq.symm","Function.update","Insert.insert","Membership.mem","Set","Set.instInsert","Set.instMembership","Set.piecewise","Set.piecewise_insert"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.biUnion_id_subset_iff_subset_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.biUnion_id_subset_iff_subset_powerset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset._proof_1_5","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Finset","Finset.card","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":693,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset.match_1_3","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.filter_powersetCard_subset","reducibility":"abbrev","statement_dag_size":130,"type_refs":["And","And.intro","Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":190,"value_refs":["And","And.casesOn","And.intro","Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_injOn_powerset_of_injOn._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_injOn_powerset_of_injOn","reducibility":null,"statement_dag_size":101,"type_refs":["DecidableEq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Set.InjOn","SetLike.coe","SetLike.instMembership"],"value_dag_size":854,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_coe","Finset.mem_image","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.InjOn","Set.InjOn.eq_iff","Set.instMembership","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_injOn_powerset_of_injOn._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_injOn_powerset_of_injOn","reducibility":null,"statement_dag_size":149,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","Iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":1194,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_coe","Finset.mem_powerset","Finset.powerset","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.eq_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_surjOn_powerset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.image_surjOn_powerset","reducibility":null,"statement_dag_size":110,"type_refs":["And","DecidableEq","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.image","Finset.instSetLike","Finset.powerset","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":1828,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_coe","Finset.mem_filter","Finset.mem_image","Finset.mem_powerset","Finset.powerset","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.mk","Membership.mem","Multiset","Multiset.Nodup","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instSetLike","Finset.mem_mk","Finset.mk","Membership.mem","Multiset","Multiset.Nodup","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.pmap"],"value_dag_size":88,"value_refs":["Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_pmap","Multiset.pmap","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset._simp_1_6","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.mem_powerset","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.val","LE.le","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.instPartialOrder","Finset.val","Finset.val_le_iff","LE.le","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":95,"type_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Eq","HeytingAlgebra.toOrderBot","Inter.inter","Membership.mem","Order.Frame.toHeytingAlgebra","Set","Set.Nonempty","Set.PairwiseDisjoint","Set.instCompleteAtomicBooleanAlgebra","Set.instInter","Set.instMembership"],"value_dag_size":99,"value_refs":["CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra","CompleteBooleanAlgebra.toCompleteDistribLattice","CompleteBooleanAlgebra.toCompleteLattice","CompleteDistribLattice.toFrame","CompleteLattice.toCompleteSemilatticeInf","CompleteSemilatticeInf.toPartialOrder","Eq","HeytingAlgebra.toOrderBot","Inter.inter","Membership.mem","Order.Frame.toHeytingAlgebra","Set","Set.Nonempty","Set.PairwiseDisjoint","Set.instCompleteAtomicBooleanAlgebra","Set.instInter","Set.instMembership","Set.pairwiseDisjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership"],"value_dag_size":44,"value_refs":["And","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.mem_inter_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership"],"value_dag_size":46,"value_refs":["Eq","Insert.insert","Membership.mem","Or","Set","Set.instInsert","Set.instMembership","Set.mem_insert_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_5","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_6","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","Exists","Or"],"value_dag_size":44,"value_refs":["And","Eq","Exists","Or","exists_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_7","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_8","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_9","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":12,"value_refs":["True","imp_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_empty_subsingleton._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_empty_subsingleton","reducibility":null,"statement_dag_size":35,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":37,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.subset_empty","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_injOn.match_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_injOn","reducibility":"abbrev","statement_dag_size":196,"type_refs":["Eq","Eq.refl","Finset","Finset.card","Finset.powersetCard","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","instLENat"],"value_dag_size":406,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Finset","Finset.card","Finset.powersetCard","HEq","HEq.refl","LE.le","Membership.mem","Nat","Set","Set.instMembership","Set.ofPred","eq_of_heq","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_map._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_map","reducibility":null,"statement_dag_size":109,"type_refs":["And","Classical.propDecidable","DFunLike.coe","Eq","Finset","Finset.card","Finset.decidableMem","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","LE.le","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1261,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.decidableMem","Finset.ext","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.map","Finset.mem_filter","Finset.mem_map","Finset.subset_iff","Function.Embedding","Function.instFunLikeEmbedding","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Nat","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_map._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_map","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_nonempty","reducibility":null,"statement_dag_size":55,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","True","instLENat"],"value_dag_size":58,"value_refs":["And","Eq","Exists","Finset","Finset.card","Finset.exists_subset_card_eq","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_nonempty._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_nonempty","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","True","instLENat"],"value_dag_size":45,"value_refs":["Finset","Finset.card","Finset.card_le_card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_self.match_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_self","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":124,"value_refs":["And","And.casesOn","And.intro","Eq","Finset","Finset.card","Finset.instPartialOrder","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_succ_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_succ_insert","reducibility":null,"statement_dag_size":102,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.decidableEq","Finset.filter","Finset.image","Finset.instInsert","Finset.instSetLike","Finset.instUnion","Finset.powerset","Finset.powersetCard","Insert.insert","Membership.mem","Nat","Nat.succ","Not","SetLike.instMembership","Union.union","instDecidableEqNat"],"value_dag_size":3694,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_insert_of_notMem","Finset.decidableEq","Finset.ext","Finset.filter","Finset.filter_congr","Finset.image","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_image","Finset.mem_powerset","Finset.mem_powersetCard","Finset.mem_union","Finset.powerset","Finset.powersetCard","Finset.subset_iff","HAdd.hAdd","Iff","Iff.of_eq","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_sup._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_sup","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_sup._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_sup","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_zero._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_zero","reducibility":null,"statement_dag_size":37,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSingleton","Finset.powersetCard","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":939,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_empty","Finset.card_ne_zero_of_mem","Finset.ext","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_powersetCard","Finset.mem_singleton","Finset.notMem_empty","Finset.powersetCard","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instOfNatNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_image._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_image","reducibility":null,"statement_dag_size":99,"type_refs":["And","DecidableEq","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.image","Finset.instSetLike","Finset.powerset","Membership.mem","SetLike.instMembership"],"value_dag_size":1716,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_filter","Finset.mem_image","Finset.mem_powerset","Finset.powerset","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_image._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_image","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","Finset","Finset.decidableEq","Finset.image","Finset.instSetLike","Finset.powerset","Membership.mem","SetLike.instMembership"],"value_dag_size":841,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableEq","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_image","Finset.mem_powerset","Finset.powerset","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert","reducibility":null,"statement_dag_size":74,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Iff","Insert.insert","LE.le","Or","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":1828,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.insert_eq_of_mem","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finset.subset_iff","Iff","Insert.insert","LE.le","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_left","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Powerset","name":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Powerset.0.Finset.powerset_insert","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":56,"value_refs":["DecidableEq","Finset","Finset.erase","Finset.instInsert","Finset.instPartialOrder","Finset.subset_insert_iff","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Equiv.image_symm_eq_preimage_of_finset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Equiv.image_symm_eq_preimage_of_finset","reducibility":null,"statement_dag_size":100,"type_refs":["DFunLike.coe","DecidableEq","Eq","Equiv","Equiv.injective","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Finset","Finset.image","Finset.instSetLike","Finset.preimage","Function.Injective.injOn","Set.preimage","SetLike.coe"],"value_dag_size":1290,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DFunLike.coe.hcongr_6","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.apply_symm_apply","Equiv.injective","Equiv.instEquivLike","Equiv.restrictPreimageFinset._proof_1","Equiv.symm","Equiv.symm_apply_apply","EquivLike.toFunLike","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.image","Finset.instSetLike","Finset.mem_image","Finset.mem_preimage","Finset.preimage","FunLike","Function.Injective.injOn","HEq.refl","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","heq_of_eq","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.disjoint_preimage._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.disjoint_preimage","reducibility":null,"statement_dag_size":85,"type_refs":["Disjoint","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.preimage","Set.InjOn","Set.preimage","SetLike.coe"],"value_dag_size":643,"value_refs":["And","And.casesOn","Classical.byContradiction","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_preimage","Finset.not_disjoint_iff","Finset.preimage","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Membership.mem","Not","Or","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_eq_preimage_of_leftInvOn_injOn._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_eq_preimage_of_leftInvOn_injOn","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Set","SetLike","SetLike.coe"],"value_dag_size":41,"value_refs":["Eq","Set","SetLike","SetLike.coe","SetLike.ext'_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_preimage._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_preimage","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.ofPred"],"value_dag_size":46,"value_refs":["And","Eq.symm","Inter.inter","Membership.mem","Set","Set.instInter","Set.instMembership","Set.ofPred","Set.sep_mem_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_subset_iff_subset_preimage._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.image_subset_iff_subset_preimage","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.sigma_preimage_mk._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.sigma_preimage_mk","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.subset_map_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.subset_map_iff","reducibility":null,"statement_dag_size":79,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":85,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instPartialOrder","Finset.subset_image_iff","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Preimage","name":"_private.Mathlib.Data.Finset.Preimage.0.Finset.subset_map_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Preimage.0.Finset.subset_map_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.fst.match_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.fst","reducibility":"abbrev","statement_dag_size":123,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","SProd.sprod","SetLike.instMembership"],"value_dag_size":158,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","SProd.sprod","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.product.match_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.product","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.snd.match_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.Nonempty.snd","reducibility":"abbrev","statement_dag_size":123,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","SProd.sprod","SetLike.instMembership"],"value_dag_size":158,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","SProd.sprod","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt","reducibility":null,"statement_dag_size":89,"type_refs":["Disjoint","DistribLattice.toLattice","Finset","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":672,"value_refs":["And","Classical.byContradiction","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.disjoint_left","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mem_filter","Iff","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Order.lt_eq_false_of_lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","LinearOrder","LinearOrder.toDecidableLT","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","eq_false","id","instDistribLatticeOfLinearOrder","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt","reducibility":null,"statement_dag_size":156,"type_refs":["Disjoint","DistribLattice.toLattice","Eq","Finset","Finset.disjUnion","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.offDiag","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":1750,"value_refs":["And","And.casesOn","Classical.byContradiction","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.disjUnion","Finset.ext","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mem_disjUnion","Finset.mem_filter","Finset.mem_offDiag","Finset.mem_product","Finset.offDiag","Iff","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Order.eq_of_le_of_le","Lean.Grind.Order.le_lt_trans","Lean.Grind.Order.le_of_eq_1","Lean.Grind.Order.le_of_eq_2","Lean.Grind.Order.le_of_not_lt","Lean.Grind.Order.lt_unsat","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toDecidableLT","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDistribLatticeOfLinearOrder","instIsLinearOrder_mathlib","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLawfulOrderLT_mathlib","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt","reducibility":null,"statement_dag_size":124,"type_refs":["DFunLike.coe","DistribLattice.toLattice","Equiv","Equiv.instEquivLike","Equiv.prodComm","EquivLike.toFunLike","Finset","Finset.filter","Finset.instSProd","Finset.instSetLike","Iff","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","Membership.mem","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","SetLike.instMembership","instDistribLatticeOfLinearOrder"],"value_dag_size":1061,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","Equiv.prodComm","Equiv.prodComm_apply","EquivLike.toFunLike","False","False.elim","Finset","Finset.filter","Finset.instSProd","Finset.instSetLike","Finset.mem_filter","Finset.mem_product","Iff","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","LinearOrder","LinearOrder.toDecidableLT","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.casesOn","Prod.fst","Prod.fst_swap","Prod.mk","Prod.snd","Prod.snd_swap","Prod.swap","SProd.sprod","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","congr","congrArg","eq_false","eq_true","id","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.card_product_filter_lt","reducibility":null,"statement_dag_size":283,"type_refs":["Disjoint","DistribLattice.toLattice","Eq","Finset","Finset.card","Finset.disjUnion","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.offDiag","LT.lt","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","Nat","Nat.choose","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instOfNatNat"],"value_dag_size":1403,"value_refs":["Bool","Bool.true","Classical.byContradiction","Disjoint","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.card","Finset.card_disjUnion","Finset.disjUnion","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSProd","Finset.offDiag","Finset.offDiag_card","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.emod_nonneg","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.mul","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder","LinearOrder.toDecidableLT","Nat","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.choose","Nat.choose_two_right","Nat.instDiv","Nat.mul_sub_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Prod","Prod.fst","Prod.snd","SProd.sprod","SemilatticeInf.toPartialOrder","congrArg","eagerReduce","id","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHDiv","instHMod","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_insert","reducibility":null,"statement_dag_size":60,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instInsert","Insert.insert","Prod","Prod.mk","instDecidableEqProd"],"value_dag_size":1395,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_diag","Finset.mem_insert","HEq","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.mk.noConfusion","Prod.snd","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","heq_eq_eq","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_inter","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instInter","Inter.inter","Prod","instDecidableEqProd"],"value_dag_size":883,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_diag","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_singleton","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Finset","Finset.diag","Finset.instSingleton","Prod","Prod.mk","Singleton.singleton"],"value_dag_size":740,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_diag","Finset.mem_singleton","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","SetLike.instMembership","Singleton.singleton","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_union","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instUnion","Prod","Union.union","instDecidableEqProd"],"value_dag_size":1112,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_diag","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_union_offDiag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.diag_union_offDiag","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instSProd","Finset.instUnion","Finset.offDiag","Prod","SProd.sprod","Union.union","instDecidableEqProd"],"value_dag_size":1150,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instSProd","Finset.instSetLike","Finset.instUnion","Finset.mem_diag","Finset.mem_offDiag","Finset.mem_product","Finset.mem_union","Finset.offDiag","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_diag_offDiag._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_diag_offDiag","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_product._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_product","reducibility":null,"statement_dag_size":67,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq.symm","Finset","Finset.disjoint_coe","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_product._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.disjoint_product","reducibility":null,"statement_dag_size":143,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Or","Prod","SProd.sprod","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","Set.instSProd"],"value_dag_size":149,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","Or","Prod","SProd.sprod","SemilatticeInf.toPartialOrder","Set","Set.disjoint_prod","Set.instBooleanAlgebra","Set.instSProd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.filter_product._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.filter_product","reducibility":null,"statement_dag_size":93,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSProd","Prod","Prod.fst","Prod.snd","SProd.sprod","instDecidableAnd"],"value_dag_size":1057,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSProd","Finset.instSetLike","Finset.mem_filter","Finset.mem_product","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableAnd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.filter_product_card._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.filter_product_card","reducibility":null,"statement_dag_size":155,"type_refs":["And","Classical.propDecidable","DecidablePred","Eq","Finset","Finset.filter","Finset.instSProd","Finset.instUnion","Not","Prod","Prod.fst","Prod.snd","SProd.sprod","Union.union","instDecidableAnd","instDecidableEqOfIff","instDecidableEqProd","instDecidableIff","instDecidableNot"],"value_dag_size":1958,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.filter","Finset.instSProd","Finset.instSetLike","Finset.instUnion","Finset.mem_filter","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableAnd","instDecidableEqOfIff","instDecidableEqProd","instDecidableIff","instDecidableNot","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.image_diag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.image_diag","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.image","Prod","Prod.mk"],"value_dag_size":1290,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.diag","Finset.ext","Finset.image","Finset.instSetLike","Finset.mem_diag","Finset.mem_image","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SetLike.instMembership","True","True.intro","and_true","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.inter_product._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.inter_product","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSProd","Inter.inter","Prod","SProd.sprod","instDecidableEqProd"],"value_dag_size":1014,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSProd","Finset.instSetLike","Finset.mem_inter","Finset.mem_product","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.nontrivial_prod_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.nontrivial_prod_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.Nonempty","Finset.card","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq.symm","Finset","Finset.Nonempty","Finset.card","Finset.card_pos","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.nontrivial_prod_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.nontrivial_prod_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.Nontrivial","Finset.card","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq.symm","Finset","Finset.Nontrivial","Finset.card","Finset.one_lt_card_iff_nontrivial","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.offDiag_insert._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.offDiag_insert","reducibility":null,"statement_dag_size":94,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSProd","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.offDiag","Insert.insert","Membership.mem","Not","Prod","SProd.sprod","SetLike.instMembership","Singleton.singleton","Union.union","instDecidableEqProd"],"value_dag_size":2377,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instInsert","Finset.instSProd","Finset.instSetLike","Finset.instSingleton","Finset.instUnion","Finset.mem_insert","Finset.mem_offDiag","Finset.mem_product","Finset.mem_singleton","Finset.mem_union","Finset.offDiag","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","Singleton.singleton","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.offDiag_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.offDiag_singleton","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":45,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.prodMap_map_product._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.prodMap_map_product","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_biUnion","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instSProd","Prod","Prod.mk","SProd.sprod"],"value_dag_size":1885,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSProd","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_product","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_eq_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_eq_biUnion","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.image","Finset.instSProd","Prod","Prod.mk","SProd.sprod"],"value_dag_size":1567,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.biUnion","Finset.ext","Finset.image","Finset.instSProd","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_image","Finset.mem_product","HEq","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.noConfusion","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","heq_eq_eq","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_eq_biUnion_right._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_eq_biUnion_right","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.image","Finset.instSProd","Prod","Prod.mk","SProd.sprod"],"value_dag_size":1573,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.biUnion","Finset.ext","Finset.image","Finset.instSProd","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_image","Finset.mem_product","HEq","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.mk.noConfusion","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","heq_eq_eq","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_image_fst._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_image_fst","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_image_snd._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_image_snd","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_inter","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSProd","Inter.inter","Prod","SProd.sprod","instDecidableEqProd"],"value_dag_size":987,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSProd","Finset.instSetLike","Finset.mem_inter","Finset.mem_product","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_inter_product._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_inter_product","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSProd","Inter.inter","Prod","SProd.sprod","instDecidableEqProd"],"value_dag_size":1092,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSProd","Finset.instSetLike","Finset.mem_inter","Finset.mem_product","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_sdiff_diag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_sdiff_diag","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instSDiff","Finset.instSProd","Finset.offDiag","Prod","SDiff.sdiff","SProd.sprod","instDecidableEqProd"],"value_dag_size":887,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instSDiff","Finset.instSProd","Finset.instSetLike","Finset.mem_diag","Finset.mem_offDiag","Finset.mem_product","Finset.mem_sdiff","Finset.offDiag","Iff","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SDiff.sdiff","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_sdiff_offDiag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_sdiff_offDiag","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.diag","Finset.instSDiff","Finset.instSProd","Finset.offDiag","Prod","SDiff.sdiff","SProd.sprod","instDecidableEqProd"],"value_dag_size":930,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.diag","Finset.ext","Finset.instSDiff","Finset.instSProd","Finset.instSetLike","Finset.mem_diag","Finset.mem_offDiag","Finset.mem_product","Finset.mem_sdiff","Finset.offDiag","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SDiff.sdiff","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_singleton","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_singleton._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_singleton","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_subset_product.match_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_subset_product","reducibility":"abbrev","statement_dag_size":122,"type_refs":["Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.mk","SProd.sprod","SetLike.instMembership"],"value_dag_size":165,"value_refs":["Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.casesOn","Prod.mk","SProd.sprod","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.product_union","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","Finset","Finset.instSProd","Finset.instUnion","Prod","SProd.sprod","Union.union","instDecidableEqProd"],"value_dag_size":1324,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSProd","Finset.instSetLike","Finset.instUnion","Finset.mem_product","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.singleton_product._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.singleton_product","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.singleton_product._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.singleton_product","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSProd","LE.le","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.fst","Prod.snd","SProd.sprod"],"value_dag_size":899,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instPartialOrder","Finset.instSProd","Finset.instSetLike","Finset.mem_image","Finset.mem_product","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.not_and","Lean.Grind.not_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_self","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product_image_fst._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product_image_fst","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product_image_snd._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product_image_snd","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Prod","name":"_private.Mathlib.Data.Finset.Prod.0.Finset.union_product._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Prod.0.Finset.union_product","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Eq","Finset","Finset.instSProd","Finset.instUnion","Prod","SProd.sprod","Union.union","instDecidableEqProd"],"value_dag_size":1290,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSProd","Finset.instSetLike","Finset.instUnion","Finset.mem_product","Finset.mem_union","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SProd.sprod","SetLike.instMembership","True","True.intro","Union.union","congr","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqProd","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.exists_nat_subset_range._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.exists_nat_subset_range","reducibility":null,"statement_dag_size":71,"type_refs":["Exists","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.range","HAdd.hAdd","Insert.insert","LE.le","Max.max","Nat","Nat.instMax","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instDecidableEqNat","instHAdd","instOfNatNat"],"value_dag_size":1427,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.mem_range","Finset.range","Finset.subset_iff","HAdd.hAdd","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.decLe","Nat.instLinearOrder","Nat.instMax","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","max_def","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.exists_nat_subset_range.match_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.exists_nat_subset_range","reducibility":"abbrev","statement_dag_size":51,"type_refs":["Exists","Exists.intro","Finset","Finset.instPartialOrder","Finset.range","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":67,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instPartialOrder","Finset.range","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_le._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_le","reducibility":null,"statement_dag_size":29,"type_refs":["Finset","Finset.instSetLike","Finset.range","LE.le","Membership.mem","Nat","SetLike.instMembership","instLENat"],"value_dag_size":342,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_sub_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_sub_ne_zero","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","HSub.hSub","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instHSub","instOfNatNat","instSubNat"],"value_dag_size":636,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_succ_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_succ_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Finset","Finset.instSetLike","Finset.range","Iff","LE.le","Membership.mem","Nat","Nat.succ","SetLike.instMembership","instLENat"],"value_dag_size":646,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","Not","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":301,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","SetLike.instMembership","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff._proof_1_4","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":248,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","SetLike.instMembership","congrArg","eagerReduce","eq_false","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff.match_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.nonempty_range_iff","reducibility":"abbrev","statement_dag_size":47,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Finset.range","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":64,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Finset.range","Membership.mem","Nat","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.notMem_range_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.notMem_range_self","reducibility":null,"statement_dag_size":21,"type_refs":["Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","Not","SetLike.instMembership"],"value_dag_size":181,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","SetLike.instMembership","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.range_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.range_add_one","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instInsert","Finset.range","HAdd.hAdd","Insert.insert","Nat","OfNat.ofNat","instAddNat","instDecidableEqNat","instHAdd","instOfNatNat"],"value_dag_size":1062,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.mem_range","Finset.range","HAdd.hAdd","HSub.hSub","Iff","Insert.insert","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.range_eq_empty_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.range_eq_empty_iff","reducibility":null,"statement_dag_size":29,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.range","Iff","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":504,"value_refs":["And","And.casesOn","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.ext","Finset.instEmptyCollection","Finset.instSetLike","Finset.nonempty_def","Finset.nonempty_range_iff","Finset.notMem_empty","Finset.range","Iff","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instOfNatNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.range_nontrivial._proof_1_2","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.range_nontrivial","reducibility":null,"statement_dag_size":37,"type_refs":["LT.lt","Membership.mem","Nat","Nat.instPreorder","OfNat.ofNat","Set","Set.Iio","Set.instMembership","instLTNat","instOfNatNat"],"value_dag_size":265,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLT","Set","Set.Iio","Set.instMembership","Set.mem_Iio","congrArg","eagerReduce","eq_false","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.range_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.range_subset","reducibility":null,"statement_dag_size":46,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.range","Iff","LE.le","LT.lt","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instLTNat"],"value_dag_size":499,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.subset_iff","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.range_subset_range._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.range_subset_range","reducibility":null,"statement_dag_size":31,"type_refs":["Finset","Finset.instPartialOrder","Finset.range","Iff","LE.le","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":956,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.range_subset","Finset.subset_iff","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.self_mem_range_succ._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.self_mem_range_succ","reducibility":null,"statement_dag_size":37,"type_refs":["Finset","Finset.instSetLike","Finset.range","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":203,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","HAdd.hAdd","HSub.hSub","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","SetLike.instMembership","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.strictMono_range._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.strictMono_range","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":47,"value_refs":["And","Finset","Finset.instPartialOrder","Finset.ssubset_def","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.Finset.subset_range._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Range.0.Finset.subset_range","reducibility":null,"statement_dag_size":46,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.range","Iff","LE.le","LT.lt","Membership.mem","Nat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instLTNat"],"value_dag_size":505,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_range","Finset.range","Finset.subset_iff","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_2","namespace":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv","reducibility":null,"statement_dag_size":34,"type_refs":["Finset","Finset.instSetLike","Finset.range","HAdd.hAdd","Membership.mem","Nat","Not","SetLike.instMembership","instAddNat","instHAdd"],"value_dag_size":108,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","Finset","Finset.instSetLike","Finset.range","HAdd.hAdd","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","SetLike.instMembership","eagerReduce","id","instAddNat","instHAdd","instOfNatNat","notMemRangeEquiv._proof_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_3","namespace":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv","reducibility":null,"statement_dag_size":61,"type_refs":["Finset","Finset.instSetLike","Finset.range","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Not","SetLike.instMembership","Subtype","Subtype.val","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":51,"value_refs":["Finset","Finset.instSetLike","Finset.range","HSub.hSub","Membership.mem","Nat","Not","SetLike.instMembership","Subtype","Subtype.val","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_2","instHSub","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_4","namespace":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv","reducibility":null,"statement_dag_size":66,"type_refs":["Finset","Finset.instSetLike","Finset.range","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Not","SetLike.instMembership","Subtype.mk","Subtype.val","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":39,"value_refs":["Finset","Finset.instSetLike","Finset.range","Membership.mem","Nat","Not","SetLike.instMembership","Subtype.mk","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_5","namespace":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv","reducibility":null,"statement_dag_size":73,"type_refs":["Finset","Finset.instSetLike","Finset.range","Function.LeftInverse","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Not","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","instAddNat","instHAdd","instHSub","instSubNat","notMemRangeEquiv._proof_1"],"value_dag_size":1016,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_range","Finset.range","Function.LeftInverse","Function.LeftInverse.eq_1","HAdd.hAdd","HEq.refl","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.congr_simp","Subtype.mk.hcongr_4","Subtype.val","True","True.intro","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_2","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_3","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_4","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","funext","heq_of_eq","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","notMemRangeEquiv._proof_1","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Range","name":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_7","namespace":"_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv","reducibility":null,"statement_dag_size":73,"type_refs":["Finset","Finset.instSetLike","Finset.range","Function.RightInverse","HAdd.hAdd","HSub.hSub","Membership.mem","Nat","Not","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","instAddNat","instHAdd","instHSub","instSubNat","notMemRangeEquiv._proof_1"],"value_dag_size":914,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.range","Function.LeftInverse","Function.LeftInverse.eq_1","Function.RightInverse","Function.RightInverse.eq_1","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","Subtype","Subtype.mk","Subtype.mk.congr_simp","Subtype.val","_private.Mathlib.Data.Finset.Range.0.notMemRangeEquiv._proof_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","notMemRangeEquiv._proof_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.Nontrivial.sdiff_singleton_nonempty._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.Nontrivial.sdiff_singleton_nonempty","reducibility":null,"statement_dag_size":37,"type_refs":["DecidableEq","Finset","Finset.Nonempty","Finset.Nontrivial","Finset.instSDiff","Finset.instSingleton","SDiff.sdiff","Singleton.singleton"],"value_dag_size":540,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.Nontrivial","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.nontrivial_def","Finset.sdiff_nonempty","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Membership.mem","Ne","Not","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","Set.Nontrivial","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.cons_sdiff_cons._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.cons_sdiff_cons","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Eq","Finset","Finset.cons","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Membership.mem","Ne","Not","SDiff.sdiff","SetLike.instMembership","Singleton.singleton"],"value_dag_size":743,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.cons","Finset.ext","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_cons","Finset.mem_sdiff","Finset.mem_singleton","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Ne","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.disjoint_injOn_union_left._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.disjoint_injOn_union_left","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","Disjoint","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instUnion","Set.InjOn","Set.ofPred","Union.union"],"value_dag_size":574,"value_refs":["Classical.byContradiction","DecidableEq","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","Finset.instUnion","Finset.union_sdiff_cancel_right","Iff","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Membership.mem","Not","SDiff.sdiff","Set","Set.InjOn","Set.InjOn.eq_1","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","Union.union","congrArg","disjoint_comm","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_cancel._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_cancel","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","Singleton.singleton"],"value_dag_size":605,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_sdiff","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_of_mem","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Insert.insert","Membership.mem","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":615,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_of_notMem","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Insert.insert","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":832,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_self_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.insert_sdiff_self_of_mem","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Insert.insert","Membership.mem","SDiff.sdiff","SetLike.instMembership","Singleton.singleton"],"value_dag_size":596,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.instSingleton","Finset.mem_insert","Finset.mem_sdiff","Finset.mem_singleton","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","LE.le","Lattice.inf","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder"],"value_dag_size":18,"value_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","Lattice.inf_le_left"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_2","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","LE.le","Lattice.inf","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder"],"value_dag_size":18,"value_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","Lattice.inf_le_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_3","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra","reducibility":null,"statement_dag_size":84,"type_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","LE.le","Lattice.inf","Lattice.toSemilatticeSup","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder"],"value_dag_size":18,"value_refs":["DecidableEq","DistribLattice.toLattice","Finset","Finset.instDistribLattice","Lattice.le_inf"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_4","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra","reducibility":null,"statement_dag_size":74,"type_refs":["DecidableEq","DistribLattice.toLattice","Eq","Finset","Finset.instDistribLattice","Finset.instSDiff","Lattice.inf","Lattice.inf_le_left","Lattice.inf_le_right","Lattice.le_inf","Lattice.toSemilatticeSup","Max.max","Min.min","SDiff.sdiff","SemilatticeInf.mk","SemilatticeInf.toMin","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder"],"value_dag_size":781,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.inf_eq_inter","Finset.instDistribLattice","Finset.instInter","Finset.instLattice","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_inter","Finset.mem_sdiff","Finset.mem_union","Finset.sup_eq_union","Iff","Inter.inter","Lattice.inf","Lattice.inf_le_left","Lattice.inf_le_right","Lattice.le_inf","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Max.max","Membership.mem","Min.min","Not","Or","Or.casesOn","SDiff.sdiff","SemilatticeInf.mk","SemilatticeInf.toMin","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_6","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra","reducibility":null,"statement_dag_size":85,"type_refs":["Bot.bot","DecidableEq","DistribLattice.toLattice","Eq","Finset","Finset.instDistribLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","Lattice.inf","Lattice.inf_le_left","Lattice.inf_le_right","Lattice.le_inf","Lattice.toSemilatticeSup","Min.min","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.mk","SemilatticeInf.toMin","SemilatticeSup.toPartialOrder"],"value_dag_size":553,"value_refs":["And","Bot.bot","Classical.byContradiction","DecidableEq","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.inf_eq_inter","Finset.instDistribLattice","Finset.instInter","Finset.instLattice","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_inter","Finset.mem_sdiff","Finset.subset_iff","Iff","Inter.inter","LE.le","Lattice.inf","Lattice.inf_le_left","Lattice.inf_le_right","Lattice.le_inf","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Min.min","Not","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SemilatticeInf.mk","SemilatticeInf.toMin","SemilatticeSup.toPartialOrder","SetLike.instMembership","True","True.intro","bot_unique","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.inter_sdiff_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.inter_sdiff_self","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instInter","Finset.instSDiff","Inter.inter","SDiff.sdiff"],"value_dag_size":366,"value_refs":["And","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instEmptyCollection","Finset.instInter","Finset.instSDiff","Finset.instSetLike","Finset.mem_inter","Finset.mem_sdiff","Finset.notMem_empty","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","forall_congr","funext","id","implies_congr","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.notMem_sdiff_of_mem_right._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.notMem_sdiff_of_mem_right","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":153,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","True","True.intro","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_insert_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_insert_of_notMem","reducibility":null,"statement_dag_size":56,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Insert.insert","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":622,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSDiff","Finset.instSetLike","Finset.mem_insert","Finset.mem_sdiff","Iff","Insert.insert","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_ssubset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_ssubset","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Finset","Finset.Nonempty","Finset.instPartialOrder","Finset.instSDiff","LE.le","LT.lt","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff"],"value_dag_size":553,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Finset.nonempty_def","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Iff","LE.le","LT.lt","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_subset_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_subset_sdiff","reducibility":null,"statement_dag_size":68,"type_refs":["DecidableEq","Finset","Finset.instPartialOrder","Finset.instSDiff","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff"],"value_dag_size":456,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_union_of_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.sdiff_union_of_subset","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","Union.union"],"value_dag_size":627,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_sdiff","Finset.mem_union","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.superset_injOn_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.superset_injOn_sdiff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Finset","Finset.instPartialOrder","Finset.instSDiff","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","Set.InjOn","Set.ofPred"],"value_dag_size":541,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instUnion","Finset.sdiff_union_of_subset","LE.le","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","Set","Set.InjOn","Set.InjOn.eq_1","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","Union.union","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SDiff","name":"_private.Mathlib.Data.Finset.SDiff.0.Finset.union_sdiff_of_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.SDiff.0.Finset.union_sdiff_of_subset","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","Union.union"],"value_dag_size":632,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.instUnion","Finset.mem_sdiff","Finset.mem_union","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SMulAntidiagonal","name":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.mem_smulAntidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.mem_smulAntidiagonal","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.mem_toFinset","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SMulAntidiagonal","name":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.smulAntidiagonal_min_smul_min._simp_1_1","namespace":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.smulAntidiagonal_min_smul_min","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SMulAntidiagonal","name":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.smulAntidiagonal_min_smul_min._simp_1_2","namespace":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.smulAntidiagonal_min_smul_min","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SMulAntidiagonal","name":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.support_smulAntidiagonal_subset_smul._proof_1_2","namespace":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.support_smulAntidiagonal_subset_smul","reducibility":null,"statement_dag_size":78,"type_refs":["Finset.Nonempty","Finset.SMulAntidiagonal","HSMul.hSMul","LE.le","Prod","SMul","Set","Set.Finite","Set.instLE","Set.ofPred","Set.smul","Set.smulAntidiagonal","instHSMul"],"value_dag_size":2541,"value_refs":["And","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.SMulAntidiagonal","Finset.instSetLike","Finset.mem_smulAntidiagonal","Finset.nonempty_def","HSMul.hSMul","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_false","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","SMul","Set","Set.Finite","Set.instEmptyCollection","Set.instLE","Set.instMembership","Set.mem_empty_iff_false","Set.mem_ofPred_eq","Set.mem_smul","Set.ofPred","Set.ofPred_false","Set.smul","Set.smulAntidiagonal","Set.subset_def","SetLike.instMembership","True","True.casesOn","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instHSMul","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SMulAntidiagonal","name":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.support_vaddAntidiagonal_subset_vadd._proof_1_2","namespace":"_private.Mathlib.Data.Finset.SMulAntidiagonal.0.Finset.support_vaddAntidiagonal_subset_vadd","reducibility":null,"statement_dag_size":78,"type_refs":["Finset.Nonempty","Finset.VAddAntidiagonal","HVAdd.hVAdd","LE.le","Prod","Set","Set.Finite","Set.instLE","Set.ofPred","Set.vadd","Set.vaddAntidiagonal","VAdd","instHVAdd"],"value_dag_size":2541,"value_refs":["And","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Nonempty","Finset.VAddAntidiagonal","Finset.instSetLike","Finset.mem_vaddAntidiagonal","Finset.nonempty_def","HVAdd.hVAdd","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_false","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.casesOn","Prod.fst","Prod.mk","Prod.snd","Set","Set.Finite","Set.instEmptyCollection","Set.instLE","Set.instMembership","Set.mem_empty_iff_false","Set.mem_ofPred_eq","Set.mem_vadd","Set.ofPred","Set.ofPred_false","Set.subset_def","Set.vadd","Set.vaddAntidiagonal","SetLike.instMembership","True","True.casesOn","True.intro","VAdd","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instHVAdd","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.filter_sigma._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.filter_sigma","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.filter_sigma._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.filter_sigma","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.mem_sigmaLift","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.pairwiseDisjoint_map_sigmaMk._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.pairwiseDisjoint_map_sigmaMk","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigmaLift_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigmaLift_nonempty","reducibility":null,"statement_dag_size":25,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.Nonempty","Finset.instEmptyCollection","Ne"],"value_dag_size":27,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.Nonempty","Finset.instEmptyCollection","Finset.nonempty_iff_ne_empty","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_eq_biUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_eq_biUnion","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_mono.match_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_mono","reducibility":"abbrev","statement_dag_size":199,"type_refs":["And","And.intro","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sigma.fst","Sigma.mk","Sigma.snd"],"value_dag_size":221,"value_refs":["And","And.casesOn","And.intro","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership","Sigma.fst","Sigma.mk","Sigma.snd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_mono.match_1_3","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sigma_mono","reducibility":"abbrev","statement_dag_size":113,"type_refs":["Finset","Finset.instSetLike","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.mk"],"value_dag_size":151,"value_refs":["Finset","Finset.instSetLike","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.casesOn","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.sup","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":90,"value_refs":["Finset","Finset.instSetLike","Finset.sup","Finset.sup_le_iff","LE.le","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toPartialOrder","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Sigma.0.Finset.sup_sigma","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Sigma","Sigma.mk"],"value_dag_size":40,"value_refs":["Sigma","Sigma.forall","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sigma","name":"_private.Mathlib.Data.Finset.Sigma.0.biSup_finsetSigma._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sigma.0.biSup_finsetSigma","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","SupSet","iSup"],"value_dag_size":74,"value_refs":["Eq.symm","Finset","Finset.iSup_coe","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","SupSet","iSup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Slice","name":"_private.Mathlib.Data.Finset.Slice.0.Set.sized_iUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Slice.0.Set.sized_iUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Slice","name":"_private.Mathlib.Data.Finset.Slice.0.Set.sized_iUnion._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Slice.0.Set.sized_iUnion","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.Injective2_disjSum._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.Injective2_disjSum","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_eq_empty","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_inj._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_inj","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_subset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_subset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjoint_map_inl_map_inr._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjoint_map_inl_map_inr","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjoint_map_inl_map_inr._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.disjoint_map_inl_map_inr","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_disjSum._proof_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_disjSum","reducibility":null,"statement_dag_size":67,"type_refs":["Disjoint","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.map","Function.Embedding","Function.Embedding.inl","Function.Embedding.inr","Function.Embedding.trans","Sum"],"value_dag_size":165,"value_refs":["Disjoint","Eq","Eq.mpr","Finset","Finset.disjoint_map","Finset.disjoint_map_inl_map_inr","Finset.instOrderBot","Finset.instPartialOrder","Finset.map","Function.Embedding","Function.Embedding.inl","Function.Embedding.inr","Function.Embedding.trans","Iff.mpr","Sum","_private.Mathlib.Data.Finset.Sum.0.Finset.map_disjSum._simp_1","congr","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_disjSum._simp_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_disjSum","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Finset","Finset.map","Function.Embedding","Function.Embedding.trans"],"value_dag_size":58,"value_refs":["Eq.symm","Finset","Finset.map","Finset.map_map","Function.Embedding","Function.Embedding.trans"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inl_subset_iff_subset_toLeft._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inl_subset_iff_subset_toLeft","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inl","Sum"],"value_dag_size":44,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Finset","Finset.disjSum","Finset.disjSum_empty","Finset.instEmptyCollection","Finset.map","Function.Embedding.inl","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inl_subset_iff_subset_toLeft._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inl_subset_iff_subset_toLeft","reducibility":null,"statement_dag_size":86,"type_refs":["And","Eq","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":91,"value_refs":["And","Finset","Finset.disjSum","Finset.disjSum_subset","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inr_subset_iff_subset_toRight._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inr_subset_iff_subset_toRight","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inr","Sum"],"value_dag_size":44,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Finset","Finset.disjSum","Finset.empty_disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inr","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inr_subset_iff_subset_toRight._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.map_inr_subset_iff_subset_toRight","reducibility":null,"statement_dag_size":86,"type_refs":["And","Eq","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":91,"value_refs":["And","Finset","Finset.disjSum","Finset.disjSum_subset","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_disjSum._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_disjSum","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inl._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inl","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inl","Sum"],"value_dag_size":44,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Finset","Finset.disjSum","Finset.disjSum_empty","Finset.instEmptyCollection","Finset.map","Function.Embedding.inl","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inl._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inl","reducibility":null,"statement_dag_size":86,"type_refs":["And","Eq","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":91,"value_refs":["And","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.subset_disjSum","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inr._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inr","reducibility":null,"statement_dag_size":39,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inr","Sum"],"value_dag_size":44,"value_refs":["EmptyCollection.emptyCollection","Eq.symm","Finset","Finset.disjSum","Finset.empty_disjSum","Finset.instEmptyCollection","Finset.map","Function.Embedding.inr","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inr._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.subset_map_inr","reducibility":null,"statement_dag_size":86,"type_refs":["And","Eq","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":91,"value_refs":["And","Finset","Finset.disjSum","Finset.instPartialOrder","Finset.subset_disjSum","Finset.toLeft","Finset.toRight","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sum","name":"_private.Mathlib.Data.Finset.Sum.0.Finset.sumEquiv._simp_2","namespace":"_private.Mathlib.Data.Finset.Sum.0.Finset.sumEquiv","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.Nonempty.of_disjSups_left.match_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.Nonempty.of_disjSups_left","reducibility":"abbrev","statement_dag_size":312,"type_refs":["And","And.intro","Disjoint","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":502,"value_refs":["And","And.casesOn","And.intro","Disjoint","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.Nonempty.of_disjSups_right.match_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.Nonempty.of_disjSups_right","reducibility":"abbrev","statement_dag_size":348,"type_refs":["And","And.intro","Disjoint","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":768,"value_refs":["And","And.casesOn","And.intro","Disjoint","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.compls_infs._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.compls_infs","reducibility":null,"statement_dag_size":36,"type_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.compls","Finset.image"],"value_dag_size":42,"value_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq.symm","Finset","Finset.compls","Finset.image","Finset.image_compl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.compls_sups._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.compls_sups","reducibility":null,"statement_dag_size":36,"type_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq","Finset","Finset.compls","Finset.image"],"value_dag_size":42,"value_refs":["BooleanAlgebra","BooleanAlgebra.toCompl","Compl.compl","DecidableEq","Eq.symm","Finset","Finset.compls","Finset.image","Finset.image_compl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_comm","reducibility":null,"statement_dag_size":35,"type_refs":["Disjoint","Eq","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["Disjoint","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","disjoint_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_disjSups_disjSups_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_disjSups_disjSups_comm","reducibility":null,"statement_dag_size":80,"type_refs":["DecidableEq","DecidableRel","Disjoint","DistribLattice","DistribLattice.toLattice","Eq","Finset","Finset.disjSups","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"],"value_dag_size":90,"value_refs":["DecidableEq","DecidableRel","Disjoint","DistribLattice","DistribLattice.toLattice","Eq.symm","Finset","Finset.disjSups","Finset.disjSups_assoc","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_left_comm._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_left_comm","reducibility":null,"statement_dag_size":80,"type_refs":["DecidableEq","DecidableRel","Disjoint","DistribLattice","DistribLattice.toLattice","Eq","Finset","Finset.disjSups","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"],"value_dag_size":90,"value_refs":["DecidableEq","DecidableRel","Disjoint","DistribLattice","DistribLattice.toLattice","Eq.symm","Finset","Finset.disjSups","Finset.disjSups_assoc","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_subset_sups._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_subset_sups","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_subset_sups.match_1_2","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_subset_sups","reducibility":"abbrev","statement_dag_size":299,"type_refs":["And","And.intro","Disjoint","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"],"value_dag_size":709,"value_refs":["And","And.casesOn","And.intro","Disjoint","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Max.max","Membership.mem","OrderBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_infs_le._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_infs_le","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_infs_le._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_infs_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":49,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_sups_le._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_sups_le","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_sups_le._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.filter_sups_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":49,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.infs_self._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.infs_self","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.mem_disjSups._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.mem_disjSups","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_infs_powerset_self._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_infs_powerset_self","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.decidableEq","Finset.hasInfs","Finset.instInter","Finset.instLattice","Finset.powerset","HasInfs.infs","Inter.inter","Lattice.toSemilatticeInf"],"value_dag_size":64,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.decidableEq","Finset.hasInfs","Finset.instInter","Finset.instLattice","Finset.powerset","Finset.powerset_inter","HasInfs.infs","Inter.inter","Lattice.toSemilatticeInf"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_inter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_inter","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powerset","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_sups_powerset_self._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_sups_powerset_self","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.decidableEq","Finset.hasSups","Finset.instLattice","Finset.instUnion","Finset.powerset","HasSups.sups","Lattice.toSemilatticeSup","Union.union"],"value_dag_size":64,"value_refs":["DecidableEq","Eq.symm","Finset","Finset.decidableEq","Finset.hasSups","Finset.instLattice","Finset.instUnion","Finset.powerset","Finset.powerset_union","HasSups.sups","Lattice.toSemilatticeSup","Union.union"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_union._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_union","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powerset","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sups","name":"_private.Mathlib.Data.Finset.Sups.0.Finset.sups_eq_self._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sups.0.Finset.sups_eq_self","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Finset","Finset.instSetLike","Set","SetLike.coe"],"value_dag_size":42,"value_refs":["Eq","Eq.symm","Finset","Finset.coe_inj","Finset.instSetLike","Set","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.Nonempty.sym.match_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.Nonempty.sym","reducibility":"abbrev","statement_dag_size":55,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instSetLike","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.isDiag_mk_of_mem_diag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.isDiag_mk_of_mem_diag","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Lean.Grind.eq_true_of_and_eq_true_right","Membership.mem","Not","SetLike.instMembership","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.not_isDiag_mk_of_mem_offDiag._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.not_isDiag_mk_of_mem_offDiag","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Finset","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":114,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Not","SetLike.instMembership","True","True.intro","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_cons._simp_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_cons","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_eq_image._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_eq_image","reducibility":null,"statement_dag_size":70,"type_refs":["And","Eq","Exists","Finset","Finset.instSetLike","Iff","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":1389,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_and_left","Lean.Grind.forall_and","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congr","congrArg","eq_false","eq_true","false_or","forall_congr","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_insert._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_insert","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union"],"value_dag_size":49,"value_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instUnion","Finset.right_eq_union","LE.le","PartialOrder.toPreorder","Preorder.toLE","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_insert._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_insert","reducibility":null,"statement_dag_size":76,"type_refs":["DecidableEq","Eq","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":82,"value_refs":["DecidableEq","Finset","Finset.image","Finset.image_subset_iff","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_mono._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_mono","reducibility":null,"statement_dag_size":48,"type_refs":["Finset","Finset.instPartialOrder","Finset.sym2","LE.le","PartialOrder.toPreorder","Preorder.toLE","Prod","Quot","Sym2.Rel"],"value_dag_size":514,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_sym2_iff","Finset.subset_iff","Finset.sym2","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLE","Prod","Quot","SetLike.instMembership","Sym2","Sym2.Rel","Sym2.instSetLike","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.mk"],"value_dag_size":56,"value_refs":["And","Finset","Finset.instSetLike","Finset.mk_mem_sym2_iff","Finset.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_toFinset","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.sym2","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","Membership.mem","Multiset","Multiset.instMembership","Multiset.mk_mem_sym2_iff","Multiset.sym2","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_univ._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym2_univ","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":54,"value_refs":["And","DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Inter.inter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter","reducibility":null,"statement_dag_size":20,"type_refs":["And","Eq"],"value_dag_size":25,"value_refs":["And","imp_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_inter","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map._simp_1_6","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","Membership.mem","Nat","Sym","Sym.instMembership","Sym.map"],"value_dag_size":72,"value_refs":["And","Eq","Exists","Membership.mem","Nat","Sym","Sym.instMembership","Sym.map","Sym.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map._simp_1_7","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Membership.mem","Nat","Subtype","Sym","Sym.attach","Sym.instMembership","True"],"value_dag_size":62,"value_refs":["Membership.mem","Nat","Subtype","Sym","Sym.attach","Sym.instMembership","Sym.mem_attach","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map._simp_1_8","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map._simp_1_9","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map.match_1_2","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":"abbrev","statement_dag_size":283,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Nat","SetLike.instMembership","Sym","Sym.instMembership","Sym.map"],"value_dag_size":390,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Nat","SetLike.instMembership","Sym","Sym.instMembership","Sym.map"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map.match_1_4","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.sym_map","reducibility":"abbrev","statement_dag_size":76,"type_refs":["Membership.mem","Nat","Subtype","Subtype.mk","Sym","Sym.instMembership"],"value_dag_size":99,"value_refs":["Membership.mem","Nat","Subtype","Subtype.casesOn","Subtype.mk","Sym","Sym.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.val_prod_eq_prod_count_pow._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.val_prod_eq_prod_count_pow","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Sym","name":"_private.Mathlib.Data.Finset.Sym.0.Finset.val_prod_eq_prod_count_pow._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Sym.0.Finset.val_prod_eq_prod_count_pow","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Membership.mem","Multiset","Multiset.instMembership","Nat","Sym","Sym.instMembership","Sym.toMultiset"],"value_dag_size":45,"value_refs":["Membership.mem","Multiset","Multiset.instMembership","Nat","Sym","Sym.instMembership","Sym.mem_coe","Sym.toMultiset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SymmDiff","name":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.coe_symmDiff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.coe_symmDiff","reducibility":null,"statement_dag_size":67,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instLattice","Finset.instSDiff","Finset.instSetLike","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","SetLike.instMembership","symmDiff"],"value_dag_size":72,"value_refs":["And","DecidableEq","Finset","Finset.instLattice","Finset.instSDiff","Finset.instSetLike","Finset.mem_symmDiff","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","SetLike.instMembership","propext","symmDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SymmDiff","name":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.coe_symmDiff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.coe_symmDiff","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Eq","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","Set","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","symmDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","Set","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","Set.mem_symmDiff","propext","symmDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SymmDiff","name":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.mem_symmDiff._simp_1_1","namespace":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.mem_symmDiff","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.SymmDiff","name":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.mem_symmDiff._simp_1_2","namespace":"_private.Mathlib.Data.Finset.SymmDiff.0.Finset.mem_symmDiff","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_biUnion","reducibility":null,"statement_dag_size":60,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion"],"value_dag_size":1642,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.mem_biUnion","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_congr._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_congr","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":1027,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.mem_biUnion","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_filter_eq_of_maps_to._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_filter_eq_of_maps_to","reducibility":null,"statement_dag_size":82,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":972,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","and_true","congrArg","congrFun'","eq_false","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_inter._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_inter","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instInter","Inter.inter"],"value_dag_size":1186,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_mono._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_mono","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":656,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_biUnion","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_nonempty._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_nonempty","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_singleton","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.image","Finset.instSingleton","Singleton.singleton"],"value_dag_size":1023,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.image","Finset.instSetLike","Finset.instSingleton","Finset.mem_biUnion","Finset.mem_image","Finset.mem_singleton","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_singleton_eq_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_singleton_eq_self","reducibility":null,"statement_dag_size":28,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instSingleton","Singleton.singleton"],"value_dag_size":758,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_biUnion","Finset.mem_singleton","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset","reducibility":null,"statement_dag_size":72,"type_refs":["DecidableEq","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1094,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_biUnion","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset_biUnion_of_subset_left._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset_biUnion_of_subset_left","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Finset","Finset.biUnion","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":638,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_biUnion","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset_iff_forall_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_subset_iff_forall_subset","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1093,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_biUnion","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_union._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_union","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instUnion","Union.union"],"value_dag_size":1435,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_biUnion","Finset.mem_union","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.bind_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.bind_toFinset","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.bind_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.bind_toFinset","reducibility":null,"statement_dag_size":60,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership"],"value_dag_size":65,"value_refs":["And","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership","Multiset.mem_bind","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_biUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_biUnion","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_biUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_biUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_disjiUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_disjiUnion","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Iff","Membership.mem","Set","Set.instMembership"],"value_dag_size":39,"value_refs":["Eq","Iff","Membership.mem","Set","Set.ext_iff","Set.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_disjiUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.coe_disjiUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion","reducibility":null,"statement_dag_size":141,"type_refs":["Disjoint","Eq","Finset","Finset.disjUnion","Finset.disjiUnion","Finset.disjiUnion_disjUnion._proof_4","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.pairwiseDisjoint_disjUnion","Set.Pairwise","Set.PairwiseDisjoint","SetLike.coe"],"value_dag_size":1917,"value_refs":["And","And.casesOn","Classical.byContradiction","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.disjUnion","Finset.disjiUnion","Finset.disjiUnion_disjUnion._proof_4","Finset.ext","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjUnion","Finset.mem_disjiUnion","Finset.pairwiseDisjoint_disjUnion","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","Set.Pairwise","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion._proof_3","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion","reducibility":null,"statement_dag_size":67,"type_refs":["Disjoint","Finset","Finset.instOrderBot","Finset.instPartialOrder","Ne"],"value_dag_size":206,"value_refs":["Classical.byContradiction","Disjoint","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instOrderBot","Finset.instPartialOrder","HEq","HEq.refl","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Ne","Not","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion._simp_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion","reducibility":null,"statement_dag_size":83,"type_refs":["Disjoint","Eq","Finset","Finset.disjiUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership"],"value_dag_size":89,"value_refs":["Disjoint","Finset","Finset.disjiUnion","Finset.disjoint_disjiUnion_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion._simp_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_disjUnion","reducibility":null,"statement_dag_size":83,"type_refs":["Disjoint","Eq","Finset","Finset.disjiUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership"],"value_dag_size":89,"value_refs":["Disjoint","Finset","Finset.disjiUnion","Finset.disjoint_disjiUnion_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_filter_eq_of_maps_to._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_filter_eq_of_maps_to","reducibility":null,"statement_dag_size":47,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.filter_eq_self","Finset.instSetLike","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_singleton","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_singleton_eq_self._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjiUnion_singleton_eq_self","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Finset","Finset.disjiUnion","Finset.disjiUnion_singleton_eq_self._proof_1","Finset.instSetLike","Finset.instSingleton","Membership.mem","Set","Set.instMembership","SetLike.coe","Singleton.singleton"],"value_dag_size":1079,"value_refs":["And","And.casesOn","Classical.byContradiction","Disjoint","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.disjiUnion","Finset.disjiUnion_singleton_eq_self._proof_1","Finset.ext","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_disjiUnion","Finset.mem_singleton","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_left._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_left","reducibility":null,"statement_dag_size":48,"type_refs":["And","DecidableEq","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instUnion","Union.union"],"value_dag_size":53,"value_refs":["And","DecidableEq","Disjoint","Finset","Finset.disjoint_union_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instUnion","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_left._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_left","reducibility":null,"statement_dag_size":55,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership"],"value_dag_size":61,"value_refs":["And","DecidableEq","Finset","Finset.forall_mem_insert","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_biUnion_right","reducibility":null,"statement_dag_size":35,"type_refs":["Disjoint","Eq","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["Disjoint","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","disjoint_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_disjiUnion_right._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.disjoint_disjiUnion_right","reducibility":null,"statement_dag_size":35,"type_refs":["Disjoint","Eq","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["Disjoint","OrderBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","disjoint_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.erase_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.erase_biUnion","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.erase"],"value_dag_size":1174,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.erase","Finset.ext","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_erase","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.filter_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.filter_biUnion","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","DecidablePred","Eq","Finset","Finset.biUnion","Finset.filter"],"value_dag_size":1154,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.filter","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.filter_disjiUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.filter_disjiUnion","reducibility":null,"statement_dag_size":77,"type_refs":["DecidablePred","Eq","Finset","Finset.disjiUnion","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.pairwiseDisjoint_filter","Set.PairwiseDisjoint","SetLike.coe"],"value_dag_size":1376,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.disjiUnion","Finset.ext","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjiUnion","Finset.mem_filter","Finset.pairwiseDisjoint_filter","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.inter_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.inter_biUnion","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instInter","Inter.inter"],"value_dag_size":1181,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_biUnion","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Finset.mem_def","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion","reducibility":null,"statement_dag_size":33,"type_refs":["DecidableEq","Eq","Membership.mem","Multiset","Multiset.dedup","Multiset.instMembership"],"value_dag_size":37,"value_refs":["DecidableEq","Membership.mem","Multiset","Multiset.dedup","Multiset.instMembership","Multiset.mem_dedup","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_biUnion","reducibility":null,"statement_dag_size":60,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership"],"value_dag_size":65,"value_refs":["And","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership","Multiset.mem_bind","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_disjiUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_disjiUnion","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":41,"value_refs":["Finset","Finset.instSetLike","Finset.mem_def","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_disjiUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.mem_disjiUnion","reducibility":null,"statement_dag_size":60,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership"],"value_dag_size":65,"value_refs":["And","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership","Multiset.mem_bind","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Eq","Finset","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Set.PairwiseDisjoint","SetLike.coe"],"value_dag_size":422,"value_refs":["And","And.casesOn","DecidableEq","Disjoint","Eq","Eq.mpr","Eq.ndrec","False","Finset","Finset.filter","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Function.onFun","Membership.mem","Ne","Not","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers._simp_1_1","_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers._simp_1_2","congrArg","forall_congr","id","implies_congr","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.pairwiseDisjoint_fibers","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.instMembership","Set.sUnion"],"value_dag_size":52,"value_refs":["And","Exists","Membership.mem","Set","Set.instMembership","Set.mem_sUnion","Set.sUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Membership.mem","Set","Set.iUnion","Set.instMembership"],"value_dag_size":48,"value_refs":["Exists","Membership.mem","Set","Set.iUnion","Set.instMembership","Set.mem_iUnion","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion._simp_1_4","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.sUnion_disjiUnion","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.singleton_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.singleton_biUnion","reducibility":null,"statement_dag_size":38,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instSingleton","Singleton.singleton"],"value_dag_size":850,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.instSingleton","Finset.mem_biUnion","Finset.mem_singleton","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.subset_biUnion_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.subset_biUnion_of_mem","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":408,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_biUnion","Finset.subset_iff","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_and","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Union","name":"_private.Mathlib.Data.Finset.Union.0.Finset.union_biUnion._proof_1_1","namespace":"_private.Mathlib.Data.Finset.Union.0.Finset.union_biUnion","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","Eq","Finset","Finset.biUnion","Finset.instUnion","Union.union"],"value_dag_size":1431,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.biUnion","Finset.ext","Finset.instSetLike","Finset.instUnion","Finset.mem_biUnion","Finset.mem_union","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Union.union","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Update","name":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_singleton","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Update","name":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset._simp_1_2","namespace":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Update","name":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset._simp_1_3","namespace":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Update","name":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset_of_subset._proof_1_3","namespace":"_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset_of_subset","reducibility":null,"statement_dag_size":116,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Function.updateFinset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype","Subtype.val"],"value_dag_size":599,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","Function.updateFinset","Function.updateFinset.eq_1","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype","Subtype.mk","Subtype.val","True","True.intro","dite","eq_false","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finset.Update","name":"_private.Mathlib.Data.Finset.Update.0.Function.update_eq_updateFinset._simp_1_1","namespace":"_private.Mathlib.Data.Finset.Update.0.Function.update_eq_updateFinset","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp._simp_1","namespace":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","List","List.instMembership","List.toFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","List","List.instMembership","List.mem_toFinset","List.toFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp._simp_2","namespace":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","Exists","List","List.instMembership","List.keys","Membership.mem","Sigma","Sigma.mk"],"value_dag_size":61,"value_refs":["Exists","List","List.instMembership","List.keys","List.mem_keys","Membership.mem","Sigma","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp._simp_3","namespace":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp","reducibility":null,"statement_dag_size":41,"type_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","List.mem_filter","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp._simp_4","namespace":"_private.Mathlib.Data.Finsupp.AList.0.AList.lookupFinsupp","reducibility":null,"statement_dag_size":65,"type_refs":["AList","AList.entries","AList.lookup","DecidableEq","Eq","List","List.instMembership","Membership.mem","Option","Option.instMembership","Sigma","Sigma.mk"],"value_dag_size":77,"value_refs":["AList","AList.entries","AList.lookup","AList.mem_lookup_iff","DecidableEq","Eq.symm","List","List.instMembership","Membership.mem","Option","Option.instMembership","Sigma","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.AList.singleton_lookupFinsupp._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.AList.0.AList.singleton_lookupFinsupp","reducibility":null,"statement_dag_size":41,"type_refs":["AList","AList.insert","AList.instEmptyCollection","AList.singleton","DecidableEq","EmptyCollection.emptyCollection","Eq"],"value_dag_size":48,"value_refs":["AList","AList.insert","AList.insert_empty","AList.instEmptyCollection","AList.singleton","DecidableEq","EmptyCollection.emptyCollection","Eq.symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.AList","name":"_private.Mathlib.Data.Finsupp.AList.0.Finsupp.toAList_lookupFinsupp._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.AList.0.Finsupp.toAList_lookupFinsupp","reducibility":null,"statement_dag_size":51,"type_refs":["AList","AList.instMembership","AList.lookup","DecidableEq","Eq","Membership.mem","Not","Option","Option.none"],"value_dag_size":56,"value_refs":["AList","AList.instMembership","AList.lookup","AList.lookup_eq_none","DecidableEq","Eq","Membership.mem","Not","Option","Option.none","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":73,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd"],"value_dag_size":78,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.HasAntidiagonal.mem_antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":33,"value_refs":["And","Eq.symm","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single._simp_1_6","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.antidiagonal_single","reducibility":null,"statement_dag_size":69,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddUnits","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","Eq","HAdd.hAdd","OfNat.ofNat","Subsingleton","Zero.toOfNat0","instHAdd"],"value_dag_size":74,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddUnits","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","Eq","HAdd.hAdd","OfNat.ofNat","Subsingleton","Zero.toOfNat0","add_eq_zero","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal","reducibility":null,"statement_dag_size":73,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd"],"value_dag_size":78,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.HasAntidiagonal.mem_antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal.match_1_4","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_prodMap_embDomain_antidiagonal","reducibility":"abbrev","statement_dag_size":347,"type_refs":["AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.embDomain","Finsupp.instAddMonoid","Function.Embedding","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","instHAdd"],"value_dag_size":675,"value_refs":["AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.embDomain","Finsupp.instAddMonoid","Function.Embedding","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal","reducibility":null,"statement_dag_size":73,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd"],"value_dag_size":78,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.HasAntidiagonal.mem_antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal.match_1_5","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.image_sumElim_product_antidiagonal","reducibility":"abbrev","statement_dag_size":701,"type_refs":["AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.instAddMonoid","Finsupp.sumElim","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Sum","instHAdd"],"value_dag_size":1616,"value_refs":["AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.instAddMonoid","Finsupp.sumElim","HAdd.hAdd","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Sum","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.instHasAntidiagonal._simp_2","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.instHasAntidiagonal","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","Eq.symm","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Antidiagonal","name":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.instHasAntidiagonal._simp_3","namespace":"_private.Mathlib.Data.Finsupp.Antidiagonal.0.Finsupp.instHasAntidiagonal","reducibility":null,"statement_dag_size":118,"type_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFunLike.coe","DecidableEq","Eq","EquivLike.toFunLike","Finsupp","Finsupp.instAdd","Finsupp.instAddZeroClass","Finsupp.toMultiset","MulZeroClass.toZero","Multiset","Multiset.instAdd","Multiset.instAddCancelCommMonoid","Multiset.toFinsupp","Nat","Nat.instAddMonoid","Nat.instMulZeroClass"],"value_dag_size":122,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","DFunLike.coe","DecidableEq","Eq","EquivLike.toFunLike","Finsupp","Finsupp.instAdd","Finsupp.instAddZeroClass","Finsupp.toMultiset","MulZeroClass.toZero","Multiset","Multiset.instAdd","Multiset.instAddCancelCommMonoid","Multiset.toFinsupp","Multiset.toFinsupp_eq_iff","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.comapDomain_single_of_not_mem_range._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.comapDomain_single_of_not_mem_range","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.curry._simp_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.curry","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.domCongr._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.domCongr","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Equiv","Equiv.trans","Finsupp","Finsupp.equivMapDomain","Zero"],"value_dag_size":77,"value_refs":["Eq.symm","Equiv","Equiv.trans","Finsupp","Finsupp.equivMapDomain","Finsupp.equivMapDomain_trans","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.embDomain_trans_apply._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.embDomain_trans_apply","reducibility":null,"statement_dag_size":82,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finsupp","Finsupp.mapDomain","Function.comp"],"value_dag_size":92,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq.symm","Finsupp","Finsupp.mapDomain","Finsupp.mapDomain_comp","Function.comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero","reducibility":null,"statement_dag_size":30,"type_refs":["EmptyCollection.emptyCollection","Eq","False","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":30,"value_refs":["EmptyCollection.emptyCollection","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","Membership.mem","SetLike.instMembership","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Finset","Finset.instSetLike","Finset.mem_preimage","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain","reducibility":null,"statement_dag_size":82,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.instSetLike","Finset.map","Membership.mem","SetLike.instMembership"],"value_dag_size":87,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","Equiv.symm","Equiv.toEmbedding","EquivLike.toFunLike","Finset","Finset.instSetLike","Finset.map","Finset.mem_map_equiv","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain._simp_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.support","Finsupp.toFun","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":65,"value_refs":["Finset","Finset.instSetLike","Finsupp","Finsupp.mem_support_toFun","Finsupp.support","Finsupp.toFun","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain_single","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":81,"value_refs":["DFunLike.coe","Eq","Eq.symm","Equiv","Equiv.eq_symm_apply","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_single","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_subtypeDomain._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_subtypeDomain","reducibility":null,"statement_dag_size":78,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":216,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Membership.mem","Ne","Not","OfNat.ofNat","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_subtypeDomain._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.extendDomain_subtypeDomain","reducibility":null,"statement_dag_size":35,"type_refs":["Decidable","Eq","Not","ite"],"value_dag_size":41,"value_refs":["Decidable","Eq","Not","ite","ite_eq_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter._simp_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq'._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq'","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Membership.mem","Not","OfNat.ofNat","Set","Set.indicator","Set.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":66,"value_refs":["Eq","Membership.mem","Not","OfNat.ofNat","Set","Set.indicator","Set.indicator_apply_eq_self","Set.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not"],"value_dag_size":18,"value_refs":["Not","not_imp_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.frange_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.frange_single","reducibility":null,"statement_dag_size":47,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp.frange","Finsupp.single","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero"],"value_dag_size":632,"value_refs":["And","Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.subset_iff","Finsupp","Finsupp.frange","Finsupp.instFunLike","Finsupp.mem_frange","Finsupp.single","Finsupp.single_apply","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","Set.mem_range","Set.range","SetLike.instMembership","Singleton.singleton","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_apply_eq_zero_iff_of_subsingletonAddUnits._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_apply_eq_zero_iff_of_subsingletonAddUnits","reducibility":null,"statement_dag_size":132,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.instZero","Not","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":320,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instFunLike","Finsupp.instZero","Finsupp.zero_apply","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","Not","OfNat.ofNat","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_comapDomain_nat_add_one._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_comapDomain_nat_add_one","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":26,"value_refs":["LT.lt","Nat","Nat.pos_iff_ne_zero","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_injOn","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_subsingletonAddUnits.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_support_of_subsingletonAddUnits","reducibility":"abbrev","statement_dag_size":213,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Finsupp","Finsupp.support","Membership.mem","SetLike.instMembership"],"value_dag_size":307,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finsupp","Finsupp.support","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_swap_sumElim._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mapDomain_swap_sumElim","reducibility":null,"statement_dag_size":82,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finsupp","Finsupp.mapDomain","Function.comp"],"value_dag_size":92,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq.symm","Finsupp","Finsupp.mapDomain","Finsupp.mapDomain_comp","Function.comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_frange.match_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_frange","reducibility":"abbrev","statement_dag_size":217,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","SetLike.instMembership","Zero"],"value_dag_size":308,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","SetLike.instMembership","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_frange.match_1_4","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_frange","reducibility":"abbrev","statement_dag_size":191,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists.intro","Finsupp","Finsupp.instFunLike","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","Set.range","Zero","Zero.toOfNat0"],"value_dag_size":277,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists.casesOn","Exists.intro","Finsupp","Finsupp.instFunLike","Membership.mem","Ne","OfNat.ofNat","Set","Set.instMembership","Set.range","Zero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_embDomain_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_embDomain_iff","reducibility":null,"statement_dag_size":148,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Iff","LE.le","Membership.mem","Not","OfNat.ofNat","Set","Set.instLE","Set.instMembership","Set.range","SetLike.coe","Zero.toOfNat0"],"value_dag_size":994,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instLE","Set.instMembership","Set.range","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_range_mapDomain_iff","reducibility":"abbrev","statement_dag_size":181,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Exists.intro","Finsupp","Finsupp.mapDomain","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":218,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Exists.casesOn","Exists.intro","Finsupp","Finsupp.mapDomain","Membership.mem","Set","Set.instMembership","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Finset","Finset.instSetLike","Finset.mem_preimage","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero._simp_1_6","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero._simp_1_7","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Exists","Sigma","Sigma.mk"],"value_dag_size":49,"value_refs":["Exists","Sigma","Sigma.exists","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_support_finsetSum.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_support_finsetSum","reducibility":"abbrev","statement_dag_size":204,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.val","Finsupp","Membership.mem","Multiset","Multiset.instMembership"],"value_dag_size":283,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.val","Finsupp","Membership.mem","Multiset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_support_finsetSum.match_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_support_finsetSum","reducibility":"abbrev","statement_dag_size":309,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Exists","Exists.intro","Finset","Finset.instSetLike","Finset.val","Finsupp","Finsupp.support","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","SetLike.instMembership"],"value_dag_size":414,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.val","Finsupp","Finsupp.support","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mk_mem_graph_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mk_mem_graph_iff","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mk_mem_graph_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mk_mem_graph_iff","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_left","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise._simp_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise._simp_3","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise._simp_4","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.mk"],"value_dag_size":39,"value_refs":["Subtype","Subtype.forall","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise._simp_5","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.piecewise","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.range_subset_insert_frange._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.range_subset_insert_frange","reducibility":null,"statement_dag_size":73,"type_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.frange","Finsupp.instFunLike","Insert.insert","LE.le","OfNat.ofNat","Set","Set.instInsert","Set.instLE","Set.range","SetLike.coe","Zero","Zero.toOfNat0"],"value_dag_size":434,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Finsupp","Finsupp.frange","Finsupp.instFunLike","Finsupp.mem_frange","Iff","Insert.insert","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","Set","Set.instInsert","Set.instLE","Set.instMembership","Set.mem_insert_iff","Set.range","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Sigma","Sigma.mk"],"value_dag_size":40,"value_refs":["Sigma","Sigma.forall","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support._simp_1_6","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support","reducibility":null,"statement_dag_size":91,"type_refs":["And","Eq","Finset","Finset.instSetLike","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.fst","Sigma.snd"],"value_dag_size":96,"value_refs":["And","Finset","Finset.instSetLike","Finset.mem_sigma","Finset.sigma","Membership.mem","SetLike.instMembership","Sigma","Sigma.fst","Sigma.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support._simp_1_7","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support._simp_1_8","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sigma_support","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership"],"value_dag_size":79,"value_refs":["Finset","Finset.instSetLike","Finset.mem_preimage","Finset.preimage","Membership.mem","Set.InjOn","Set.preimage","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.subtypeDomain_eq_iff_forall._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.subtypeDomain_eq_iff_forall","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.subtypeDomain_eq_iff_forall._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.subtypeDomain_eq_iff_forall","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Subtype","Subtype.mk"],"value_dag_size":39,"value_refs":["Subtype","Subtype.forall","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sumElim_eq_add._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sumElim_eq_add","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Function.Injective","Sum","Sum.inl","True"],"value_dag_size":22,"value_refs":["Function.Injective","Sum","Sum.inl","Sum.inl_injective","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sumElim_eq_add._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.sumElim_eq_add","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Function.Injective","Sum","Sum.inr","True"],"value_dag_size":22,"value_refs":["Function.Injective","Sum","Sum.inr","Sum.inr_injective","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_extendDomain_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_extendDomain_subset","reducibility":null,"statement_dag_size":63,"type_refs":["DecidablePred","Finset","Finset.instSetLike","Finsupp","Finsupp.extendDomain","Finsupp.support","LE.le","Set","Set.instLE","Set.ofPred","SetLike.coe","Subtype","Zero"],"value_dag_size":444,"value_refs":["Classical.byContradiction","DFunLike.coe","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Finsupp","Finsupp.extendDomain","Finsupp.extendDomain_apply","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","LE.le","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","SetLike.coe","SetLike.instMembership","Subtype","Subtype.mk","True","True.intro","Zero","Zero.toOfNat0","dite","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_mapDomain_embedding._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_mapDomain_embedding","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_mapDomain_embedding._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.support_mapDomain_embedding","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Basic","name":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.uncurry._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.uncurry","reducibility":null,"statement_dag_size":61,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":64,"value_refs":["Disjoint","Finset","Finset.disjoint_iff_ne","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.mem_foldr_sup_support_iff","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","Exists","Or"],"value_dag_size":44,"value_refs":["And","Eq","Exists","Or","exists_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","List","List.instMembership","List.toFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","List","List.instMembership","List.mem_toFinset","List.toFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.List.support_sum_eq","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.BigOperators","name":"_private.Mathlib.Data.Finsupp.BigOperators.0.Multiset.support_sum_eq._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.BigOperators.0.Multiset.support_sum_eq","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain._proof_3","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain","reducibility":null,"statement_dag_size":128,"type_refs":["And","DFunLike.coe","Eq","Finset.val","Finsupp","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Multiset","Multiset.instMembership","Set","Set.instMembership","Set.ofPred","Zero"],"value_dag_size":373,"value_refs":["And","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset.val","Finsupp","Finsupp.support","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Membership.mem","Multiset","Multiset.instMembership","Nonempty","Nonempty.intro","Not","Set","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","Zero","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain._proof_7","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain","reducibility":null,"statement_dag_size":140,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.map","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Iff","Membership.mem","Multiset.find?","Not","OfNat.ofNat","Option","PUnit","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":1295,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.decEq","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Finset.mem_val","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.embDomain.match_1.congr_eq_1","Finsupp.embDomain.match_1.congr_eq_2","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","HEq","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Membership.mem","Multiset","Multiset.find?","Multiset.find?_eq_none_iff","Multiset.find?_eq_some_iff","Multiset.instMembership","Not","OfNat.ofNat","Option","Option.none","Option.some","Or","PUnit","PUnit.casesOn","Set.Subsingleton","Set.ofPred","SetLike.instMembership","True","True.intro","Unit","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.splitter","congrArg","eq_true","false_or","forall_congr","forall_not_of_not_exists","heq_eq_eq","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.eq_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finsupp.embDomain.match_1","Option","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","Finsupp.embDomain.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.eq_2","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Finsupp.embDomain.match_1","Option","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","Finsupp.embDomain.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.splitter","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Finsupp.embDomain.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply","reducibility":null,"statement_dag_size":148,"type_refs":["Classical.choose","Classical.decEq","DFunLike.coe","Eq","Exists","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Multiset.find?","OfNat.ofNat","Option","PUnit","Zero","Zero.toOfNat0"],"value_dag_size":975,"value_refs":["And","Classical.byContradiction","Classical.choose","Classical.decEq","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","Exists.choose_spec","False","Finset","Finset.instSetLike","Finset.mem_val","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.embDomain.match_1.congr_eq_1","Finsupp.embDomain.match_1.congr_eq_2","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","FunLike","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Membership.mem","Multiset","Multiset.find?","Multiset.find?_eq_none_iff","Multiset.find?_eq_some_iff","Multiset.instMembership","Ne","Nonempty","Nonempty.intro","Not","OfNat.ofNat","Option","Option.none","Option.some","PUnit","PUnit.casesOn","Set.Subsingleton","Set.ofPred","SetLike.instMembership","True","True.intro","Unit","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.splitter","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply","reducibility":null,"statement_dag_size":138,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Exists","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Multiset.find?","Not","OfNat.ofNat","Option","PUnit","Zero","Zero.toOfNat0"],"value_dag_size":544,"value_refs":["And","Classical.byContradiction","Classical.decEq","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.embDomain.match_1.congr_eq_2","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","HEq","Iff","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","Membership.mem","Multiset","Multiset.find?","Multiset.find?_eq_some_iff","Multiset.instMembership","Not","OfNat.ofNat","Option","Option.none","Option.some","PUnit","PUnit.casesOn","Set.Subsingleton","Set.ofPred","True","True.intro","Unit","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.splitter","eq_false","eq_true","heq_eq_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply_self._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply_self","reducibility":null,"statement_dag_size":73,"type_refs":["And","DFunLike.coe","Eq","Finset.val","Finsupp","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Multiset","Multiset.instMembership","Set.Subsingleton","Set.ofPred","Zero"],"value_dag_size":47,"value_refs":["DFunLike.coe","Finsupp","Finsupp.embDomain._proof_4","Function.Embedding","Function.instFunLikeEmbedding","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply_self._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply_self","reducibility":null,"statement_dag_size":136,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.instFunLike","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Multiset.find?","OfNat.ofNat","Option","PUnit","Zero","Zero.toOfNat0"],"value_dag_size":827,"value_refs":["And","Classical.byContradiction","Classical.decEq","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.mem_val","Finset.val","Finsupp","Finsupp.embDomain._proof_4","Finsupp.embDomain.match_1","Finsupp.embDomain.match_1.congr_eq_1","Finsupp.embDomain.match_1.congr_eq_2","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","FunLike","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","HEq","HEq.refl","Iff","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Membership.mem","Multiset","Multiset.find?","Multiset.find?_eq_none_iff","Multiset.find?_eq_some_iff","Multiset.instMembership","Ne","Nonempty","Nonempty.intro","Not","OfNat.ofNat","Option","Option.none","Option.some","PUnit","PUnit.casesOn","Set.Subsingleton","Set.ofPred","SetLike.instMembership","True","True.intro","Unit","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain.match_1.splitter","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_apply_self._proof_1_2","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_mapRange._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_mapRange","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Finsupp","Finsupp.embDomain","Finsupp.mapRange","Function.Embedding","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":1025,"value_refs":["Classical.byContradiction","Classical.choose","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","False","Finsupp","Finsupp.embDomain","Finsupp.embDomain_apply","Finsupp.embDomain_apply_self","Finsupp.ext","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mapRange_apply","FunLike","Function.Embedding","Function.instFunLikeEmbedding","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_of_notMem_range._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.embDomain_of_notMem_range","reducibility":null,"statement_dag_size":90,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.embDomain","Finsupp.instFunLike","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Not","OfNat.ofNat","Set","Set.instMembership","Set.range","Zero","Zero.toOfNat0"],"value_dag_size":321,"value_refs":["Classical.byContradiction","Classical.choose","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.choose","False","Finsupp","Finsupp.embDomain","Finsupp.embDomain_apply","Finsupp.instFunLike","Function.Embedding","Function.instFunLikeEmbedding","Iff","Lean.Grind.dite_cond_eq_false'","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Membership.mem","Not","OfNat.ofNat","Set","Set.instMembership","Set.mem_range","Set.range","True","True.intro","Zero","Zero.toOfNat0","dite","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.ext_iff'.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.ext_iff'","reducibility":"abbrev","statement_dag_size":212,"type_refs":["And","And.intro","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","SetLike.instMembership","Zero"],"value_dag_size":234,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","SetLike.instMembership","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.mapRange_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.mapRange_eq_zero","reducibility":null,"statement_dag_size":56,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Zero"],"value_dag_size":61,"value_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.ext_iff","Finsupp.instFunLike","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.onFinsetSupport.eq_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.onFinsetSupport","reducibility":null,"statement_dag_size":59,"type_refs":["Classical.decEq","Eq","Finset","Finset.filter","Finsupp.onFinsetSupport","Ne","OfNat.ofNat","Zero","Zero.toOfNat0","instDecidableNot"],"value_dag_size":27,"value_refs":["Eq.refl","Finset","Finsupp.onFinsetSupport","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange","reducibility":null,"statement_dag_size":100,"type_refs":["DFunLike.coe","Eq","Exists","Finsupp","Finsupp.instFunLike","Finsupp.mapRange","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":323,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mapRange_apply","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._proof_1_4","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange","reducibility":null,"statement_dag_size":98,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.decidableMem","Finset.instSetLike","Finsupp","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","ite"],"value_dag_size":359,"value_refs":["And","Classical.not_imp._simp_1","Classical.propDecidable","DFunLike.coe","Eq","Eq.refl","Eq.trans","False","Finset","Finset.decidableMem","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff._simp_1","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","True","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","forall_congr","implies_congr_ctx","implies_true","instDecidableNot","ite","ite_congr","ite_eq_left_iff._simp_1","ite_not","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._proof_1_5","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange","reducibility":null,"statement_dag_size":424,"type_refs":["And","Classical.not_imp._simp_1","Classical.propDecidable","DFunLike.coe","Eq","Eq.refl","Eq.trans","False","Finset","Finset.decidableMem","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mem_support_iff._simp_1","Finsupp.onFinset","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","True","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","forall_congr","implies_congr_ctx","implies_true","instDecidableNot","ite","ite_congr","ite_eq_left_iff._simp_1","ite_not","not_false_eq_true","of_eq_true"],"value_dag_size":1249,"value_refs":["And","Classical.byContradiction","Classical.not_imp._simp_1","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mapRange_apply","Finsupp.mem_support_iff","Finsupp.mem_support_iff._simp_1","Finsupp.onFinset","Finsupp.onFinset_apply","Finsupp.support","Finsupp.support_onFinset_subset","HEq","HEq.refl","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._proof_1_4","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","id","implies_congr_ctx","implies_true","instDecidableNot","ite","ite_cond_eq_true","ite_congr","ite_eq_left_iff._simp_1","ite_not","not_false_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.range_mapRange","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.ofPred"],"value_dag_size":33,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_ofPred","Set.ofPred","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_mapRange_of_injective._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_mapRange_of_injective","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","Finset","Finsupp","Finsupp.mapRange","Finsupp.support","Function.Injective","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":800,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mapRange_apply","Finsupp.mem_support_iff","Finsupp.support","Function.Injective","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Ne","Nonempty","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.instNonempty","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_onFinset_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_onFinset_subset","reducibility":null,"statement_dag_size":74,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finsupp.onFinset","Finsupp.support","LE.le","Membership.mem","Ne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":419,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.onFinset","Finsupp.onFinset_apply","Finsupp.support","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_subset_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.support_subset_iff","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Iff","LE.le","Membership.mem","Not","OfNat.ofNat","Set","Set.instLE","Set.instMembership","SetLike.coe","Zero","Zero.toOfNat0"],"value_dag_size":757,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.mem_coe","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instLE","Set.instMembership","Set.subset_def","SetLike.coe","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Defs","name":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.zipWith._proof_1","namespace":"_private.Mathlib.Data.Finsupp.Defs.0.Finsupp.zipWith","reducibility":null,"statement_dag_size":149,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.instUnion","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Union.union","Zero","Zero.toOfNat0"],"value_dag_size":564,"value_refs":["Classical.byContradiction","Classical.decEq","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","SetLike.instMembership","True","True.intro","Union.union","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Fin","name":"_private.Mathlib.Data.Finsupp.Fin.0.Finsupp.cons_support._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Fin.0.Finsupp.cons_support","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Fintype","name":"_private.Mathlib.Data.Finsupp.Fintype.0.Finsupp.infinite_of_left.match_1","namespace":"_private.Mathlib.Data.Finsupp.Fintype.0.Finsupp.infinite_of_left","reducibility":"abbrev","statement_dag_size":70,"type_refs":["Exists","Exists.intro","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":92,"value_refs":["Exists","Exists.casesOn","Exists.intro","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff","reducibility":null,"statement_dag_size":106,"type_refs":["Classical.propDecidable","Eq","Finset","Finset.decidableMem","Finset.instSetLike","Iff","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","dite"],"value_dag_size":845,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instSetLike","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","dite","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff","reducibility":null,"statement_dag_size":99,"type_refs":["And","Classical.propDecidable","Eq","Finset","Finset.decidableMem","Finset.instSetLike","Iff","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","dite"],"value_dag_size":1051,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instSetLike","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congr","congrArg","dite","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not"],"value_dag_size":18,"value_refs":["Not","not_imp_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_self_iff._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_self_iff","reducibility":null,"statement_dag_size":163,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset","Finset.Subtype.fintype","Finset.decidableMem","Finset.filter","Finset.instSetLike","Finset.map","Finset.univ","Finsupp","Finsupp.instFunLike","Function.Embedding.subtype","Iff","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Subtype","Subtype.val","Zero","Zero.toOfNat0","instDecidableNot","ite"],"value_dag_size":292,"value_refs":["Classical.decEq","DFunLike.coe","Eq","Eq.rec","Finset","Finset.Subtype.fintype","Finset.decidableMem","Finset.filter","Finset.instSetLike","Finset.map","Finset.univ","Finsupp","Finsupp.indicator._proof_1","Finsupp.instFunLike","Function.Embedding.subtype","Iff","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Subtype","Subtype.val","Zero","Zero.toOfNat0","dite","dite_eq_ite","funext","instDecidableNot","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_self_iff._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_self_iff","reducibility":null,"statement_dag_size":87,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finsupp","Finsupp.indicator","Finsupp.instFunLike","Finsupp.support","Iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero"],"value_dag_size":2130,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.decEq","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.Subtype.fintype","Finset.decidableMem","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.map","Finset.subset_iff","Finset.univ","Finsupp","Finsupp.coe_mk","Finsupp.ext","Finsupp.indicator","Finsupp.indicator._proof_1","Finsupp.indicator.eq_1","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.mk","Finsupp.mk.congr_simp","Finsupp.support","Function.Embedding.subtype","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subtype","Subtype.val","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_self_iff._proof_1_2","congrArg","congrFun","dite","dite_eq_ite","eq_false","eq_true","funext","id","instDecidableNot","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator","reducibility":null,"statement_dag_size":61,"type_refs":["DecidableEq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","SetLike.instMembership"],"value_dag_size":128,"value_refs":["And","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Membership.mem","SetLike.instMembership","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator","reducibility":null,"statement_dag_size":116,"type_refs":["DFunLike.coe","DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_of_mem_inter_left","Finsupp","Finsupp.indicator","Finsupp.instFunLike","Inter.inter","Membership.mem","SetLike.instMembership","Zero"],"value_dag_size":996,"value_refs":["And","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Finset.mem_of_mem_inter_left","Finsupp","Finsupp.ext","Finsupp.indicator","Finsupp.indicator_apply","Finsupp.instFunLike","HEq","HEq.refl","Iff","Inter.inter","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator._proof_1_1","congrArg","dite","dite_eq_ite","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Indicator","name":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_singleton","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Interval","name":"_private.Mathlib.Data.Finsupp.Interval.0.Finsupp.instLocallyFiniteOrder._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Interval.0.Finsupp.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":116,"type_refs":["And","DFunLike.coe","DecidableEq","Eq","Finset","Finset.instSetLike","Finset.zero","Finsupp","Finsupp.instFunLike","Finsupp.rangeIcc","LE.le","LocallyFiniteOrder","Membership.mem","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero"],"value_dag_size":126,"value_refs":["And","DFunLike.coe","DecidableEq","Finset","Finset.instSetLike","Finset.zero","Finsupp","Finsupp.instFunLike","Finsupp.mem_rangeIcc_apply_iff","Finsupp.rangeIcc","LE.le","LocallyFiniteOrder","Membership.mem","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Lex","name":"_private.Mathlib.Data.Finsupp.Lex.0.Finsupp.Lex.addLeftStrictMono.match_1","namespace":"_private.Mathlib.Data.Finsupp.Lex.0.Finsupp.Lex.addLeftStrictMono","reducibility":"abbrev","statement_dag_size":513,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.intro","Finsupp","Finsupp.instFunLike","Finsupp.instLTLex","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","ofLex"],"value_dag_size":761,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists.casesOn","Exists.intro","Finsupp","Finsupp.instFunLike","Finsupp.instLTLex","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","ofLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Lex","name":"_private.Mathlib.Data.Finsupp.Lex.0.Finsupp.Lex.single_strictAnti._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Lex.0.Finsupp.Lex.single_strictAnti","reducibility":null,"statement_dag_size":92,"type_refs":["And","DFunLike.coe","Eq","Exists","Finsupp","Finsupp.Lex","Finsupp.instFunLike","Zero"],"value_dag_size":100,"value_refs":["And","DFunLike.coe","Eq","Exists","Finsupp","Finsupp.Lex","Finsupp.instFunLike","Finsupp.lex_def","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.bot_lt_toWithBotSyn_apply_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.bot_lt_toWithBotSyn_apply_iff","reducibility":null,"statement_dag_size":48,"type_refs":["Bot.bot","Eq","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":52,"value_refs":["Bot.bot","LT.lt","Ne","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","bot_lt_iff_ne_bot","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_le_iff_of_unique._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_le_iff_of_unique","reducibility":null,"statement_dag_size":176,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.partialOrder","Finsupp.instAdd","LE.le","Lattice.toSemilatticeInf","Lex","LinearOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","WellFoundedGT","instDistribLatticeOfLinearOrder","toLex"],"value_dag_size":181,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.partialOrder","Finsupp.instAdd","LE.le","Lattice.toSemilatticeInf","Lex","LinearOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.lex_le_iff","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","WellFoundedGT","instDistribLatticeOfLinearOrder","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_le_iff_of_unique._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_le_iff_of_unique","reducibility":null,"statement_dag_size":121,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.partialOrder","Finsupp.instFunLike","Inhabited.default","LE.le","Lex","LinearOrder","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Unique","Unique.instInhabited","Zero","ofLex"],"value_dag_size":129,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.le_iff_of_unique","Finsupp.Lex.partialOrder","Finsupp.instFunLike","Inhabited.default","LE.le","Lex","LinearOrder","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Unique","Unique.instInhabited","Zero","ofLex","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_lt_iff_of_unique._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_lt_iff_of_unique","reducibility":null,"statement_dag_size":183,"type_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.instAdd","Finsupp.instLTLex","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","WellFoundedGT","instDistribLatticeOfLinearOrder","instLTNat","toLex"],"value_dag_size":188,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","AddEquiv","AddEquiv.instEquivLike","AddMonoid.toAddZeroClass","DFunLike.coe","DistribLattice.toLattice","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.instAdd","Finsupp.instLTLex","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MonomialOrder.addCommMonoidSyn","MonomialOrder.lex","MonomialOrder.lex_lt_iff","MonomialOrder.linearOrderSyn","MonomialOrder.syn","MonomialOrder.toSyn","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","WellFoundedGT","instDistribLatticeOfLinearOrder","instLTNat","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_lt_iff_of_unique._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.MonomialOrder.lex_lt_iff_of_unique","reducibility":null,"statement_dag_size":112,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.instFunLike","Finsupp.instLTLex","Inhabited.default","LT","LT.lt","Lex","Preorder","Preorder.toLT","Unique","Unique.instInhabited","Zero","ofLex"],"value_dag_size":120,"value_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.lt_iff_of_unique","Finsupp.instFunLike","Finsupp.instLTLex","Inhabited.default","LT","LT.lt","Lex","Preorder","Preorder.toLT","Unique","Unique.instInhabited","Zero","ofLex","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.instIsOrderedCancelAddMonoidLexFinsupp._simp_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.0.instIsOrderedCancelAddMonoidLexFinsupp","reducibility":null,"statement_dag_size":52,"type_refs":["Add","AddLeftMono","AddLeftReflectLE","Eq","HAdd.hAdd","LE","LE.le","instHAdd"],"value_dag_size":60,"value_refs":["Add","AddLeftMono","AddLeftReflectLE","HAdd.hAdd","LE","LE.le","add_le_add_iff_left","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat._simp_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat","reducibility":null,"statement_dag_size":52,"type_refs":["Add","AddLeftReflectLT","AddLeftStrictMono","Eq","HAdd.hAdd","LT","LT.lt","instHAdd"],"value_dag_size":60,"value_refs":["Add","AddLeftReflectLT","AddLeftStrictMono","HAdd.hAdd","LT","LT.lt","add_lt_add_iff_left","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat._simp_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat","reducibility":null,"statement_dag_size":40,"type_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","instHAdd"],"value_dag_size":46,"value_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","add_right_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat._simp_3","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat","reducibility":null,"statement_dag_size":52,"type_refs":["Add","AddLeftMono","AddLeftReflectLE","Eq","HAdd.hAdd","LE","LE.le","instHAdd"],"value_dag_size":60,"value_refs":["Add","AddLeftMono","AddLeftReflectLE","HAdd.hAdd","LE","LE.le","add_le_add_iff_left","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.isStrictOrder._simp_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.isStrictOrder","reducibility":null,"statement_dag_size":180,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","DegLex","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Prod","Prod.Lex.instLT","Prod.mk","instLTNat","ofDegLex","toLex"],"value_dag_size":184,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","DegLex","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.DegLex.lt_def","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Prod","Prod.Lex.instLT","Prod.mk","instLTNat","ofDegLex","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.isStrictOrder._simp_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.isStrictOrder","reducibility":null,"statement_dag_size":159,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","DegLex","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Or","instLTNat","ofDegLex","toLex"],"value_dag_size":164,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","DegLex","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.DegLex.lt_iff","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Or","instLTNat","ofDegLex","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.le_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.le_iff","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","le_iff_eq_or_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.le_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.le_iff","reducibility":null,"statement_dag_size":50,"type_refs":["DFunLike.coe","EmbeddingLike","Eq","FunLike"],"value_dag_size":58,"value_refs":["DFunLike.coe","EmbeddingLike","EmbeddingLike.apply_eq_iff_eq","Eq","FunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.lt_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.lt_iff","reducibility":null,"statement_dag_size":180,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","DegLex","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Prod","Prod.Lex.instLT","Prod.mk","instLTNat","ofDegLex","toLex"],"value_dag_size":184,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","DegLex","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLTDegLexNat","Finsupp.DegLex.lt_def","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instLTLex","LT","LT.lt","Lex","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Prod","Prod.Lex.instLT","Prod.mk","instLTNat","ofDegLex","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.lt_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.lt_iff","reducibility":null,"statement_dag_size":98,"type_refs":["And","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","LT","LT.lt","Lex","Or","Prod","Prod.Lex.instLT","Prod.fst","Prod.snd","toLex"],"value_dag_size":104,"value_refs":["And","DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","LT","LT.lt","Lex","Or","Prod","Prod.Lex.instLT","Prod.Lex.toLex_lt_toLex","Prod.fst","Prod.snd","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.orderBot._simp_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.orderBot","reducibility":null,"statement_dag_size":182,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","DegLex","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLinearOrderDegLexNat","Finsupp.Lex.partialOrder","Finsupp.degree","Finsupp.instAddZeroClass","LE.le","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLTNat","ofDegLex","toLex"],"value_dag_size":187,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","DegLex","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.DegLex.instLinearOrderDegLexNat","Finsupp.DegLex.le_iff","Finsupp.Lex.partialOrder","Finsupp.degree","Finsupp.instAddZeroClass","LE.le","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLTNat","ofDegLex","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.orderBot._simp_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.orderBot","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.single_strictAnti._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.single_strictAnti","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.MonomialOrder.DegLex","name":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.single_strictAnti._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.single_strictAnti","reducibility":null,"statement_dag_size":103,"type_refs":["DFunLike.coe","DistribLattice.toLattice","Eq","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.instLTLex","Finsupp.single","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLTNat","instOfNatNat","toLex"],"value_dag_size":107,"value_refs":["DFunLike.coe","DistribLattice.toLattice","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Finsupp","Finsupp.Lex.single_lt_iff","Finsupp.instLTLex","Finsupp.single","LT.lt","Lattice.toSemilatticeInf","Lex","LinearOrder","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLTNat","instOfNatNat","propext","toLex"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Multiset","name":"_private.Mathlib.Data.Finsupp.Multiset.0.Finsupp.orderIsoMultiset._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Multiset.0.Finsupp.orderIsoMultiset","reducibility":null,"statement_dag_size":67,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.instLE","LE","LE.le","Zero"],"value_dag_size":73,"value_refs":["DFunLike.coe","Finsupp","Finsupp.instFunLike","Finsupp.instLE","Finsupp.le_def","LE","LE.le","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Multiset","name":"_private.Mathlib.Data.Finsupp.Multiset.0.Finsupp.orderIsoMultiset._simp_2","namespace":"_private.Mathlib.Data.Finsupp.Multiset.0.Finsupp.orderIsoMultiset","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","Eq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":52,"value_refs":["DecidableEq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Multiset.le_iff_count","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Multiset","name":"_private.Mathlib.Data.Finsupp.Multiset.0.Multiset.toFinsupp._simp_3","namespace":"_private.Mathlib.Data.Finsupp.Multiset.0.Multiset.toFinsupp","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Multiset","name":"_private.Mathlib.Data.Finsupp.Multiset.0.Multiset.toFinsupp._simp_4","namespace":"_private.Mathlib.Data.Finsupp.Multiset.0.Multiset.toFinsupp","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.mem_neLocus","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.neLocus_comm._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.neLocus_comm","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.neLocus_eq_empty._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.neLocus_eq_empty","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.NeLocus","name":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.subset_mapRange_neLocus._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.subset_mapRange_neLocus","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Option","name":"_private.Mathlib.Data.Finsupp.Option.0.Finsupp.embDomain_some_some._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Option.0.Finsupp.embDomain_some_some","reducibility":null,"statement_dag_size":29,"type_refs":["DFunLike.coe","Eq","Function.Embedding","Function.Embedding.some","Function.instFunLikeEmbedding","Option","Option.some"],"value_dag_size":32,"value_refs":["DFunLike.coe","Eq.symm","Function.Embedding","Function.Embedding.some","Function.Embedding.some_apply","Function.instFunLikeEmbedding","Option","Option.some"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.add_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.add_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.add_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.add_eq_zero_iff","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.disjoint_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.disjoint_iff","reducibility":null,"statement_dag_size":61,"type_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder"],"value_dag_size":66,"value_refs":["Bot.bot","Disjoint","Eq","Min.min","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","disjoint_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.disjoint_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.disjoint_iff","reducibility":null,"statement_dag_size":56,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finsupp","Finsupp.instZero","Finsupp.support","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":66,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.instEmptyCollection","Finsupp","Finsupp.instZero","Finsupp.support","Finsupp.support_eq_empty","OfNat.ofNat","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_le_embDomain_iff_le._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_le_embDomain_iff_le","reducibility":null,"statement_dag_size":67,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.instLE","LE","LE.le","Zero"],"value_dag_size":73,"value_refs":["DFunLike.coe","Finsupp","Finsupp.instFunLike","Finsupp.instLE","Finsupp.le_def","LE","LE.le","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_lt_embDomain_iff_lt._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_lt_embDomain_iff_lt","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":43,"value_refs":["And","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT","lt_iff_le_not_ge","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_lt_embDomain_iff_lt._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.embDomain_lt_embDomain_iff_lt","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","Finsupp","Finsupp.embDomain","Finsupp.instLE","Function.Embedding","LE","LE.le","Std.Refl","Zero"],"value_dag_size":94,"value_refs":["Finsupp","Finsupp.embDomain","Finsupp.embDomain_le_embDomain_iff_le","Finsupp.instLE","Function.Embedding","LE","LE.le","Std.Refl","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.isLowerSet_range_embDomain._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.isLowerSet_range_embDomain","reducibility":null,"statement_dag_size":94,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":134,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","Not","OfNat.ofNat","True","True.intro","eq_false","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.orderBot._simp_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.orderBot","reducibility":null,"statement_dag_size":67,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.instLE","LE","LE.le","Zero"],"value_dag_size":73,"value_refs":["DFunLike.coe","Finsupp","Finsupp.instFunLike","Finsupp.instLE","Finsupp.le_def","LE","LE.le","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.single_le_sum._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.single_le_sum","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.subset_support_tsub._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.subset_support_tsub","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_sup._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_sup","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not","Or"],"value_dag_size":18,"value_refs":["Not","Or","imp_iff_not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":105,"type_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub"],"value_dag_size":113,"value_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub","propext","tsub_eq_zero_iff_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Not"],"value_dag_size":17,"value_refs":["Not","not_imp_not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","IsBotZeroClass","LE","LE.le","OfNat.ofNat","True","Zero","Zero.toOfNat0"],"value_dag_size":41,"value_refs":["IsBotZeroClass","LE","LE.le","OfNat.ofNat","Zero","Zero.toOfNat0","eq_true","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Order","name":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub._simp_1_6","namespace":"_private.Mathlib.Data.Finsupp.Order.0.Finsupp.support_tsub","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Pointwise","name":"_private.Mathlib.Data.Finsupp.Pointwise.0.Finsupp.pointwise_smul_support_finite._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Pointwise.0.Finsupp.pointwise_smul_support_finite","reducibility":null,"statement_dag_size":100,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","HSMul.hSMul","Not","OfNat.ofNat","SMulZeroClass","SMulZeroClass.toSMul","Zero","Zero.toOfNat0","instHSMul"],"value_dag_size":209,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instFunLike","HSMul.hSMul","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Not","OfNat.ofNat","SMulZeroClass","SMulZeroClass.toSMul","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id","instHSMul","smul_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.SMul","name":"_private.Mathlib.Data.Finsupp.SMul.0.Finsupp.faithfulSMul.match_1","namespace":"_private.Mathlib.Data.Finsupp.SMul.0.Finsupp.faithfulSMul","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.SMulWithZero","name":"_private.Mathlib.Data.Finsupp.SMulWithZero.0.Finsupp.support_smul._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.SMulWithZero.0.Finsupp.support_smul","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Sigma","name":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_apply_of_ne._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_apply_of_ne","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Function.Embedding","Function.Embedding.sigmaMk","Function.instFunLikeEmbedding","Membership.mem","Ne","Not","Set","Set.instMembership","Set.range","Sigma","Sigma.mk"],"value_dag_size":341,"value_refs":["Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Function.Embedding","Function.Embedding.sigmaMk","Function.Embedding.sigmaMk_apply","Function.instFunLikeEmbedding","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Membership.mem","Ne","Not","Set","Set.instMembership","Set.mem_range","Set.range","Sigma","Sigma.mk","Sigma.mk.inj","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Sigma","name":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_single","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":86,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.inj","Sigma.snd","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Sigma","name":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_single._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_single","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Finsupp","Finsupp.embSigma","Finsupp.single","Sigma","Sigma.mk","Zero"],"value_dag_size":1399,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.embSigma","Finsupp.embSigma_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","HEq","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","Sigma","Sigma.fst","Sigma.instDecidableEqSigma","Sigma.mk","Sigma.mk.hcongr_4","Sigma.mk.inj","Sigma.snd","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Sigma.0.Finsupp.embSigma_single._proof_1_1","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.apply_single'._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.apply_single'","reducibility":null,"statement_dag_size":97,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":392,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one'._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one'","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Finset","Finset.card","Finset.card_eq_one","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one'._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one'","reducibility":null,"statement_dag_size":74,"type_refs":["And","Eq","Exists","Finset","Finset.instSingleton","Finsupp","Finsupp.single","Finsupp.support","Ne","OfNat.ofNat","Singleton.singleton","Zero","Zero.toOfNat0"],"value_dag_size":79,"value_refs":["And","Eq","Exists","Finset","Finset.instSingleton","Finsupp","Finsupp.single","Finsupp.support","Finsupp.support_eq_singleton'","Ne","OfNat.ofNat","Singleton.singleton","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq","Exists","Finset","Finset.card","Finset.card_eq_one","Finset.instSingleton","Nat","OfNat.ofNat","Singleton.singleton","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_eq_one","reducibility":null,"statement_dag_size":81,"type_refs":["And","DFunLike.coe","Eq","Finset","Finset.instSingleton","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.support","Ne","OfNat.ofNat","Singleton.singleton","Zero","Zero.toOfNat0"],"value_dag_size":86,"value_refs":["And","DFunLike.coe","Eq","Finset","Finset.instSingleton","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.support","Finsupp.support_eq_singleton","Ne","OfNat.ofNat","Singleton.singleton","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one'._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one'","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["Exists","Finset","Finset.card","Finset.card_le_one_iff_subset_singleton","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one'._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one'","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Exists","Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp","Finsupp.single","Finsupp.support","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero"],"value_dag_size":73,"value_refs":["Eq","Exists","Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp","Finsupp.single","Finsupp.support","Finsupp.support_subset_singleton'","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","Exists","Finset","Finset.card","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["Exists","Finset","Finset.card","Finset.card_le_one_iff_subset_singleton","Finset.instPartialOrder","Finset.instSingleton","LE.le","Nat","Nonempty","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.card_support_le_one","reducibility":null,"statement_dag_size":75,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.support","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero"],"value_dag_size":80,"value_refs":["DFunLike.coe","Eq","Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.support","Finsupp.support_subset_singleton","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.coe_update._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.coe_update","reducibility":null,"statement_dag_size":58,"type_refs":["DFunLike.coe","DecidableEq","Eq","Finsupp","Finsupp.instFunLike","Finsupp.update","Function.update","Zero"],"value_dag_size":531,"value_refs":["Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Function.update","Function.update.eq_1","HEq.symm","HEq.trans","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","Or","Or.casesOn","True","True.intro","Zero","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update._proof_1","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","funext","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding"],"value_dag_size":63,"value_refs":["DFunLike.coe","Eq","Eq.mpr_prop","Eq.refl","Exists","Function.Embedding","Function.instFunLikeEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single","reducibility":null,"statement_dag_size":61,"type_refs":["DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":127,"value_refs":["DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Function.Embedding","Function.instFunLikeEmbedding","Iff","Lean.Grind.iff_eq","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","True","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_1","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single","reducibility":null,"statement_dag_size":103,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.embDomain","Finsupp.instFunLike","Finsupp.single","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Set","Set.instMembership","Set.range","Zero"],"value_dag_size":1137,"value_refs":["Classical.byContradiction","Classical.choose","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","Exists.choose_spec","False","Finsupp","Finsupp.embDomain","Finsupp.embDomain_apply","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","FunLike","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Nonempty","Nonempty.intro","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instMembership","Set.mem_range","Set.range","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_1","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_2","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_4","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single","reducibility":null,"statement_dag_size":105,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.embDomain","Finsupp.instFunLike","Finsupp.single","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","Not","Set","Set.instMembership","Set.range","Zero"],"value_dag_size":478,"value_refs":["Classical.byContradiction","Classical.choose","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.choose","False","Finsupp","Finsupp.embDomain","Finsupp.embDomain_apply","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Function.Embedding","Function.instFunLikeEmbedding","Iff","Lean.Grind.dite_cond_eq_false'","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Membership.mem","Not","OfNat.ofNat","Set","Set.instMembership","Set.mem_range","Set.range","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.embDomain_single._proof_1_1","congrArg","dite","dite_congr","eq_false","eq_true","forall_not_of_not_exists","id","ite","ite_cond_eq_false","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.eq_single_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.eq_single_iff","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase._proof_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase","reducibility":null,"statement_dag_size":90,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset","Finset.erase","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Iff","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","ite"],"value_dag_size":404,"value_refs":["And","Classical.byContradiction","Classical.decEq","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.erase","Finset.instSetLike","Finset.mem_erase","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_apply._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_apply","reducibility":null,"statement_dag_size":35,"type_refs":["Decidable","Eq","True","ite"],"value_dag_size":42,"value_refs":["Decidable","Eq","True","ite","ite_eq_ite","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_eq_update_zero._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_eq_update_zero","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.update","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":283,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_idem._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_idem","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finsupp","Finsupp.erase","Zero"],"value_dag_size":329,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_ne","reducibility":null,"statement_dag_size":53,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.erase","Finsupp.instFunLike","Ne","Zero"],"value_dag_size":180,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.instFunLike","Lean.Grind.nestedDecidable","Ne","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_of_notMem_support._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_of_notMem_support","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.erase","Finsupp.support","Membership.mem","Not","SetLike.instMembership","Zero"],"value_dag_size":429,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","FunLike","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_same._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_same","reducibility":null,"statement_dag_size":51,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.erase","Finsupp.instFunLike","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":166,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.instFunLike","Not","OfNat.ofNat","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_self","eq_true","id","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_single","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.instZero","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":404,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.instZero","Finsupp.single","Finsupp.single_apply","Finsupp.zero_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_single_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_single_ne","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.single","Ne","Zero"],"value_dag_size":488,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Ne","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_update_eq_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_update_eq_erase","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.update","Zero"],"value_dag_size":380,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_update_of_ne._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_update_of_ne","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.update","Ne","Zero"],"value_dag_size":661,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Ne","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.mapRange_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.mapRange_single","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","Finsupp","Finsupp.mapRange","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":540,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.mapRange","Finsupp.mapRange_apply","Finsupp.single","Finsupp.single_apply","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.mem_support_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.mem_support_single","reducibility":null,"statement_dag_size":68,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply_eq_zero","OfNat.ofNat","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.nontrivial_iff.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.nontrivial_iff","reducibility":"abbrev","statement_dag_size":39,"type_refs":["And","And.intro","Nonempty","Nontrivial"],"value_dag_size":53,"value_refs":["And","And.casesOn","And.intro","Nonempty","Nontrivial"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single._proof_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single","reducibility":null,"statement_dag_size":83,"type_refs":["Classical.decEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Iff","Membership.mem","Not","OfNat.ofNat","Pi.single","SetLike.instMembership","Singleton.singleton","Zero","Zero.toOfNat0","ite"],"value_dag_size":708,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.decEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.instEmptyCollection","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.notMem_empty","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","Pi.single","Pi.single_apply","SetLike.instMembership","Singleton.singleton","True","True.intro","Zero","Zero.toOfNat0","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_eq_zero","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_mem._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_mem","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Finsupp","Finsupp.instFunLike","Finsupp.single","Insert.insert","Membership.mem","OfNat.ofNat","Set","Set.instInsert","Set.instMembership","Set.instSingletonSet","Singleton.singleton","Zero","Zero.toOfNat0"],"value_dag_size":324,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instInsert","Set.instMembership","Set.instSingletonSet","Set.mem_insert_iff","Set.mem_singleton_iff","Singleton.singleton","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_apply_ne_zero","reducibility":null,"statement_dag_size":68,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply_eq_zero","OfNat.ofNat","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_pi_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_pi_single","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_single_iff._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_single_iff","reducibility":null,"statement_dag_size":111,"type_refs":["And","DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.single","Not","OfNat.ofNat","Or","Zero","Zero.toOfNat0"],"value_dag_size":530,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","Not","OfNat.ofNat","Or","True","True.intro","Zero","Zero.toOfNat0","congr","congrArg","eq_false","eq_self","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_single_iff._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_single_iff","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Finsupp","Finsupp.single","OfNat.ofNat","Or","Zero","Zero.toOfNat0"],"value_dag_size":296,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finsupp","Finsupp.instZero","Finsupp.single","Finsupp.single_zero","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","congr","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_eq_zero","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single","reducibility":null,"statement_dag_size":56,"type_refs":["DFunLike.coe","Eq","Exists","Function.Embedding","Function.instFunLikeEmbedding"],"value_dag_size":65,"value_refs":["DFunLike.coe","Eq","Eq.mpr_prop","Eq.refl","Exists","Function.Embedding","Function.instFunLikeEmbedding"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single._proof_1_3","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single","reducibility":null,"statement_dag_size":156,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finset.map","Finsupp","Finsupp.embDomain","Finsupp.instFunLike","Finsupp.single","Finsupp.support","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","Zero"],"value_dag_size":1207,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.choose","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.choose","False","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Finsupp","Finsupp.embDomain","Finsupp.embDomain_apply","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Finsupp.support","FunLike","Function.Embedding","Function.Embedding.injective","Function.Injective","Function.instFunLikeEmbedding","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.leftInv","Lean.Grind.leftInv_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Nonempty","Nonempty.intro","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single._proof_1_2","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_embDomain_single","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_single_apply._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_of_single_apply","reducibility":null,"statement_dag_size":74,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.instZero","Finsupp.single","Zero"],"value_dag_size":517,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.instZero","Finsupp.single","Finsupp.single_apply","Finsupp.single_zero","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","congr","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_swap._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.single_swap","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_eq_singleton'.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_eq_singleton'","reducibility":"abbrev","statement_dag_size":160,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.single","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":232,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.single","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_erase._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_erase","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finsupp","Finsupp.erase","Finsupp.support","Zero"],"value_dag_size":1040,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.mem_erase","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_single_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_single_subset","reducibility":null,"statement_dag_size":47,"type_refs":["Finset","Finset.instPartialOrder","Finset.instSingleton","Finsupp.single","Finsupp.support","LE.le","PartialOrder.toPreorder","Preorder.toLE","Singleton.singleton","Zero"],"value_dag_size":381,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Finset.subset_iff","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.single","Finsupp.single_apply","Finsupp.support","Iff","LE.le","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_subset_singleton'.match_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_subset_singleton'","reducibility":"abbrev","statement_dag_size":91,"type_refs":["Eq","Exists","Exists.intro","Finsupp","Finsupp.single","Zero"],"value_dag_size":116,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.single","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finset.instInsert","Finsupp","Finsupp.support","Finsupp.update","Insert.insert","OfNat.ofNat","Zero","Zero.toOfNat0","ite"],"value_dag_size":1873,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Finsupp.update","Finsupp.update_apply","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_ne_zero","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finsupp","Finsupp.support","Finsupp.update","Insert.insert","Ne","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":1229,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Finsupp.update","Finsupp.update_apply","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_subset._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_subset","reducibility":null,"statement_dag_size":61,"type_refs":["DecidableEq","Finset","Finset.instInsert","Finset.instPartialOrder","Finsupp","Finsupp.support","Finsupp.update","Insert.insert","LE.le","PartialOrder.toPreorder","Preorder.toLE","Zero"],"value_dag_size":456,"value_refs":["Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instInsert","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_insert","Finset.subset_iff","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Finsupp.update","Finsupp.update_apply","Iff","Insert.insert","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Ne","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_zero._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.support_update_zero","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","Eq","Finset","Finset.erase","Finsupp","Finsupp.support","Finsupp.update","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":1076,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.erase","Finset.ext","Finset.instSetLike","Finset.mem_erase","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Finsupp.update","Finsupp.update_apply","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update._proof_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":30,"value_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update._proof_2","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update","reducibility":null,"statement_dag_size":109,"type_refs":["Classical.decEq","DFunLike.coe","Eq","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Function.update","Iff","Insert.insert","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","ite"],"value_dag_size":1816,"value_refs":["And","And.casesOn","Classical.byContradiction","Classical.decEq","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Finset.mem_erase","Finset.mem_insert","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Function.update","Function.update.eq_1","HEq.symm","HEq.trans","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update._proof_1","congrArg","dite","dite_congr","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_apply._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_apply","reducibility":null,"statement_dag_size":169,"type_refs":["Classical.decEq","DFunLike.coe","DecidableEq","Eq","Eq.rec","Eq.symm","Finset","Finset.erase","Finset.instInsert","Finsupp","Finsupp.instFunLike","Finsupp.mk","Finsupp.support","Finsupp.update._proof_3","Insert.insert","Not","OfNat.ofNat","Zero","Zero.toOfNat0","dite","ite"],"value_dag_size":683,"value_refs":["Classical.byContradiction","Classical.decEq","DFunLike.coe","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.erase","Finset.instInsert","Finset.instSetLike","Finsupp","Finsupp.coe_mk","Finsupp.instFunLike","Finsupp.mk","Finsupp.support","Finsupp.update._proof_3","Function.update","HEq.symm","HEq.trans","Iff","Insert.insert","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Membership.mem","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","Zero","Zero.toOfNat0","congrFun","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_comm._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_comm","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Finsupp","Finsupp.update","Ne","Zero"],"value_dag_size":645,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Ne","Not","Or","Or.casesOn","True","True.intro","Zero","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_erase_eq_update._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_erase_eq_update","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Finsupp","Finsupp.erase","Finsupp.update","Zero"],"value_dag_size":390,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.erase","Finsupp.erase_apply","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_idem._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_idem","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finsupp","Finsupp.update","Zero"],"value_dag_size":366,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","Or","Or.casesOn","True","True.intro","Zero","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_self._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.update_self","reducibility":null,"statement_dag_size":44,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Finsupp.update","Zero"],"value_dag_size":348,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","DFunLike.coe.hcongr_6","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.update","Finsupp.update_apply","FunLike","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Not","Or","Or.casesOn","True","True.intro","Zero","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Single","name":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.zipWith_single_single._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Single.0.Finsupp.zipWith_single_single","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","Finsupp","Finsupp.single","Finsupp.zipWith","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":819,"value_refs":["Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.ext","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Finsupp.zipWith","Finsupp.zipWith_apply","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_of_heq","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.ToDFinsupp","name":"_private.Mathlib.Data.Finsupp.ToDFinsupp.0.DFinsupp.toFinsupp._simp_1","namespace":"_private.Mathlib.Data.Finsupp.ToDFinsupp.0.DFinsupp.toFinsupp","reducibility":null,"statement_dag_size":99,"type_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":106,"value_refs":["DFinsupp","DFinsupp.instDFunLike","DFinsupp.mem_support_iff","DFinsupp.support","DFunLike.coe","Decidable","DecidableEq","Finset","Finset.instSetLike","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff","reducibility":null,"statement_dag_size":96,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finset","Finset.instSetLike","Finset.sum","Membership.mem","OfNat.ofNat","SetLike.instMembership","Subsingleton","Zero.toOfNat0"],"value_dag_size":102,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddUnits","AddZero.toZero","AddZeroClass.toAddZero","Eq","Finset","Finset.instSetLike","Finset.sum","Finset.sum_eq_zero_iff","Membership.mem","OfNat.ofNat","SetLike.instMembership","Subsingleton","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":74,"value_refs":["DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","Not"],"value_dag_size":13,"value_refs":["Not","not_imp_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_eq_zero_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_preimage_add._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.degree_preimage_add","reducibility":null,"statement_dag_size":108,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","HAdd.hAdd","LE.le","Nat","Nat.instAddCommMonoid","instAddNat","instHAdd","instLENat"],"value_dag_size":437,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.refl","Eq.symm","False","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MulZeroClass.toZero","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq._proof_1_2","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq","reducibility":null,"statement_dag_size":115,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","HAdd.hAdd","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":378,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.refl","False","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MulZeroClass.toZero","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq._proof_1_4","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq","reducibility":null,"statement_dag_size":84,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","LE.le","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instOfNatNat"],"value_dag_size":363,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","HAdd.hAdd","HSub.hSub","Iff","Int","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.leaf","Membership.mem","MulZeroClass.toZero","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","True","Zero.toOfNat0","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastNat","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.exists_le_degree_eq","reducibility":null,"statement_dag_size":125,"type_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0"],"value_dag_size":131,"value_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.degree_eq_zero_iff","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_eq","reducibility":null,"statement_dag_size":85,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Set","Set.instLE","Set.ofPred","instLENat"],"value_dag_size":607,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","MulZeroClass.toZero","Nat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","True","eagerReduce","eq_false","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_le._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_le","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["Eq","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","eq_false","one_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_lt._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_degree_lt","reducibility":null,"statement_dag_size":87,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","DFunLike.coe","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Set","Set.instLE","Set.ofPred","instLENat","instLTNat"],"value_dag_size":708,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","MulZeroClass.toZero","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_eq._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_eq","reducibility":null,"statement_dag_size":110,"type_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","DFunLike.coe","Eq","Finsupp","Finsupp.instAddZeroClass","Finsupp.weight","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.ofPred","instLENat","instMulZeroClassOfSemiring"],"value_dag_size":656,"value_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.instAddZeroClass","Finsupp.weight","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","MulZeroClass.toZero","Nat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instSemiring","NatCast.natCast","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","True","eagerReduce","eq_false","id","instLENat","instMulZeroClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Finset","Finset.instSetLike","Finset.mem_coe","Membership.mem","Set","Set.instMembership","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_3","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":73,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd"],"value_dag_size":78,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","Eq","Finset","Finset.HasAntidiagonal","Finset.HasAntidiagonal.antidiagonal","Finset.HasAntidiagonal.mem_antidiagonal","Finset.instSetLike","HAdd.hAdd","Membership.mem","Prod","Prod.fst","Prod.snd","SetLike.instMembership","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_4","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le._simp_1_6","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_le","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_lt._proof_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.finite_of_nat_weight_lt","reducibility":null,"statement_dag_size":112,"type_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","DFunLike.coe","Finsupp","Finsupp.instAddZeroClass","Finsupp.weight","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.ofPred","instLENat","instLTNat","instMulZeroClassOfSemiring"],"value_dag_size":749,"value_refs":["AddCommMonoid.toAddMonoid","AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddMonoidWithOne.toAddMonoid","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.instAddZeroClass","Finsupp.weight","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","MulZeroClass.toZero","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Nat.instSemiring","NatCast.natCast","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMulZeroClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.image_pow_eq_finsuppProd_image._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.image_pow_eq_finsuppProd_image","reducibility":null,"statement_dag_size":146,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.degree","Finsupp.instAdd","Finsupp.instAddZeroClass","Finsupp.instZero","Finsupp.single","Finsupp.support","HSMul.hSMul","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","Set","Set.NSMul","Set.image","Set.instLE","Set.ofPred","SetLike.coe","instHSMul","instOfNatNat"],"value_dag_size":151,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","Eq","Eq.symm","Finset","Finset.instSetLike","Finsupp","Finsupp.degree","Finsupp.instAdd","Finsupp.instAddZeroClass","Finsupp.instZero","Finsupp.nsmul_single_one_image","Finsupp.single","Finsupp.support","HSMul.hSMul","LE.le","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","OfNat.ofNat","Set","Set.NSMul","Set.image","Set.instLE","Set.ofPred","SetLike.coe","instHSMul","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_degree._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_degree","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":76,"value_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.notMem_support_iff","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_degree._simp_1_2","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_degree","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","IsBotZeroClass","LE","LE.le","OfNat.ofNat","True","Zero","Zero.toOfNat0"],"value_dag_size":41,"value_refs":["IsBotZeroClass","LE","LE.le","OfNat.ofNat","Zero","Zero.toOfNat0","eq_true","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_weight._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.le_weight","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":76,"value_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.notMem_support_iff","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image._proof_1_6","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image","reducibility":null,"statement_dag_size":202,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instFunLike","Finsupp.single","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Not","OfNat.ofNat","Set","Set.instMembership","instOfNatNat"],"value_dag_size":635,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","Classical.byContradiction","Classical.propDecidable","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instFunLike","Finsupp.single","Finsupp.single_apply","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instAddMonoid","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","Or.casesOn","Set","Set.instMembership","True","True.intro","Zero.toOfNat0","congrArg","eq_false","eq_true","id","instOfNatNat","ite","ite_cond_eq_false","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image","reducibility":null,"statement_dag_size":125,"type_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0"],"value_dag_size":131,"value_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","DFunLike.coe","Eq","Finsupp","Finsupp.degree","Finsupp.degree_eq_zero_iff","Finsupp.instAddZeroClass","Finsupp.instZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image._simp_1_5","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image","reducibility":null,"statement_dag_size":83,"type_refs":["Add","And","Eq","Exists","HAdd.hAdd","Membership.mem","Set","Set.add","Set.instMembership","instHAdd"],"value_dag_size":88,"value_refs":["Add","And","Eq","Exists","HAdd.hAdd","Membership.mem","Set","Set.add","Set.instMembership","Set.mem_add","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image._simp_1_8","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image.match_1_3","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.nsmul_single_one_image","reducibility":"abbrev","statement_dag_size":270,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.support","HAdd.hAdd","LE.le","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","OfNat.ofNat","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.coe","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":331,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.degree","Finsupp.instAddZeroClass","Finsupp.support","HAdd.hAdd","LE.le","Membership.mem","MulZeroClass.toZero","Nat","Nat.instAddCommMonoid","Nat.instMulZeroClass","OfNat.ofNat","Set","Set.instLE","Set.instMembership","Set.ofPred","SetLike.coe","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Finsupp.Weight","name":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.range_single_one._simp_1_1","namespace":"_private.Mathlib.Data.Finsupp.Weight.0.Finsupp.range_single_one","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range"],"value_dag_size":46,"value_refs":["LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range","Set.range_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Basic","name":"_private.Mathlib.Data.Fintype.Basic.0.Fin.univ_image_getElem'._proof_1","namespace":"_private.Mathlib.Data.Fintype.Basic.0.Fin.univ_image_getElem'","reducibility":null,"statement_dag_size":30,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Basic","name":"_private.Mathlib.Data.Fintype.Basic.0.Fintype.subtypeEq'._simp_1","namespace":"_private.Mathlib.Data.Fintype.Basic.0.Fintype.subtypeEq'","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Basic","name":"_private.Mathlib.Data.Fintype.Basic.0.Multiset.bijective_iff_map_univ_eq_univ.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Basic.0.Multiset.bijective_iff_map_univ_eq_univ","reducibility":"abbrev","statement_dag_size":137,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset.univ","Finset.val","Fintype","Membership.mem","Multiset","Multiset.instMembership"],"value_dag_size":209,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset.univ","Finset.val","Fintype","Membership.mem","Multiset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Basic","name":"_private.Mathlib.Data.Fintype.Basic.0.exists_seq_of_forall_finset_exists'._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Basic.0.exists_seq_of_forall_finset_exists'","reducibility":null,"statement_dag_size":45,"type_refs":["LT.lt","Nat","Ne","Std.Symm","instLTNat"],"value_dag_size":591,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","Std.Symm","Std.Symm.casesOn","eagerReduce","eq_false","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.BigOperators","name":"_private.Mathlib.Data.Fintype.BigOperators.0.Finset.prod_toFinset_eq_subtype._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.BigOperators.0.Finset.prod_toFinset_eq_subtype","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.toFinset","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.mem_toFinset","Set.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finite.injective_iff_bijective._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finite.injective_iff_bijective","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Finite","Function.Injective","Function.Surjective"],"value_dag_size":26,"value_refs":["Finite","Finite.injective_iff_surjective","Function.Injective","Function.Surjective","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finite.surjective_iff_bijective._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finite.surjective_iff_bijective","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Finite","Function.Injective","Function.Surjective"],"value_dag_size":26,"value_refs":["Finite","Finite.injective_iff_surjective","Function.Injective","Function.Surjective","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":43,"value_refs":["And","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT","lt_iff_le_not_ge","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finite.wellFounded_of_trans_of_irrefl","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":51,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Finset.card_univ_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Finset.card_univ_sdiff","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Finset","Finset.card","Finset.instSDiff","Finset.univ","Fintype","Fintype.card","HSub.hSub","Nat","SDiff.sdiff","instHSub","instSubNat"],"value_dag_size":299,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.card_sdiff_of_subset","Finset.card_univ","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_univ","Finset.subset_iff","Finset.univ","Fintype","Fintype.card","HSub.hSub","Iff","LE.le","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Nat","Not","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","congrArg","eq_false","eq_true","id","instHSub","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_fin_lt_of_le.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_fin_lt_of_le","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Fin","Fin.mk","Fin.val","LT.lt","Nat","Subtype","Subtype.mk","instLTNat"],"value_dag_size":119,"value_refs":["Fin","Fin.casesOn","Fin.mk","Fin.val","LT.lt","Nat","Subtype","Subtype.casesOn","Subtype.mk","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_fin_lt_of_le.match_1_3","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_fin_lt_of_le","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":41,"value_refs":["Fin","Fin.casesOn","Fin.mk","LT.lt","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_lt_of_injective_not_surjective.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_lt_of_injective_not_surjective","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Eq","Exists","Exists.intro","Not"],"value_dag_size":92,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_range_le.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_range_le","reducibility":"abbrev","statement_dag_size":72,"type_refs":["Eq","Exists.intro","Membership.mem","Set","Set.Elem","Set.instMembership","Set.range","Subtype.mk"],"value_dag_size":138,"value_refs":["Eq","Exists.casesOn","Exists.intro","Membership.mem","Set","Set.Elem","Set.instMembership","Set.range","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.toFinset","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.mem_toFinset","Set.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl","reducibility":null,"statement_dag_size":33,"type_refs":["Compl.compl","Eq","Membership.mem","Not","Set","Set.instCompl","Set.instMembership"],"value_dag_size":36,"value_refs":["Compl.compl","Membership.mem","Not","Set","Set.instCompl","Set.instMembership","Set.mem_compl_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.card_subtype_compl","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.ofPred"],"value_dag_size":33,"value_refs":["Membership.mem","Set","Set.instMembership","Set.mem_ofPred","Set.ofPred","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["And","Eq","Finset","Finset.Subset.antisymm_iff","Finset.instPartialOrder","LE.le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton"],"value_dag_size":59,"value_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.subset_singleton_iff'","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton"],"value_dag_size":50,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.instSingleton","Finset.singleton_subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one._simp_1_4","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one._simp_1_5","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.existsUnique_iff_card_one","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":51,"value_refs":["DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Finset.card","Finset.univ","Fintype","Fintype.card","Nat"],"value_dag_size":25,"value_refs":["Eq.symm","Finset.card","Finset.card_univ","Finset.univ","Fintype","Fintype.card","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff","reducibility":null,"statement_dag_size":75,"type_refs":["And","Eq","Exists","Finset","Finset.card","Finset.instSetLike","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["And","Exists","Finset","Finset.card","Finset.instSetLike","Finset.two_lt_card_iff","LT.lt","Membership.mem","Nat","Ne","OfNat.ofNat","SetLike.instMembership","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Card","name":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Card.0.Fintype.two_lt_card_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___unexpand_Finset_card_1","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":240,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0._aux_Mathlib_Data_Fintype_CardEmbedding___unexpand_Fintype_card_1","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":240,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0.«_aux_Mathlib_Data_Fintype_CardEmbedding___macroRules__private_Mathlib_Data_Fintype_CardEmbedding_0_term|_|_1»","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":230,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0.«_aux_Mathlib_Data_Fintype_CardEmbedding___macroRules__private_Mathlib_Data_Fintype_CardEmbedding_0_term‖_‖_1»","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":229,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0.«term|_|»","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":56,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.CardEmbedding","name":"_private.Mathlib.Data.Fintype.CardEmbedding.0.«term‖_‖»","namespace":"_private.Mathlib.Data.Fintype.CardEmbedding.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":56,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Finset.eq_univ_iff_forall._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Finset.eq_univ_iff_forall","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.decidablePiFintype._simp_1","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.decidablePiFintype","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.subsingleton._simp_3","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.subsingleton","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Finset","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership"],"value_dag_size":43,"value_refs":["Eq","Finset","Finset.ext_iff","Finset.instSetLike","Iff","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.subsingleton.match_1","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Fintype.subsingleton","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Finset","Finset.instSetLike","Fintype","Fintype.mk","Membership.mem","SetLike.instMembership"],"value_dag_size":63,"value_refs":["Finset","Finset.instSetLike","Fintype","Fintype.casesOn","Fintype.mk","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Mathlib.Meta.delabFinsetFilter.match_1","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Mathlib.Meta.delabFinsetFilter","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Array","Lean.Expr","List.cons","List.nil","List.toArray"],"value_dag_size":205,"value_refs":["Array","Array.getLit","Array.size","Array.toArrayLit_eq","Bool","Bool.true","Decidable.decide","Eq","Eq.ndrec","Eq.refl","Eq.symm","LT.lt","Lean.Expr","List.cons","List.nil","List.toArray","Nat","Nat.decLt","Not","OfNat.ofNat","dite","id","instDecidableEqNat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Defs","name":"_private.Mathlib.Data.Fintype.Defs.0.Mathlib.Meta.delabFinsetFilter.match_3","namespace":"_private.Mathlib.Data.Fintype.Defs.0.Mathlib.Meta.delabFinsetFilter","reducibility":"abbrev","statement_dag_size":37,"type_refs":["Array","Lean.Expr","List.cons","List.nil","List.toArray"],"value_dag_size":228,"value_refs":["Array","Array.getLit","Array.size","Array.toArrayLit_eq","Bool","Bool.true","Decidable.decide","Eq","Eq.ndrec","Eq.refl","Eq.symm","LT.lt","Lean.Expr","List.cons","List.nil","List.toArray","Nat","Nat.decLt","Not","OfNat.ofNat","dite","id","instDecidableEqNat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Equiv","Nonempty","Nonempty.intro"],"value_dag_size":41,"value_refs":["Equiv","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Equiv","Nonempty","Nonempty.intro","Unit"],"value_dag_size":39,"value_refs":["Equiv","Nonempty","Nonempty.casesOn","Nonempty.intro","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff.match_1_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":66,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff_nonempty_unique.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff_nonempty_unique","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":66,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff_nonempty_unique.match_1_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_eq_one_iff_nonempty_unique","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nonempty","Nonempty.intro","Unique"],"value_dag_size":34,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro","Unique"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_le_one_iff.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_le_one_iff","reducibility":"abbrev","statement_dag_size":86,"type_refs":["Eq","Fintype","Fintype.card","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":136,"value_refs":["Eq","Fintype","Fintype.card","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_le_one_iff.match_1_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Fintype.card_le_one_iff","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":66,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.exists_of_card_eq_finset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.exists_of_card_eq_finset","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.exists_of_card_le_finset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.exists_of_card_le_finset","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range"],"value_dag_size":46,"value_refs":["LE.le","Membership.mem","Set","Set.instLE","Set.instMembership","Set.range","Set.range_subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.nonempty_iff_card_le.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Function.Embedding.nonempty_iff_card_le","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Function.Embedding","Nonempty","Nonempty.intro"],"value_dag_size":41,"value_refs":["Function.Embedding","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial._simp_5","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":40,"value_refs":["Eq","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Membership.mem","SetLike.instMembership","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial.match_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Exists","Exists.intro","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","Not","SetLike.instMembership","Singleton.singleton"],"value_dag_size":133,"value_refs":["Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.instSingleton","Membership.mem","Not","SetLike.instMembership","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial.match_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.instNontrivial","reducibility":"abbrev","statement_dag_size":93,"type_refs":["EmptyCollection.emptyCollection","Exists","Exists.intro","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":121,"value_refs":["EmptyCollection.emptyCollection","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite","reducibility":"regular","statement_dag_size":9,"type_refs":["Infinite","Nat"],"value_dag_size":93,"value_refs":["Classical.choose","Classical.decEq","Finset","Finset.instSetLike","Infinite","InvImage","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","WellFounded.Nat.fix","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_1","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_2","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_5","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["InvImage","LT.lt","Nat","instLTNat"],"value_dag_size":28,"value_refs":["InvImage","LT.lt","Nat","id","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_10","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_11","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":63,"type_refs":["Classical.decEq","Exists","Finset","Finset.instSetLike","Infinite","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_10","instLTNat"],"value_dag_size":63,"value_refs":["Classical.decEq","Iff.mp","Infinite","Infinite.exists_notMem_finset","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_2","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["InvImage","LT.lt","Nat","instLTNat"],"value_dag_size":28,"value_refs":["InvImage","LT.lt","Nat","id","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_4","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_5","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":79,"type_refs":["Classical.decEq","Exists","Finset","Finset.instSetLike","Infinite","InvImage","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_3","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_4","instLTNat"],"value_dag_size":148,"value_refs":["Classical.decEq","Eq","Eq.ndrec","Eq.refl","Exists","Finset","Finset.instSetLike","Iff.mp","Infinite","Infinite.exists_notMem_finset","InvImage","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","id","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_7","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":63,"type_refs":["Classical.decEq","Exists","Finset","Finset.instSetLike","Infinite","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_7","instLTNat"],"value_dag_size":63,"value_refs":["Classical.decEq","Iff.mp","Infinite","Infinite.exists_notMem_finset","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_9","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.range","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.range","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux.eq_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":75,"type_refs":["Classical.choose","Classical.decEq","Eq","Finset","Finset.instSetLike","Infinite","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","instLTNat"],"value_dag_size":120,"value_refs":["Classical.choose","Classical.decEq","Eq.refl","Eq.trans","Finset","Finset.instSetLike","Infinite","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux.eq_def","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux.eq_def","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","reducibility":null,"statement_dag_size":77,"type_refs":["Classical.choose","Classical.decEq","Eq","Finset","Finset.instSetLike","Infinite","LT.lt","Membership.mem","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","instLTNat"],"value_dag_size":608,"value_refs":["Classical.choose","Classical.decEq","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.trans","Exists","Finset","Finset.instSetLike","Iff.mp","Infinite","Infinite.exists_notMem_finset","InvImage","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_range","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Not","SetLike.instMembership","WellFounded.Nat.fix","WellFounded.Nat.fix_eq","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_1","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_2","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_5","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","congrArg","funext","have_body_congr'","id","instLTNat","wfParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux_injective","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.Infinite","reducibility":null,"statement_dag_size":15,"type_refs":["Function.Injective","Infinite","Nat","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux"],"value_dag_size":458,"value_refs":["Classical.choose","Classical.choose_spec","Classical.decEq","Classical.em","Decidable.byContradiction","DecidableEq","Eq","Eq.mpr","Eq.refl","Eq.symm","Exists","Exists.intro","Finset","Finset.instSetLike","Iff.mp","Iff.mpr","Infinite","Infinite.exists_notMem_finset","LE.le","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_pmap","Multiset.mem_range","Multiset.mem_toFinset","Multiset.pmap","Multiset.range","Multiset.toFinset","Nat","Nat.instLinearOrder","Nat.instPartialOrder","Not","Or","Or.casesOn","SetLike.instMembership","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_6","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux._proof_8","_private.Mathlib.Data.Fintype.EquivFin.0.Infinite.natEmbeddingAux.eq_1","congrArg","id","instDecidableEqNat","instLENat","instLTNat","le_of_not_ge","lt_of_le_of_ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.finite_iff_nonempty_fintype.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.finite_iff_nonempty_fintype","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Fintype","Nonempty","Nonempty.intro"],"value_dag_size":34,"value_refs":["Fintype","Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.instInfiniteMultisetOfNonempty.match_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.instInfiniteMultisetOfNonempty","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.isEmpty_fintype.match_1_1","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.isEmpty_fintype","reducibility":"abbrev","statement_dag_size":27,"type_refs":["False","Fintype","IsEmpty","IsEmpty.mk"],"value_dag_size":37,"value_refs":["False","Fintype","IsEmpty","IsEmpty.casesOn","IsEmpty.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.EquivFin","name":"_private.Mathlib.Data.Fintype.EquivFin.0.isEmpty_fintype.match_1_3","namespace":"_private.Mathlib.Data.Fintype.EquivFin.0.isEmpty_fintype","reducibility":"abbrev","statement_dag_size":24,"type_refs":["Finite","Infinite","Infinite.mk","Not"],"value_dag_size":35,"value_refs":["Finite","Infinite","Infinite.casesOn","Infinite.mk","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.Iio_last_eq_map._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.Iio_last_eq_map","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":35,"value_refs":["Fin","Fin.lt_def","Fin.val","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.Ioi_zero_eq_map._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.Ioi_zero_eq_map","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Fin","Fin.instOfNat","LT.lt","Nat","Ne","NeZero","OfNat.ofNat","Zero.ofOfNat0","instLTFin","instOfNatNat"],"value_dag_size":47,"value_refs":["Fin","Fin.instOfNat","Fin.pos_iff_ne_zero","LT.lt","Nat","Ne","NeZero","OfNat.ofNat","Zero.ofOfNat0","instLTFin","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_univ_eq_vector_get_eq_count._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_univ_eq_vector_get_eq_count","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_val_lt._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_val_lt","reducibility":null,"statement_dag_size":53,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","instDecidableAnd"],"value_dag_size":61,"value_refs":["And","DecidablePred","Eq.symm","Finset","Finset.filter","Finset.filter_filter","instDecidableAnd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_val_lt._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.card_filter_val_lt","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Exists","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":42,"value_refs":["Exists","Fin","Fin.exists_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":78,"type_refs":["DecidablePred","Fin","Fin.fintype","Fin.instLocallyFiniteOrderBot","Fin.instPartialOrder","Finset","Finset.Iio","Finset.filter","Finset.instPartialOrder","Finset.univ","LE.le","Nat","Not","PartialOrder.toPreorder","Preorder.toLE","instLEFin"],"value_dag_size":407,"value_refs":["And","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.fintype","Fin.instIsLinearOrder","Fin.instLawfulOrderLT","Fin.instLocallyFiniteOrderBot","Fin.instPartialOrder","Finset","Finset.Iio","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_Iio","Finset.mem_filter","Finset.subset_iff","Finset.univ","Iff","LE.le","LT.lt","Lean.Grind.Order.le_of_not_lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Membership.mem","Nat","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","eq_false","eq_true","id","instLEFin","instLTFin","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_2","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":74,"type_refs":["DecidablePred","Fin","Fin.fintype","Fin.val","Finset.card","Finset.filter","Finset.univ","LE.le","LT.lt","Nat","Not","instLENat","instLTNat"],"value_dag_size":425,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.fintype","Fin.val","Finset.card","Finset.filter","Finset.univ","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_3","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":86,"type_refs":["DecidablePred","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.filter","Finset.instPartialOrder","Finset.univ","LE.le","LT.lt","Nat","Nat.decLt","Not","PartialOrder.toPreorder","Preorder.toLE","instLENat","instLTNat"],"value_dag_size":765,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.filter","Finset.filter_congr","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_filter","Finset.subset_iff","Finset.univ","HAdd.hAdd","Iff","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.ToInt.toInt","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_4","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":80,"type_refs":["DecidablePred","Fin","Fin.fintype","Fin.val","Finset.card","Finset.filter","Finset.univ","LE.le","LinearOrder.toPartialOrder","Min.min","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instLENat","instMinNat"],"value_dag_size":648,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.fintype","Fin.val","Finset.card","Finset.filter","Finset.univ","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.decLe","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","min_def","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_5","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":46,"type_refs":["DecidablePred","Fin","Fin.fintype","Finset","Finset.filter","Finset.instSetLike","Finset.univ","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":157,"value_refs":["And","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.fintype","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Finset.mem_univ","Finset.univ","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Membership.mem","Nat","Not","SetLike.instMembership","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp._proof_1_6","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Fin.lt_card_filter_univ_iff_apply_of_imp","reducibility":null,"statement_dag_size":116,"type_refs":["DecidablePred","Eq","False","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.filter","Finset.instSetLike","Finset.univ","LE.le","LT.lt","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.decLt","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","instLTNat"],"value_dag_size":619,"value_refs":["And","Bool","Bool.true","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.fintype","Fin.val","Finset","Finset.card","Finset.filter","Finset.filter_congr","Finset.instSetLike","Finset.mem_filter","Finset.univ","HAdd.hAdd","Iff","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.ToInt.toInt","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.cast","Nat.decLe","Nat.decLt","Nat.instLinearOrder","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eagerReduce","eq_true","funext","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Fin","name":"_private.Mathlib.Data.Fintype.Fin.0.Finset.image_fin_univ._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Fin.0.Finset.image_fin_univ","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Exists","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":42,"value_refs":["Exists","Fin","Fin.exists_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Inv","name":"_private.Mathlib.Data.Fintype.Inv.0.Fintype.choose_subtype_eq._simp_1","namespace":"_private.Mathlib.Data.Fintype.Inv.0.Fintype.choose_subtype_eq","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Order","name":"_private.Mathlib.Data.Fintype.Order.0.Fintype.toCompleteDistribLatticeMinimalAxioms._simp_1","namespace":"_private.Mathlib.Data.Fintype.Order.0.Fintype.toCompleteDistribLatticeMinimalAxioms","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.toFinset","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Finset","Finset.instSetLike","Fintype","Membership.mem","Set","Set.Elem","Set.instMembership","Set.mem_toFinset","Set.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.fintypePerm._simp_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.fintypePerm","reducibility":null,"statement_dag_size":73,"type_refs":["DFunLike.coe","DecidableEq","Eq","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","Finset","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership","permsOfFinset"],"value_dag_size":77,"value_refs":["DFunLike.coe","DecidableEq","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","Finset","Finset.instSetLike","Membership.mem","Ne","SetLike.instMembership","mem_perms_of_finset_iff","permsOfFinset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.length_permsOfList.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.length_permsOfList","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList","reducibility":"abbrev","statement_dag_size":205,"type_refs":["And","And.intro","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.intro","HMul.hMul","List","List.instMembership","Membership.mem","instHMul","permsOfList"],"value_dag_size":289,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.casesOn","Exists.intro","HMul.hMul","List","List.instMembership","Membership.mem","instHMul","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList.match_1_3","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList","reducibility":"abbrev","statement_dag_size":249,"type_refs":["And","And.intro","DecidableEq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.intro","HMul.hMul","List","List.instMembership","List.map","Membership.mem","instHMul","permsOfList"],"value_dag_size":354,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.casesOn","Exists.intro","HMul.hMul","List","List.instMembership","List.map","Membership.mem","instHMul","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList.match_1_5","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_of_mem_permsOfList","reducibility":"abbrev","statement_dag_size":115,"type_refs":["DecidableEq","Equiv.Perm","List","List.cons","List.instMembership","List.nil","Membership.mem","permsOfList"],"value_dag_size":164,"value_refs":["DecidableEq","Equiv.Perm","List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._proof_1_2","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":123,"type_refs":["DFunLike.coe","DecidableEq","Eq","Equiv","Equiv.Perm","Equiv.instEquivLike","Equiv.swap","EquivLike.toFunLike","List","List.cons","List.instMembership","Membership.mem","Ne","Not"],"value_dag_size":934,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","DFunLike.coe.hcongr_6","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.Perm","Equiv.instEquivLike","Equiv.swap","Equiv.swap_apply_def","EquivLike.toFunLike","False","False.elim","FunLike","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Ne","Not","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._simp_1_6","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._simp_1_7","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._simp_1_8","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem._simp_1_9","namespace":"_private.Mathlib.Data.Fintype.Perm.0.mem_permsOfList_of_mem","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList","reducibility":"abbrev","statement_dag_size":51,"type_refs":["List","List.Nodup","List.cons","List.nil"],"value_dag_size":77,"value_refs":["List","List.Nodup","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList.match_1_10","namespace":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList","reducibility":"abbrev","statement_dag_size":173,"type_refs":["And","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.intro","HMul.hMul","List","List.instMembership","Membership.mem","instHMul","permsOfList"],"value_dag_size":215,"value_refs":["And","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.casesOn","Exists.intro","HMul.hMul","List","List.instMembership","Membership.mem","instHMul","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList.match_1_6","namespace":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList","reducibility":"abbrev","statement_dag_size":248,"type_refs":["And","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.intro","GetElem.getElem","HMul.hMul","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instHMul","instLTNat","permsOfList"],"value_dag_size":306,"value_refs":["And","DecidableEq","Eq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","HMul.hMul","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instHMul","instLTNat","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList.match_1_8","namespace":"_private.Mathlib.Data.Fintype.Perm.0.nodup_permsOfList","reducibility":"abbrev","statement_dag_size":249,"type_refs":["And","And.intro","DecidableEq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.intro","HMul.hMul","List","List.instMembership","List.map","Membership.mem","instHMul","permsOfList"],"value_dag_size":354,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Equiv.Perm","Equiv.Perm.instMul","Equiv.swap","Exists","Exists.casesOn","Exists.intro","HMul.hMul","List","List.instMembership","List.map","Membership.mem","instHMul","permsOfList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.permsOfFinset._simp_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.permsOfFinset","reducibility":null,"statement_dag_size":66,"type_refs":["DFunLike.coe","DecidableEq","Eq","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","List","List.instMembership","Membership.mem","Ne","permsOfList"],"value_dag_size":70,"value_refs":["DFunLike.coe","DecidableEq","Equiv.Perm","Equiv.instEquivLike","EquivLike.toFunLike","List","List.instMembership","Membership.mem","Ne","mem_permsOfList_iff","permsOfList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1.eq_1","namespace":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","Unit","Unit.unit","permsOfList.match_1"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","Unit","permsOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1.eq_2","namespace":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","Unit","permsOfList.match_1"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","Unit","permsOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Perm","name":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1.splitter","namespace":"_private.Mathlib.Data.Fintype.Perm.0.permsOfList.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["permsOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Finset.piDiag_subset_piFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Finset.piDiag_subset_piFinset","reducibility":null,"statement_dag_size":91,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.decidableExistsAndFinsetCoe","Finset.filter","Finset.instSetLike","Finset.piDiag","Fintype","Fintype.piFinset","Function.const","Membership.mem","SetLike.instMembership"],"value_dag_size":99,"value_refs":["And","DecidableEq","Eq","Eq.symm","Exists","Finset","Finset.decidableExistsAndFinsetCoe","Finset.filter","Finset.instSetLike","Finset.piDiag","Finset.piFinset_filter_const","Fintype","Fintype.piFinset","Function.const","Membership.mem","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.filter_piFinset_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.filter_piFinset_of_notMem","reducibility":null,"statement_dag_size":86,"type_refs":["DecidableEq","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Fintype","Fintype.piFinset","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":491,"value_refs":["And","Classical.byContradiction","DecidableEq","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Finset.mem_filter","Finset.notMem_empty","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Membership.mem","Not","Or","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_4","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":15,"type_refs":["Eq"],"value_dag_size":19,"value_refs":["forall_prop_of_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_5","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_6","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset._simp_1_7","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.mem_piFinset","reducibility":null,"statement_dag_size":96,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.pi","Membership.mem","SetLike.instMembership"],"value_dag_size":102,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.mem_pi","Finset.pi","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset._simp_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Exists"],"value_dag_size":37,"value_refs":["Classical.skolem","Exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image._simp_1_3","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_image","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_inter._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_inter","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Fintype","Fintype.decidablePiFintype","Fintype.piFinset","Inter.inter"],"value_dag_size":1184,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Fintype","Fintype.decidablePiFintype","Fintype.mem_piFinset","Fintype.piFinset","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_singleton._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_singleton","reducibility":null,"statement_dag_size":67,"type_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instSingleton","Fintype","Fintype.piFinset","Iff","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":734,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.instSingleton","Finset.mem_singleton","Fintype","Fintype.mem_piFinset","Fintype.piFinset","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Not","Or","Or.casesOn","SetLike.instMembership","Singleton.singleton","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_eq_filter_piFinset_mem._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_eq_filter_piFinset_mem","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":30,"value_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_eq_filter_piFinset_mem._proof_1_4","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_eq_filter_piFinset_mem","reducibility":null,"statement_dag_size":103,"type_refs":["DecidableEq","Eq","Finset","Finset.decidableMem","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Fintype","Fintype.piFinset","Function.update","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":1676,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.decidableMem","Finset.ext","Finset.filter","Finset.instPartialOrder","Finset.instSetLike","Finset.instSetLike.hcongr_1","Finset.mem_filter","Finset.subset_iff","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Function.update","Function.update.eq_1","HEq","HEq.refl","HEq.symm","HEq.trans","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Membership.mem.hcongr_5","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","SetLike.instMembership.hcongr_3","True","True.intro","_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_eq_filter_piFinset_mem._proof_1_1","congrArg","congrFun'","dite","dite_cond_eq_true","dite_congr","eq_false","eq_of_heq","eq_self","eq_true","forall_congr","funext","heq_of_eq","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq","reducibility":null,"statement_dag_size":16,"type_refs":["Eq"],"value_dag_size":30,"value_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq._proof_1_4","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":68,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq._proof_1_7","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq","reducibility":null,"statement_dag_size":98,"type_refs":["DecidableEq","Eq","Finset","Finset.filter","Finset.instSetLike","Finset.instSingleton","Fintype","Fintype.piFinset","Function.update","Membership.mem","SetLike.instMembership","Singleton.singleton"],"value_dag_size":1789,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.ext","Finset.filter","Finset.instSetLike","Finset.instSetLike.hcongr_1","Finset.instSingleton","Finset.instSingleton.hcongr_1","Finset.mem_filter","Finset.mem_singleton","Fintype","Fintype.mem_piFinset","Fintype.piFinset","Function.update","Function.update.eq_1","HEq","HEq.refl","HEq.symm","HEq.trans","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eqRec_heq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Membership.mem","Membership.mem.hcongr_5","Not","Or","Or.casesOn","SetLike.instMembership","SetLike.instMembership.hcongr_3","Singleton.singleton","Singleton.singleton.hcongr_4","True","True.intro","_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq._proof_1_1","_private.Mathlib.Data.Fintype.Pi.0.Fintype.piFinset_update_singleton_eq_filter_piFinset_eq._proof_1_4","cast","cast_heq","congrArg","congrFun'","dite","dite_cond_eq_true","dite_congr","eq_false","eq_of_heq","eq_self","eq_true","forall_congr","funext","heq_of_eq","id","implies_congr","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_cons._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_cons","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Exists","Fin","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat"],"value_dag_size":72,"value_refs":["Exists","Fin","Fin.exists_iff_succ","Fin.instOfNat","Fin.succ","HAdd.hAdd","Nat","Nat.instNeZeroSucc","OfNat.ofNat","Or","instAddNat","instHAdd","instNeZeroNatHAdd_1","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_snoc._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_snoc","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Exists","Fin","Fin.castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":57,"value_refs":["Exists","Fin","Fin.castSucc","Fin.exists_iff_castSucc","Fin.last","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pi","name":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_snoc._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_snoc","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Pigeonhole","name":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Finite.exists_ne_map_eq_of_infinite._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Finite.exists_ne_map_eq_of_infinite","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Pigeonhole","name":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Fintype.exists_ne_map_eq_of_card_lt.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Fintype.exists_ne_map_eq_of_card_lt","reducibility":"abbrev","statement_dag_size":234,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Ne","SetLike.instMembership"],"value_dag_size":510,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","Ne","SetLike.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Pigeonhole","name":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Function.Embedding.isEmpty_of_card_lt.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Pigeonhole.0.Function.Embedding.isEmpty_of_card_lt","reducibility":"abbrev","statement_dag_size":181,"type_refs":["And","And.intro","DFunLike.coe","Eq","Exists","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Ne"],"value_dag_size":305,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","Eq","Exists","Exists.casesOn","Exists.intro","Function.Embedding","Function.instFunLikeEmbedding","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Prod","name":"_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership"],"value_dag_size":42,"value_refs":["Eq","Finset","Finset.eq_univ_iff_forall","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Prod","name":"_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Prod","name":"_private.Mathlib.Data.Fintype.Prod.0.Pi.infinite_of_exists_right.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Prod.0.Pi.infinite_of_exists_right","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":39,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Prod","name":"_private.Mathlib.Data.Fintype.Prod.0.Pi.infinite_of_left._simp_1","namespace":"_private.Mathlib.Data.Fintype.Prod.0.Pi.infinite_of_left","reducibility":null,"statement_dag_size":64,"type_refs":["And","DecidableEq","Eq","Function.update","Ne"],"value_dag_size":71,"value_refs":["And","DecidableEq","Eq","Function.update","Function.update_eq_iff","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_1.splitter","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_1","reducibility":"abbrev","statement_dag_size":33,"type_refs":["List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":1,"value_refs":["Quotient.listChoice.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3.eq_1","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3","reducibility":null,"statement_dag_size":106,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.listChoice.match_3","Setoid"],"value_dag_size":104,"value_refs":["Eq.refl","List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.listChoice.match_3","Setoid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3.eq_2","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3","reducibility":null,"statement_dag_size":125,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.listChoice.match_3","Setoid"],"value_dag_size":121,"value_refs":["Eq.refl","List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.listChoice.match_3","Setoid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3.splitter","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice.match_3","reducibility":"abbrev","statement_dag_size":101,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Setoid"],"value_dag_size":1,"value_refs":["Quotient.listChoice.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice_mk.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice_mk","reducibility":"abbrev","statement_dag_size":33,"type_refs":["List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":182,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice_mk.match_1_3","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.listChoice_mk","reducibility":"abbrev","statement_dag_size":84,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":130,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.list_ind.match_1_1","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.list_ind","reducibility":"abbrev","statement_dag_size":33,"type_refs":["List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":182,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","Membership.mem","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Fintype.Quotient","name":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.list_ind.match_1_3","namespace":"_private.Mathlib.Data.Fintype.Quotient.0.Quotient.list_ind","reducibility":"abbrev","statement_dag_size":236,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.mk","Setoid"],"value_dag_size":338,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Quotient","Quotient.mk","Setoid"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.disjoint_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.disjoint_toFinset","reducibility":null,"statement_dag_size":67,"type_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe"],"value_dag_size":76,"value_refs":["BiheytingAlgebra.toCoheytingAlgebra","BiheytingAlgebra.toHeytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Disjoint","Eq.symm","Finset","Finset.disjoint_coe","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","GeneralizedCoheytingAlgebra.toLattice","HeytingAlgebra.toOrderBot","Lattice.toSemilatticeInf","SemilatticeInf.toPartialOrder","Set","Set.instBooleanAlgebra","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_ssubset_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_ssubset_toFinset","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Finset","Finset.instPartialOrder","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":47,"value_refs":["And","Finset","Finset.instPartialOrder","Finset.ssubset_def","LE.le","LT.lt","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_ssubset_toFinset._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_ssubset_toFinset","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Finset","Finset.instPartialOrder","Fintype","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.Elem","Set.instLE","Set.toFinset"],"value_dag_size":60,"value_refs":["Finset","Finset.instPartialOrder","Fintype","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.Elem","Set.instLE","Set.toFinset","Set.toFinset_subset_toFinset","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_subset_toFinset._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_subset_toFinset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_symmDiff._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_symmDiff","reducibility":null,"statement_dag_size":69,"type_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","Eq","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","Set","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","symmDiff"],"value_dag_size":73,"value_refs":["And","BiheytingAlgebra.toCoheytingAlgebra","BooleanAlgebra.toBiheytingAlgebra","CoheytingAlgebra.toGeneralizedCoheytingAlgebra","GeneralizedCoheytingAlgebra.toLattice","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","Set","Set.instBooleanAlgebra","Set.instMembership","Set.instSDiff","Set.mem_symmDiff","propext","symmDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sets","name":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_symmDiff._simp_1_2","namespace":"_private.Mathlib.Data.Fintype.Sets.0.Set.toFinset_symmDiff","reducibility":null,"statement_dag_size":67,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instLattice","Finset.instSDiff","Finset.instSetLike","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","SetLike.instMembership","symmDiff"],"value_dag_size":72,"value_refs":["And","DecidableEq","Finset","Finset.instLattice","Finset.instSDiff","Finset.instSetLike","Finset.mem_symmDiff","Lattice.toSemilatticeSup","Membership.mem","Not","Or","SemilatticeSup.toMax","SetLike.instMembership","propext","symmDiff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sigma","name":"_private.Mathlib.Data.Fintype.Sigma.0.Sigma.forall._simp_1","namespace":"_private.Mathlib.Data.Fintype.Sigma.0.Sigma.forall","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Sigma","Sigma.mk"],"value_dag_size":40,"value_refs":["Sigma","Sigma.forall","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Finset.exists_equiv_extend_of_card_eq._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Finset.exists_equiv_extend_of_card_eq","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toLeft_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toLeft_eq_empty","reducibility":null,"statement_dag_size":82,"type_refs":["And","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.map","Finset.toLeft","Finset.toRight","Function.Embedding.inr","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":86,"value_refs":["And","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.map","Finset.subset_map_inr","Finset.toLeft","Finset.toRight","Function.Embedding.inr","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toLeft_eq_univ._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toLeft_eq_univ","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.map","Finset.toLeft","Function.Embedding.inl","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":68,"value_refs":["Finset","Finset.instPartialOrder","Finset.map","Finset.map_inl_subset_iff_subset_toLeft","Finset.toLeft","Function.Embedding.inl","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toRight_eq_empty._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toRight_eq_empty","reducibility":null,"statement_dag_size":82,"type_refs":["And","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.map","Finset.toLeft","Finset.toRight","Function.Embedding.inl","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":86,"value_refs":["And","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instPartialOrder","Finset.map","Finset.subset_map_inl","Finset.toLeft","Finset.toRight","Function.Embedding.inl","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toRight_eq_univ._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Finset.toRight_eq_univ","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.map","Finset.toRight","Function.Embedding.inr","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum"],"value_dag_size":68,"value_refs":["Finset","Finset.instPartialOrder","Finset.map","Finset.map_inr_subset_iff_subset_toRight","Finset.toRight","Function.Embedding.inr","LE.le","PartialOrder.toPreorder","Preorder.toLE","Sum","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.Set.MapsTo.exists_equiv_extend_of_card_eq._simp_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.Set.MapsTo.exists_equiv_extend_of_card_eq","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe"],"value_dag_size":54,"value_refs":["Eq.symm","Finset","Finset.coe_subset","Finset.instPartialOrder","Finset.instSetLike","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instLE","SetLike.coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Sum","name":"_private.Mathlib.Data.Fintype.Sum.0.image_subtype_univ_ssubset_image_univ._proof_1_1","namespace":"_private.Mathlib.Data.Fintype.Sum.0.image_subtype_univ_ssubset_image_univ","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableEq","DecidablePred","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.univ","Fintype","LT.lt","Membership.mem","Not","PartialOrder.toPreorder","Preorder.toLT","SetLike.instMembership","Subtype","Subtype.fintype","Subtype.val"],"value_dag_size":1198,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_image","Finset.mem_univ","Finset.ssubset_iff_subset_ne","Finset.subset_iff","Finset.univ","Fintype","HEq","HEq.refl","Iff","LE.le","LT.lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.of_forall_eq_false","Lean.Grind.or_of_and_eq_false","Membership.mem","Ne","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.fintype","Subtype.mk","Subtype.val","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Fintype.Vector","name":"_private.Mathlib.Data.Fintype.Vector.0.Sym.Sym'.instFinite._proof_1","namespace":"_private.Mathlib.Data.Fintype.Vector.0.Sym.Sym'.instFinite","reducibility":null,"statement_dag_size":13,"type_refs":["Finite","Nat","Sym.Sym'"],"value_dag_size":24,"value_refs":["Finite","List.Vector","List.Vector.Perm.isSetoid","List.Vector.instFinite","Nat","Quotient.finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FunLike.IsApply","name":"_private.Mathlib.Data.FunLike.IsApply.0.FunLike.coe_one_eq_id_iff._simp_1_1","namespace":"_private.Mathlib.Data.FunLike.IsApply.0.FunLike.coe_one_eq_id_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FunLike.IsApply","name":"_private.Mathlib.Data.FunLike.IsApply.0.FunLike.coe_one_iff._simp_1_1","namespace":"_private.Mathlib.Data.FunLike.IsApply.0.FunLike.coe_one_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DFunLike","DFunLike.coe","Eq"],"value_dag_size":51,"value_refs":["DFunLike","DFunLike.coe","DFunLike.ext_iff","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.FunLike.IsApply","name":"_private.Mathlib.Data.FunLike.IsApply.0.pow_apply_eq_iterate._simp_1_1","namespace":"_private.Mathlib.Data.FunLike.IsApply.0.pow_apply_eq_iterate","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Nat","Nat.iterate","Nat.succ"],"value_dag_size":31,"value_refs":["Eq.symm","Function.iterate_succ_apply'","Nat","Nat.iterate","Nat.succ"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor._aux_Mathlib_Data_Holor___unexpand_Holor_mul_1","namespace":"_private.Mathlib.Data.Holor.0.Holor","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":247,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add","reducibility":"abbrev","statement_dag_size":188,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","HAdd.hAdd","Holor","Holor.CPRankMax","Holor.CPRankMax.succ","Holor.CPRankMax1","Holor.instAdd","List","Mul","Nat","Nat.succ","OfNat.ofNat","instHAdd","instOfNatNat"],"value_dag_size":912,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HAdd.hAdd","HEq","HEq.refl","Holor","Holor.CPRankMax","Holor.CPRankMax.casesOn","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","List","Mul","Nat","Nat.Internal.elimOffset","Nat.casesOn","Nat.ctorIdx","Nat.succ","Nat.zero","OfNat.ofNat","Zero.toOfNat0","eq_of_heq","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add.match_1_3","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add","reducibility":"abbrev","statement_dag_size":86,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Holor","Holor.CPRankMax","Holor.CPRankMax.zero","Holor.instZero","List","Mul","Nat","OfNat.ofNat","Unit","Zero.toOfNat0","instOfNatNat"],"value_dag_size":504,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HAdd.hAdd","HEq","HEq.refl","Holor","Holor.CPRankMax","Holor.CPRankMax.casesOn","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","List","Mul","Nat","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","Unit","Unit.unit","Zero.toOfNat0","eq_of_heq","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add.match_1_9","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_add","reducibility":"abbrev","statement_dag_size":460,"type_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","HAdd.hAdd","Holor","Holor.CPRankMax","Holor.CPRankMax.below","Holor.CPRankMax.below.succ","Holor.CPRankMax.succ","Holor.CPRankMax1","Holor.instAdd","List","Mul","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":2126,"value_refs":["AddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HAdd.hAdd","HEq","HEq.refl","Holor","Holor.CPRankMax","Holor.CPRankMax.below","Holor.CPRankMax.below.casesOn","Holor.CPRankMax.below.succ","Holor.CPRankMax.below.zero","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","List","Mul","Nat","Nat.Internal.elimOffset","Nat.casesOn","Nat.ctorIdx","Nat.succ","Nat.zero","OfNat.ofNat","Zero.toOfNat0","eq_of_heq","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul._simp_1_3","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul","reducibility":null,"statement_dag_size":58,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Holor","Holor.CPRankMax","Holor.instZero","List","Mul","Nat","OfNat.ofNat","True","Zero.toOfNat0","instOfNatNat"],"value_dag_size":60,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Holor","Holor.CPRankMax","Holor.CPRankMax.zero","Holor.instZero","List","Mul","Nat","OfNat.ofNat","Zero.toOfNat0","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul","reducibility":"abbrev","statement_dag_size":229,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","HAdd.hAdd","Holor","Holor.CPRankMax","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","List","List.cons","List.nil","Nat","Nat.succ","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Zero.toOfNat0","instHAdd","instOfNatNat"],"value_dag_size":1394,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HAdd.hAdd","HEq","HEq.refl","Holor","Holor.CPRankMax","Holor.CPRankMax.casesOn","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","List","List.cons","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.casesOn","Nat.ctorIdx","Nat.succ","Nat.zero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Zero.toOfNat0","eq_of_heq","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul.match_1_8","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_mul","reducibility":"abbrev","statement_dag_size":486,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","HAdd.hAdd","HAppend.hAppend","Holor","Holor.CPRankMax","Holor.CPRankMax.below","Holor.CPRankMax.below.succ","Holor.CPRankMax.below.zero","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","Holor.mul","List","List.cons","List.instAppend","List.nil","Nat","Nat.succ","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Zero.toOfNat0","instHAdd","instHAppendOfAppend","instOfNatNat"],"value_dag_size":2887,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Distrib.toMul","Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HAdd.hAdd","HAppend.hAppend","HEq","HEq.refl","Holor","Holor.CPRankMax","Holor.CPRankMax.below","Holor.CPRankMax.below.casesOn","Holor.CPRankMax.below.succ","Holor.CPRankMax.below.zero","Holor.CPRankMax.succ","Holor.CPRankMax.zero","Holor.CPRankMax1","Holor.instAdd","Holor.instZero","Holor.mul","List","List.cons","List.instAppend","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.casesOn","Nat.ctorIdx","Nat.succ","Nat.zero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","Zero.toOfNat0","eq_of_heq","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_sum._proof_1_2","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_sum","reducibility":null,"statement_dag_size":169,"type_refs":["AddCommMonoid.toAddMonoid","Classical.decEq","Distrib.toMul","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Finset.sum","HMul.hMul","Holor","Holor.CPRankMax","Holor.instAddCommMonoid","Insert.insert","List","Membership.mem","Nat","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","SetLike.instMembership","instHMul","instMulNat"],"value_dag_size":429,"value_refs":["AddCommMonoid.toAddMonoid","Classical.byContradiction","Classical.decEq","Distrib.toMul","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.card","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Finset.sum","HMul.hMul","Holor","Holor.CPRankMax","Holor.instAddCommMonoid","Iff","Insert.insert","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","List","Membership.mem","Nat","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","Not","Or","SetLike.instMembership","True","True.intro","eq_false","eq_true","id","instHMul","instMulNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_sum._simp_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_sum","reducibility":null,"statement_dag_size":58,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","Holor","Holor.CPRankMax","Holor.instZero","List","Mul","Nat","OfNat.ofNat","True","Zero.toOfNat0","instOfNatNat"],"value_dag_size":60,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Holor","Holor.CPRankMax","Holor.CPRankMax.zero","Holor.instZero","List","Mul","Nat","OfNat.ofNat","Zero.toOfNat0","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_upper_bound.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.cprankMax_upper_bound","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Holor","List","List.cons","List.nil","Nat"],"value_dag_size":69,"value_refs":["Holor","List","List.casesOn","List.cons","List.nil","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.holor_index_cons_decomp.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.holor_index_cons_decomp","reducibility":"abbrev","statement_dag_size":198,"type_refs":["Eq","Holor.holor_index_cons_decomp._proof_1","HolorIndex","LT.lt","List","List.Forall₂","List.cons","List.nil","Nat","Subtype.mk","Subtype.val","instLTNat"],"value_dag_size":354,"value_refs":["Eq","Holor.holor_index_cons_decomp._proof_1","HolorIndex","LT.lt","List","List.Forall₂","List.casesOn","List.cons","List.nil","Nat","Subtype.casesOn","Subtype.mk","Subtype.val","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.mul_assoc._simp_1_1","namespace":"_private.Mathlib.Data.Holor.0.Holor.mul_assoc","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","HEq","True","cast"],"value_dag_size":31,"value_refs":["Eq","HEq","cast","cast_heq","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.sum_unitVec_mul_slice._simp_1_2","namespace":"_private.Mathlib.Data.Holor.0.Holor.sum_unitVec_mul_slice","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.«_aux_Mathlib_Data_Holor___macroRules__private_Mathlib_Data_Holor_0_Holor_term_⊗__1»","namespace":"_private.Mathlib.Data.Holor.0.Holor","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":231,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.Holor.«term_⊗_»","namespace":"_private.Mathlib.Data.Holor.0.Holor","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":58,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.drop_drop.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.drop_drop","reducibility":"abbrev","statement_dag_size":73,"type_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.mk","instHAppendOfAppend","instLTNat"],"value_dag_size":91,"value_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.casesOn","Subtype.mk","instHAppendOfAppend","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.drop_take.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.drop_take","reducibility":"abbrev","statement_dag_size":73,"type_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.mk","instHAppendOfAppend","instLTNat"],"value_dag_size":91,"value_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.casesOn","Subtype.mk","instHAppendOfAppend","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.take.match_1.eq_1","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.take.match_1","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HAppend.hAppend","HolorIndex","HolorIndex.take.match_1","List","List.instAppend","Nat","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["Eq.refl","HAppend.hAppend","HolorIndex","HolorIndex.take.match_1","List","List.instAppend","Nat","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.take.match_1.splitter","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.take.match_1","reducibility":"abbrev","statement_dag_size":40,"type_refs":["HAppend.hAppend","HolorIndex","List","List.instAppend","Nat","instHAppendOfAppend"],"value_dag_size":1,"value_refs":["HolorIndex.take.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.take_take._simp_1_6","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.take_take","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","True","instAddNat","instHAdd","instLENat"],"value_dag_size":28,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.le_add_right","eq_true","instAddNat","instHAdd","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Holor","name":"_private.Mathlib.Data.Holor.0.HolorIndex.take_take.match_1_1","namespace":"_private.Mathlib.Data.Holor.0.HolorIndex.take_take","reducibility":"abbrev","statement_dag_size":73,"type_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.mk","instHAppendOfAppend","instLTNat"],"value_dag_size":91,"value_refs":["HAppend.hAppend","HolorIndex","LT.lt","List","List.Forall₂","List.instAppend","Nat","Subtype.casesOn","Subtype.mk","instHAppendOfAppend","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Ineq","name":"_private.Mathlib.Data.Ineq.0.Mathlib.instReprIneq.repr.match_1","namespace":"_private.Mathlib.Data.Ineq.0.Mathlib.instReprIneq.repr","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Mathlib.Ineq","Mathlib.Ineq.eq","Mathlib.Ineq.le","Mathlib.Ineq.lt","Unit"],"value_dag_size":36,"value_refs":["Mathlib.Ineq","Mathlib.Ineq.casesOn","Mathlib.Ineq.eq","Mathlib.Ineq.le","Mathlib.Ineq.lt","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Basic","name":"_private.Mathlib.Data.Int.Basic.0.Int.dvd_natCast._simp_1_1","namespace":"_private.Mathlib.Data.Int.Basic.0.Int.dvd_natCast","reducibility":null,"statement_dag_size":28,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Nat","Nat.cast","Nat.instDvd","instNatCastInt"],"value_dag_size":36,"value_refs":["Dvd.dvd","Eq.symm","Int","Int.instDvd","Int.natCast_dvd_natCast","Nat","Nat.cast","Nat.instDvd","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Basic","name":"_private.Mathlib.Data.Int.Basic.0.Int.dvd_natCast._simp_1_2","namespace":"_private.Mathlib.Data.Int.Basic.0.Int.dvd_natCast","reducibility":null,"statement_dag_size":23,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Int.instNegInt","Neg.neg"],"value_dag_size":25,"value_refs":["Dvd.dvd","Int","Int.instDvd","Int.instNegInt","Int.neg_dvd","Neg.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Basic","name":"_private.Mathlib.Data.Int.Basic.0.Int.natCast_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Int.Basic.0.Int.natCast_dvd","reducibility":null,"statement_dag_size":28,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Nat","Nat.cast","Nat.instDvd","instNatCastInt"],"value_dag_size":36,"value_refs":["Dvd.dvd","Eq.symm","Int","Int.instDvd","Int.natCast_dvd_natCast","Nat","Nat.cast","Nat.instDvd","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Basic","name":"_private.Mathlib.Data.Int.Basic.0.Int.natCast_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Int.Basic.0.Int.natCast_dvd","reducibility":null,"statement_dag_size":22,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Int.instNegInt","Neg.neg"],"value_dag_size":24,"value_refs":["Dvd.dvd","Int","Int.dvd_neg","Int.instDvd","Int.instNegInt","Neg.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":57,"value_refs":["Eq.refl","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1.eq_2","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":57,"value_refs":["Eq.refl","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1.eq_3","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":57,"value_refs":["Eq.refl","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1.eq_4","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":57,"value_refs":["Eq.refl","Int","Int.bitwise.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1.splitter","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bitwise.match_1","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":1,"value_refs":["Int.bitwise.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_add._simp_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_add","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_add_div2.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_add_div2","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_mul._simp_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_mul","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Nat","Nat.cast","Nat.succ","OfNat.ofNat","instHAdd","instNatCastInt","instOfNat"],"value_dag_size":37,"value_refs":["Eq.symm","HAdd.hAdd","Int","Int.instAdd","Int.natCast_succ","Nat","Nat.cast","Nat.succ","OfNat.ofNat","instHAdd","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_neg._simp_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.bodd_neg","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","Int","Int.instNegInt","Int.negOfNat","Int.ofNat","Nat","Neg.neg"],"value_dag_size":20,"value_refs":["Eq.symm","Int","Int.instNegInt","Int.negOfNat","Int.negOfNat_eq","Int.ofNat","Nat","Neg.neg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Int","Int.div2.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":30,"value_refs":["Eq.refl","Int","Int.div2.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1.eq_2","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Int","Int.div2.match_1","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":30,"value_refs":["Eq.refl","Int","Int.div2.match_1","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1.splitter","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2.match_1","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":1,"value_refs":["Int.div2.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2_val.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.div2_val","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.lnot_bit.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.lnot_bit","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'._simp_1_3","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HShiftRight.hShiftRight","Int","Int.instShiftRight_mathlib","Nat","Nat.cast","Nat.instShiftRight","instHShiftRightOfShiftRight","instNatCastInt"],"value_dag_size":41,"value_refs":["Eq.symm","HShiftRight.hShiftRight","Int","Int.instShiftRight_mathlib","Int.shiftRight_natCast","Nat","Nat.cast","Nat.instShiftRight","instHShiftRightOfShiftRight","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'._simp_1_4","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HAdd.hAdd","HShiftRight.hShiftRight","Int","Int.instAdd","Int.instShiftRight_mathlib","Nat","Nat.cast","instHAdd","instHShiftRightOfShiftRight","instNatCastInt"],"value_dag_size":48,"value_refs":["Eq.symm","HAdd.hAdd","HShiftRight.hShiftRight","Int","Int.instAdd","Int.instShiftRight_mathlib","Int.shiftRight_add'","Nat","Nat.cast","instHAdd","instHShiftRightOfShiftRight","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_add'","reducibility":"abbrev","statement_dag_size":56,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":99,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_eq_mul_pow.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_eq_mul_pow","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":42,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right._proof_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HMul.hMul","HPow.hPow","HShiftLeft.hShiftLeft","Int","Int.instHShiftLeftNat","Int.instMul","Int.instNatPow","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","OfNat.ofNat","instHMul","instHPow","instNatCastInt","instOfNatAtLeastTwo","instOfNatNat","instPowNat"],"value_dag_size":215,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HMul.hMul","HPow.hPow","HShiftLeft.hShiftLeft","Int","Int.instHShiftLeftNat","Int.instMul","Int.instNatPow","Int.shiftLeft_eq'","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_pow","Lean.Grind.Semiring.npow","Lean.Grind.instCommRingInt","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Not","OfNat.ofNat","True","True.intro","congrArg","congrFun'","eq_false","eq_true","id","instHMul","instHPow","instNatCastInt","instNatPowNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right._proof_1_3","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.instMul","Int.instNatPow","Int.instNegInt","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatCastInt","instNatPowNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.natCast_pow","Lean.Grind.Semiring.npow","Lean.Grind.Semiring.toAdd","Lean.Grind.Semiring.toMul","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right._simp_1_2","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_natCast_right","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Nat","Nat.cast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq.symm","HAdd.hAdd","Int","Int.instAdd","Int.natCast_add_one","Nat","Nat.cast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftRight_add'.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.shiftRight_add'","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":52,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Int","Int.negSucc","Int.ofNat","Int.testBit.match_1","Nat"],"value_dag_size":40,"value_refs":["Eq.refl","Int","Int.negSucc","Int.ofNat","Int.testBit.match_1","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1.eq_2","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Int","Int.negSucc","Int.ofNat","Int.testBit.match_1","Nat"],"value_dag_size":40,"value_refs":["Eq.refl","Int","Int.negSucc","Int.ofNat","Int.testBit.match_1","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1.splitter","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit.match_1","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":1,"value_refs":["Int.testBit.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_bit_succ.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_bit_succ","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_bit_zero.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_bit_zero","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_lnot.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.testBit_lnot","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":42,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Int.zero_shiftLeft'.match_1_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Int.zero_shiftLeft'","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Bitwise","name":"_private.Mathlib.Data.Int.Bitwise.0.Nat.xor.eq_1","namespace":"_private.Mathlib.Data.Int.Bitwise.0.Nat.xor","reducibility":null,"statement_dag_size":19,"type_refs":["Bool","Eq","Nat","Nat.bitwise","Nat.xor","bne","instBEqOfDecidableEq","instDecidableEqBool"],"value_dag_size":8,"value_refs":["Eq.refl","Nat","Nat.xor"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_10","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":144,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Eq","Int","Int.cast","Int.instLTInt","LT.lt","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass"],"value_dag_size":152,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Int","Int.cast","Int.cast_lt","Int.instLTInt","LT.lt","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_11","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":143,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Eq","Int","Int.cast","Int.instLEInt","LE.le","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass"],"value_dag_size":151,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Int","Int.cast","Int.cast_le","Int.instLEInt","LE.le","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":72,"type_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","Eq","FloorRing","Int","Int.cast","Int.ceil","Int.instLEInt","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":78,"value_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","FloorRing","Int","Int.cast","Int.ceil","Int.ceil_le","Int.instLEInt","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":72,"type_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","Eq","FloorRing","Int","Int.cast","Int.ceil","Int.instLTInt","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":78,"value_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","FloorRing","Int","Int.cast","Int.ceil","Int.instLTInt","Int.lt_ceil","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":121,"type_refs":["DivInvMonoid.toDiv","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul"],"value_dag_size":129,"value_refs":["DivInvMonoid.toDiv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","div_le_iff₀","instHDiv","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_7","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":119,"type_refs":["DivInvMonoid.toDiv","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul"],"value_dag_size":127,"value_refs":["DivInvMonoid.toDiv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul","lt_div_iff₀","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":52,"type_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","instHMul","semigroupDvd"],"value_dag_size":56,"value_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","dvd_iff_exists_eq_mul_left","instHMul","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_dvd_eq","reducibility":null,"statement_dag_size":64,"type_refs":["AddCommGroupWithOne.toAddGroupWithOne","AddGroupWithOne.toIntCast","Distrib.toMul","Eq","HMul.hMul","Int","Int.cast","Int.instMul","NonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul"],"value_dag_size":70,"value_refs":["AddCommGroupWithOne.toAddGroupWithOne","AddGroupWithOne.toIntCast","Distrib.toMul","Eq.symm","HMul.hMul","Int","Int.cast","Int.cast_mul","Int.instMul","NonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":62,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":73,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Eq.symm","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","eq_sub_iff_add_eq","instHAdd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Int","Int.ModEq"],"value_dag_size":21,"value_refs":["Int","Int.ModEq","Int.modEq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_7","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":67,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub"],"value_dag_size":74,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub","propext","sub_lt_sub_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq","reducibility":null,"statement_dag_size":67,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LE","LE.le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub"],"value_dag_size":74,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LE","LE.le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub","propext","sub_le_sub_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_10","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":144,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Eq","Int","Int.cast","Int.instLTInt","LT.lt","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass"],"value_dag_size":152,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Int","Int.cast","Int.cast_lt","Int.instLTInt","LT.lt","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_11","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":143,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Eq","Int","Int.cast","Int.instLEInt","LE.le","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass"],"value_dag_size":151,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommGroupWithOne","AddCommGroupWithOne.toAddCommGroup","AddCommGroupWithOne.toAddCommMonoidWithOne","AddCommGroupWithOne.toAddGroupWithOne","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoidWithOne.toAddCommMonoid","AddCommSemigroup.toAddCommMagma","AddGroupWithOne.toAddMonoidWithOne","AddGroupWithOne.toIntCast","AddLeftMono","AddMonoidWithOne.toOne","Int","Int.cast","Int.cast_le","Int.instLEInt","LE.le","NeZero","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","ZeroLEOneClass","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":72,"type_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","Eq","FloorRing","Int","Int.cast","Int.floor","Int.instLTInt","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":78,"value_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","FloorRing","Int","Int.cast","Int.floor","Int.floor_lt","Int.instLTInt","LT.lt","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLT","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":72,"type_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","Eq","FloorRing","Int","Int.cast","Int.floor","Int.instLEInt","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":78,"value_refs":["AddGroupWithOne.toIntCast","DistribLattice.toLattice","FloorRing","Int","Int.cast","Int.floor","Int.instLEInt","Int.le_floor","LE.le","Lattice.toSemilatticeInf","LinearOrder","PartialOrder.toPreorder","Preorder.toLE","Ring","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":119,"type_refs":["DivInvMonoid.toDiv","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul"],"value_dag_size":127,"value_refs":["DivInvMonoid.toDiv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","div_lt_iff₀","instHDiv","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_7","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":121,"type_refs":["DivInvMonoid.toDiv","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul"],"value_dag_size":129,"value_refs":["DivInvMonoid.toDiv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","HMul.hMul","LE.le","LT.lt","MonoidWithZero.toMulZeroOneClass","MulPosReflectLT","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instHDiv","instHMul","le_div_iff₀","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":52,"type_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","instHMul","semigroupDvd"],"value_dag_size":56,"value_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","dvd_iff_exists_eq_mul_left","instHMul","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq","reducibility":null,"statement_dag_size":64,"type_refs":["AddCommGroupWithOne.toAddGroupWithOne","AddGroupWithOne.toIntCast","Distrib.toMul","Eq","HMul.hMul","Int","Int.cast","Int.instMul","NonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul"],"value_dag_size":70,"value_refs":["AddCommGroupWithOne.toAddGroupWithOne","AddGroupWithOne.toIntCast","Distrib.toMul","Eq.symm","HMul.hMul","Int","Int.cast","Int.cast_mul","Int.instMul","NonAssocRing","NonAssocRing.toAddCommGroupWithOne","NonAssocRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":62,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":73,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Eq.symm","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","eq_sub_iff_add_eq","instHAdd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Int","Int.ModEq"],"value_dag_size":21,"value_refs":["Int","Int.ModEq","Int.modEq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_7","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":67,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub"],"value_dag_size":74,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub","propext","sub_lt_sub_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_modEq_eq","reducibility":null,"statement_dag_size":67,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LE","LE.le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub"],"value_dag_size":74,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LE","LE.le","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHSub","propext","sub_le_sub_iff_right"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._proof_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":71,"type_refs":["And","False","Int","Int.ModEq","Int.instLEInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.cast","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":418,"value_refs":["And","And.left","Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.ModEq","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","id","instDecidableEqBool","instHAdd","instHSub","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.ModEq","Nat","Nat.ModEq","Nat.cast","instNatCastInt"],"value_dag_size":37,"value_refs":["Eq.symm","Int","Int.ModEq","Int.natCast_modEq_iff","Nat","Nat.ModEq","Nat.cast","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.ModEq","Nat","Nat.ModEq","Nat.cast","instNatCastInt"],"value_dag_size":31,"value_refs":["Int","Int.ModEq","Int.natCast_modEq_iff","Nat","Nat.ModEq","Nat.cast","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast.match_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast","reducibility":"abbrev","statement_dag_size":132,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","Eq","Int","Int.ModEq","Int.instRing","LE.le","LT.lt","Nat","Nat.cast","Nat.instPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","instNatCastInt"],"value_dag_size":156,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","Eq","Int","Int.ModEq","Int.instRing","LE.le","LT.lt","Nat","Nat.cast","Nat.instPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._proof_1_8","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":67,"type_refs":["And","Int","Int.ModEq","Int.instLEInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.cast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":375,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.ModEq","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_2","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_3","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_4","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_5","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.ModEq","Nat","Nat.ModEq","Nat.cast","instNatCastInt"],"value_dag_size":37,"value_refs":["Eq.symm","Int","Int.ModEq","Int.natCast_modEq_iff","Nat","Nat.ModEq","Nat.cast","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast._simp_1_9","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Int","Int.ModEq","Nat","Nat.ModEq","Nat.cast","instNatCastInt"],"value_dag_size":31,"value_refs":["Int","Int.ModEq","Int.natCast_modEq_iff","Nat","Nat.ModEq","Nat.cast","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast.match_1_6","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ioc_filter_modEq_cast","reducibility":"abbrev","statement_dag_size":132,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.intro","Eq","Int","Int.ModEq","Int.instRing","LE.le","LT.lt","Nat","Nat.cast","Nat.instPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","instNatCastInt"],"value_dag_size":156,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","And.intro","Eq","Int","Int.ModEq","Int.instRing","LE.le","LT.lt","Nat","Nat.cast","Nat.instPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.CardIntervalMod","name":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.count_modEq_card_eq_ceil._simp_1_1","namespace":"_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.count_modEq_card_eq_ceil","reducibility":null,"statement_dag_size":61,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHAdd","instHSub"],"value_dag_size":68,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","HAdd.hAdd","HSub.hSub","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instHAdd","instHSub","sub_sub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Cast.Basic","name":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_add._simp_1_3","namespace":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_add","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Nat","Nat.cast","instAddNat","instHAdd","instNatCastInt"],"value_dag_size":41,"value_refs":["Eq.symm","HAdd.hAdd","Int","Int.instAdd","Int.natCast_add","Nat","Nat.cast","instAddNat","instHAdd","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Basic","name":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_add.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_add","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":79,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Basic","name":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_neg.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Basic.0.Int.cast_neg","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":59,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Basic","name":"_private.Mathlib.Data.Int.Cast.Basic.0.Nat.cast_pred.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Basic.0.Nat.cast_pred","reducibility":"abbrev","statement_dag_size":56,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Lemmas","name":"_private.Mathlib.Data.Int.Cast.Lemmas.0.AddMonoidHom.ext_int.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Lemmas.0.AddMonoidHom.ext_int","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Cast.Lemmas","name":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute._simp_1_3","namespace":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute","reducibility":null,"statement_dag_size":39,"type_refs":["Commute","Eq","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg"],"value_dag_size":44,"value_refs":["Commute","Commute.neg_left_iff","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Cast.Lemmas","name":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute._simp_1_4","namespace":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute","reducibility":null,"statement_dag_size":38,"type_refs":["Commute","Eq","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg"],"value_dag_size":43,"value_refs":["Commute","Commute.neg_right_iff","HasDistribNeg","HasDistribNeg.toInvolutiveNeg","InvolutiveNeg.toNeg","Mul","Neg.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Lemmas","name":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Lemmas.0.Int.cast_commute","reducibility":"abbrev","statement_dag_size":32,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":44,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Cast.Lemmas","name":"_private.Mathlib.Data.Int.Cast.Lemmas.0.zsmul_eq_mul.match_1_1","namespace":"_private.Mathlib.Data.Int.Cast.Lemmas.0.zsmul_eq_mul","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":32,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.DivMod","name":"_private.Mathlib.Data.Int.DivMod.0.Int.mul_ediv_le_mul_ediv_assoc._proof_1_1","namespace":"_private.Mathlib.Data.Int.DivMod.0.Int.mul_ediv_le_mul_ediv_assoc","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","OfNat.ofNat","Or","instOfNat"],"value_dag_size":276,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instHAdd","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","Nat.cast","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"],"value_dag_size":478,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.mpr","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instAddMonoid","Int.instMul","Int.instRing","Int.instSemiring","Int.instSub","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","Nat.cast","Nat.cast_zero","OfNat.ofNat","Ring.toAddGroupWithOne","Trans.trans","True","Zero.toOfNat0","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_3","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_4","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_5","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_6","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_7","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast.match_1_1","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","add_zero","congr","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","instTransEq","mul_one","of_eq_true","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_3","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":979,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_one_mul","Int.Internal.Linear.mul_eq_kxk","Int.Internal.Linear.norm_eq","Int.Internal.Linear.of_var_eq_mul","Int.Internal.Linear.var_eq","Int.fib","Int.fib_add_two","Int.fib_one","Int.fib_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_4","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAdd.hAdd","Int","Int.fib","Int.instAdd","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":468,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_5","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":418,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_6","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":501,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_true","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast._proof_1_7","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":null,"statement_dag_size":103,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":2005,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.d_stepk","Lean.Grind.CommRing.Stepwise.imp_keq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.instNoNatZeroDivisorsInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast.match_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_natCast","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Int","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":64,"value_refs":["Int","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two","reducibility":null,"statement_dag_size":113,"type_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.instAddCommSemigroup","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","Nat.fib","Nat.instAddCommSemigroup","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":571,"value_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulR","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.instAdd","Int.instAddCommSemigroup","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Int.pow_one","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.fib","Nat.instAddCommSemigroup","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two._proof_1_2","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instNegInt","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":841,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two._proof_1_3","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_add_two","reducibility":null,"statement_dag_size":81,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","HAdd.hAdd","HMul.hMul","LE.le","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instNonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":374,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Bool","Bool.true","Classical.byContradiction","Distrib.toMul","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","Nat.instNonAssocSemiring","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatAtLeastTwo","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_dvd","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Int","Int.fib","Nat","Nat.cast","Nat.fib","instNatCastInt"],"value_dag_size":21,"value_refs":["Eq.symm","Int","Int.fib","Int.fib_natCast","Nat","Nat.cast","Nat.fib","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","Nat.cast","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"],"value_dag_size":75,"value_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","Nat.brecOn","Nat.cast","OfNat.ofNat","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._f","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._f","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":"abbrev","statement_dag_size":90,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","Nat.below","Nat.cast","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"],"value_dag_size":695,"value_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.mpr","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instAddCommSemigroup","Int.instAddGroup","Int.instAddMonoid","Int.instMul","Int.instRing","Int.instSemiring","Int.instSub","MulZeroClass.toZero","MulZeroClass.zero_mul","MulZeroOneClass.toMulOneClass","Nat","Nat.below","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.succ","Neg.neg","OfNat.ofNat","One.toOfNat1","Ring.toAddGroupWithOne","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","Trans.trans","True","Zero.toOfNat0","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_3","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_4","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_5","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_6","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add.match_1_1","add_comm","add_zero","congr","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","instTransEq","of_eq_true","one_mul","sub_self","zero_add","zero_sub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_3","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAdd.hAdd","Int","Int.fib","Int.instAdd","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":474,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_4","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":418,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_5","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":501,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_true","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add._proof_1_6","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":1907,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add.match_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_add","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Int","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Int","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_dvd","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int","reducibility":null,"statement_dag_size":25,"type_refs":["Dvd.dvd","Int","Int.fib","Int.instDvd","Nat","Nat.cast","instNatCastInt"],"value_dag_size":181,"value_refs":["Dvd.dvd","Eq","Eq.mpr","Eq.refl","Eq.symm","Iff.mpr","Int","Int.fib","Int.fib_natCast","Int.gcd","Int.gcd_eq_left_iff_dvd","Int.gcd_fib","Int.instDvd","Int.instLEInt","Int.natCast_nonneg._simp_1","LE.le","Nat","Nat.cast","Nat.fib","OfNat.ofNat","congrArg","id","instNatCastInt","instOfNat","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Nat","Nat.cast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"],"value_dag_size":82,"value_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Nat","Nat.brecOn","Nat.cast","Neg.neg","OfNat.ofNat","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._f","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._f","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","reducibility":"abbrev","statement_dag_size":95,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Nat","Nat.below","Nat.cast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat"],"value_dag_size":751,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toOne","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.mpr","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instAddCommGroup","Int.instAddCommSemigroup","Int.instAddGroup","Int.instAddMonoid","Int.instMul","Int.instNegInt","Int.instRing","Int.instSemiring","Int.instSub","MulZeroClass.mul_zero","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","Nat","Nat.below","Nat.cast","Nat.cast_one","Nat.cast_zero","Nat.succ","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","One.toOfNat1","Ring.toAddGroupWithOne","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Trans.trans","True","Zero.toOfNat0","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_3","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_4","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_5","_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast.match_1_1","add_comm","add_neg_cancel","add_zero","congr","congrArg","congrFun'","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","instTransEq","mul_one","neg_zero","of_eq_true","sub_eq_neg_add","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_3","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instNegInt","Int.instSub","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNatNat"],"value_dag_size":837,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_4","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","reducibility":null,"statement_dag_size":105,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":683,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_true","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast._proof_1_5","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","reducibility":null,"statement_dag_size":105,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":2276,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast.match_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_neg_natCast_add_neg_natCast","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_of_odd._proof_1_2","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_of_odd","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Int","Int.fib","Int.instSemiring","Int.natAbs","Nat.fib","NatCast.natCast","Odd","instNatCastInt"],"value_dag_size":1661,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat_coeff","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.fib","Int.fib.eq_1","Int.instAdd","Int.instDecidablePredEven","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","Int.instSemiring","Int.natAbs","Int.not_odd_iff_even","Int.odd_iff","Int.toNat","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.Omega.Int.ofNat_natAbs","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.cast","Nat.fib","NatCast.natCast","Neg.neg","Not","Odd","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSub","OfNat.ofNat","instHAdd","instHMul","instHSub","instOfNat"],"value_dag_size":642,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_one","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","OfNat.ofNat","instHAdd","instHMul","instHPow","instHSub","instOfNat","instOfNatNat"],"value_dag_size":648,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_eq","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHPow","instHSub","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_one_pos._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_one_pos","reducibility":null,"statement_dag_size":48,"type_refs":["HAdd.hAdd","HMul.hMul","Int","Int.fib","Int.instAdd","Int.instLTInt","Int.instMul","LT.lt","OfNat.ofNat","instHAdd","instHMul","instOfNat"],"value_dag_size":822,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat_coeff","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.norm_le","Int.Internal.Linear.norm_le_coeff_tight","Int.decLe","Int.fib","Int.fib_two_mul_add_one_eq_natFib_natAbs","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.natAbs","Int.not_le_eq","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Omega.Int.ofNat_natAbs","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.fib","Nat.fib_pos","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Basic","name":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_two._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul_add_two","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMul","Int.instSemiring","Int.instSub","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","OfNat.ofNat","One.toOfNat1","instHAdd","instHMul","instHSub","instMulZeroOneClassOfSemiring","instOfNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSemiring","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","Nat","Neg.neg","Not","OfNat.ofNat","One.toOfNat1","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHSub","instMulZeroOneClassOfSemiring","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_add_sq_sub_fib_mul_fib_add_two_mul._proof_1_2","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_add_sq_sub_fib_mul_fib_add_two_mul","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Int.natAbs","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHPow","instHSub","instOfNat","instOfNatNat"],"value_dag_size":5688,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.fib_succ_mul_fib_pred_sub_fib_sq","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Int.instSub","Int.natAbs","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.d_stepk","Lean.Grind.CommRing.Stepwise.div","Lean.Grind.CommRing.Stepwise.imp_keq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.instCommRingInt","Lean.Grind.instNoNatZeroDivisorsInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instHAdd","instHMul","instHPow","instHSub","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_add_sq_sub_fib_mul_fib_add_two_mul._simp_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_add_sq_sub_fib_mul_fib_add_two_mul","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":62,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","HAdd.hAdd","HSub.hSub","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","add_sub","instHAdd","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":404,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddGroupWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","Eq","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instAddCommGroup","Int.instAddGroup","Int.instAddMonoid","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instRing","Int.instSemiring","Int.instSub","Monoid.toMulOneClass","Monoid.toNPow","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Nat.cast","Nat.cast_zero","Nat.instAddMonoidWithOne","Nat.instAtLeastTwoHAddOfNat","Nat.instCharZero","Nat.instNeZeroSucc","Nat.recAux","Neg.neg","Not","OfNat.ofNat","OfNat.ofNat_ne_zero._simp_1","One.toOfNat1","Ring.toAddGroupWithOne","Semiring.toMonoidWithZero","SubNegMonoid.toNeg","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","True","Zero.toOfNat0","_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq._proof_1_1","congr","congrArg","congrFun'","eq_self","instHAdd","instHMul","instHPow","instHSub","instMulZeroOneClassOfSemiring","instNatCastInt","instOfNat","instOfNatNat","mul_one","not_false_eq_true","of_eq_true","pow_zero","sub_zero","zero_add","zero_pow","zero_sub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq._proof_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq","reducibility":null,"statement_dag_size":124,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":1704,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulR","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.fib","Int.fib_add_two","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Int.instSub","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Int.pow_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq._proof_1_3","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq","reducibility":null,"statement_dag_size":176,"type_refs":["AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","Even","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instAddCommGroup","Int.instAddGroup","Int.instDecidablePredEven","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","instAddNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite"],"value_dag_size":3068,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.even_coe_nat","Int.even_iff","Int.fib","Int.instAdd","Int.instAddCommGroup","Int.instAddGroup","Int.instDecidablePredEven","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Int.instSub","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.cast","Nat.even_iff","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat","instPowNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq._simp_1_1","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq","reducibility":null,"statement_dag_size":60,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","instHAdd"],"value_dag_size":66,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","instHAdd","neg_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Fib.Lemmas","name":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq._simp_1_2","namespace":"_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_succ_mul_fib_pred_sub_fib_sq","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":93,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.fib","Int.instAdd","Int.instMonoid","Int.instMul","Int.instNegInt","Int.instSub","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Neg.neg","OfNat.ofNat","_private.Mathlib.Data.Int.Fib.Lemmas.0.Int.fib_natCast_succ_mul_fib_natCast_pred_sub_fib_natCast_sq","instHAdd","instHMul","instHPow","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Commute.pow_eq_pow_iff_of_coprime._simp_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Commute.pow_eq_pow_iff_of_coprime","reducibility":null,"statement_dag_size":55,"type_refs":["DivInvMonoid","DivInvMonoid.toMonoid","DivInvMonoid.toZPow","Eq","HPow.hPow","Int","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","ZPow.toPow","instHPow","instNatCastInt"],"value_dag_size":61,"value_refs":["DivInvMonoid","DivInvMonoid.toMonoid","DivInvMonoid.toZPow","Eq.symm","HPow.hPow","Int","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","ZPow.toPow","instHPow","instNatCastInt","zpow_natCast"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Commute.pow_eq_pow_iff_of_coprime._simp_1_2","namespace":"_private.Mathlib.Data.Int.GCD.0.Commute.pow_eq_pow_iff_of_coprime","reducibility":null,"statement_dag_size":52,"type_refs":["DivInvMonoid.toZPow","DivisionMonoid","DivisionMonoid.toDivInvMonoid","Eq","HMul.hMul","HPow.hPow","Int","Int.instMul","ZPow.toPow","instHMul","instHPow"],"value_dag_size":59,"value_refs":["DivInvMonoid.toZPow","DivisionMonoid","DivisionMonoid.toDivInvMonoid","Eq.symm","HMul.hMul","HPow.hPow","Int","Int.instMul","ZPow.toPow","instHMul","instHPow","zpow_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.dvd_of_dvd_mul_left_of_gcd_one._simp_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.dvd_of_dvd_mul_left_of_gcd_one","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instMul","instHAdd","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instMul","Int.mul_add","instHAdd","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.exists_gcd_one'.match_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.exists_gcd_one'","reducibility":"abbrev","statement_dag_size":139,"type_refs":["And","Eq","Exists","Exists.intro","HMul.hMul","Int","Int.gcd","Int.instMul","Nat","Nat.cast","OfNat.ofNat","instHMul","instNatCastInt","instOfNatNat"],"value_dag_size":204,"value_refs":["And","Eq","Exists","Exists.casesOn","Exists.intro","HMul.hMul","Int","Int.gcd","Int.instMul","Nat","Nat.cast","OfNat.ofNat","instHMul","instNatCastInt","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_eq_gcd_ab.match_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_eq_gcd_ab","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Int","Int.negSucc","Int.ofNat","Nat"],"value_dag_size":79,"value_refs":["Int","Int.casesOn","Int.negSucc","Int.ofNat","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear._simp_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear","reducibility":null,"statement_dag_size":62,"type_refs":["Dvd.dvd","Eq","Exists","HAdd.hAdd","HMul.hMul","Int","Int.gcd","Int.instAdd","Int.instMul","Nat","Nat.cast","Nat.instDvd","instHAdd","instHMul","instNatCastInt"],"value_dag_size":72,"value_refs":["Dvd.dvd","Eq","Eq.symm","Exists","HAdd.hAdd","HMul.hMul","Int","Int.gcd","Int.gcd_dvd_iff","Int.instAdd","Int.instMul","Nat","Nat.cast","Nat.instDvd","instHAdd","instHMul","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear._simp_1_2","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear","reducibility":null,"statement_dag_size":26,"type_refs":["Dvd.dvd","Eq","Monoid","Monoid.toSemigroup","True","semigroupDvd"],"value_dag_size":27,"value_refs":["Dvd.dvd","Monoid","Monoid.toSemigroup","dvd_refl","eq_true","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear._simp_1_3","namespace":"_private.Mathlib.Data.Int.GCD.0.Int.gcd_least_linear","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.P","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat","reducibility":"regular","statement_dag_size":11,"type_refs":["Int","Nat","Prod"],"value_dag_size":59,"value_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instMul","Nat","Nat.cast","Prod","_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1","instHAdd","instHMul","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.P.eq_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.P","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instMul","Nat","Nat.cast","Prod","Prod.mk","_private.Mathlib.Data.Int.GCD.0.Nat.P","instHAdd","instHMul","instNatCastInt"],"value_dag_size":32,"value_refs":["Eq.refl","Int","Nat","Prod","Prod.mk","_private.Mathlib.Data.Int.GCD.0.Nat.P"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.P","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Int","Nat","Prod","Prod.mk"],"value_dag_size":54,"value_refs":["Int","Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Int","Nat","Prod","Prod.mk","_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1"],"value_dag_size":45,"value_refs":["Eq.refl","Int","Nat","Prod","Prod.mk","_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1.splitter","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1","reducibility":"abbrev","statement_dag_size":30,"type_refs":["Int","Nat","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["_private.Mathlib.Data.Int.GCD.0.Nat.P.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.exists_mul_mod_eq_of_coprime._proof_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.exists_mul_mod_eq_of_coprime","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","Or","instLTNat","instOfNatNat"],"value_dag_size":321,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.exists_mul_mod_eq_of_coprime._proof_1_2","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.exists_mul_mod_eq_of_coprime","reducibility":null,"statement_dag_size":22,"type_refs":["LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":253,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Int","LT.lt","Nat","Nat.succ","Nat.xgcdAux.match_1","OfNat.ofNat","Prod","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq.refl","Int","LT.lt","Nat","Nat.succ","Nat.xgcdAux.match_1","OfNat.ofNat","Prod","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1.eq_2","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","Int","LT.lt","Nat","Nat.succ","Nat.xgcdAux.match_1","OfNat.ofNat","Prod","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.refl","Int","LT.lt","Nat","Nat.succ","Nat.xgcdAux.match_1","OfNat.ofNat","Prod","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1.splitter","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux.match_1","reducibility":"abbrev","statement_dag_size":58,"type_refs":["Int","LT.lt","Nat","Nat.succ","OfNat.ofNat","Prod","instLTNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.xgcdAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.Nat.xgcdAux_P","namespace":"_private.Mathlib.Data.Int.GCD.0.Nat","reducibility":null,"statement_dag_size":53,"type_refs":["Int","Nat","Nat.xgcdAux","Prod","Prod.mk","_private.Mathlib.Data.Int.GCD.0.Nat.P"],"value_dag_size":932,"value_refs":["AddCommGroup.toDivisionAddCommMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","CommMagma.toMul","CommSemigroup.toCommMagma","Eq","Eq.mpr","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.add_mul","Int.emod_def","Int.instAdd","Int.instAddCommGroup","Int.instAddCommSemigroup","Int.instAddGroup","Int.instCommSemigroup","Int.instDiv","Int.instMod","Int.instMul","Int.instSemigroup","Int.instSub","Int.mul_sub","LT.lt","Nat","Nat.cast","Nat.gcd.induction","Nat.instMod","Nat.xgcdAux","Nat.xgcdAux_rec","Nat.xgcd_zero_left","OfNat.ofNat","Prod","Prod.mk","Semigroup.toMul","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","True","_private.Mathlib.Data.Int.GCD.0.Nat.P","add_comm","add_sub_assoc","congrArg","forall_congr","id","imp_self._simp_1","implies_congr","implies_true","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLTNat","instNatCastInt","instOfNatNat","mul_assoc","mul_comm","of_eq_true","sub_add_eq_add_sub","sub_sub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.gcd_nsmul_eq_zero.match_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.gcd_nsmul_eq_zero","reducibility":"abbrev","statement_dag_size":187,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddZero.toZero","AddZeroClass.toAddZero","And","And.intro","Eq","HSMul.hSMul","NSMul.toSMul","Nat","OfNat.ofNat","Zero.toOfNat0","instHSMul"],"value_dag_size":204,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddMonoid.toNSMul","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","And.intro","Eq","HSMul.hSMul","NSMul.toSMul","Nat","OfNat.ofNat","Zero.toOfNat0","instHSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.pow_eq_one_iff_of_coprime._simp_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.pow_eq_one_iff_of_coprime","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toOne","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.gcd","OfNat.ofNat","One.toOfNat1","instHPow"],"value_dag_size":80,"value_refs":["And","Eq","Eq.symm","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toOne","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.gcd","OfNat.ofNat","One.toOfNat1","instHPow","pow_gcd_eq_one","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.GCD","name":"_private.Mathlib.Data.Int.GCD.0.pow_gcd_eq_one.match_1_1","namespace":"_private.Mathlib.Data.Int.GCD.0.pow_gcd_eq_one","reducibility":"abbrev","statement_dag_size":192,"type_refs":["And","And.intro","Eq","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toOne","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","One.toOfNat1","instHPow"],"value_dag_size":208,"value_refs":["And","And.casesOn","And.intro","Eq","HPow.hPow","Monoid","Monoid.toMulOneClass","Monoid.toNPow","MulOne.toOne","MulOneClass.toMulOne","NPow.toPow","Nat","OfNat.ofNat","One.toOfNat1","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.ediv_of_neg_of_pos.match_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.ediv_of_neg_of_pos","reducibility":"abbrev","statement_dag_size":127,"type_refs":["Eq","Eq.refl","Exists","Exists.intro","HAdd.hAdd","Int","Int.instAdd","Int.instLTInt","Int.negSucc","LT.lt","Nat","Nat.cast","OfNat.ofNat","instHAdd","instNatCastInt","instOfNat"],"value_dag_size":444,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","HEq","HEq.refl","Int","Int.instAdd","Int.instLTInt","Int.negSucc","LT.lt","Nat","Nat.cast","OfNat.ofNat","eq_of_heq","instHAdd","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_10","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","instHAdd","instHSub"],"value_dag_size":118,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.eq_eq_true","Int.instAdd","Int.instSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHAdd","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_4","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":225,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.instAdd","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Not","OfNat.ofNat","True","congrArg","eagerReduce","eq_self","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_6","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Int.negSucc","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNat","instOfNatNat"],"value_dag_size":386,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.instAdd","Int.instMul","Int.instNegInt","Int.instSub","Int.negSucc","Int.negSucc_eq","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_8","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'","reducibility":null,"statement_dag_size":25,"type_refs":["HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.negSucc","LE.le","Nat","instHAdd"],"value_dag_size":198,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.negSucc","Int.negSucc_eq","Int.not_le_eq","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1.eq_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Int.inductionOn'.pos.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Int.inductionOn'.pos.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1.eq_2","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Int.inductionOn'.pos.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Int.inductionOn'.pos.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1.splitter","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Int.inductionOn'.pos.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HSub.hSub","Int","Int.instLEInt","Int.instSub","Int.toNat","LE.le","NatCast.natCast","instHSub","instNatCastInt"],"value_dag_size":573,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.toNat","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_10","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":40,"type_refs":["HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","Nat.cast","instHAdd","instHSub","instNatCastInt"],"value_dag_size":21,"value_refs":["HSub.hSub","Int","Int.inductionOn'.pos._proof_1","Int.instSub","Int.toNat","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_11","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":211,"type_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.pos","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","Nat","NatCast.natCast","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_1","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_2","cast","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":1128,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","HEq.refl","HEq.symm","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.inductionOn'._proof_1","Int.inductionOn'._proof_5","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.pos","Int.inductionOn'.pos._proof_1","Int.inductionOn'.pos.eq_2","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.toNat","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.instCommRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.cast","Nat.succ","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_1","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_10","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_2","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_6","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_7","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_8","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_9","cast","cast_heq","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_2","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":656,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.toNat","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_6","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","NatCast.natCast","instHAdd","instHSub","instNatCastInt"],"value_dag_size":568,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.toNat","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_7","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","Nat","NatCast.natCast","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":112,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","Nat","NatCast.natCast","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_2","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_8","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","NatCast.natCast","instHAdd","instHSub","instNatCastInt"],"value_dag_size":83,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.toNat","LE.le","NatCast.natCast","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_1","instHAdd","instHSub","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_9","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Int.toNat","Nat","Nat.cast","OfNat.ofNat","instAddNat","instHAdd","instHSub","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":26,"value_refs":["HSub.hSub","Int","Int.inductionOn'._proof_5","Int.instSub","Int.toNat","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_10","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":263,"type_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.inductionOn'._proof_7","Int.inductionOn'._proof_9","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.pos","Int.inductionOn'.pos.match_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.le_rfl","Int.negSucc","Int.toNat","LE.le","Nat","OfNat.ofNat","PUnit","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_2","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_3","cast","instAddNat","instHAdd","instHSub","instOfNat","instOfNatNat"],"value_dag_size":1382,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","HEq.refl","HEq.symm","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_unsat","Int.decLe","Int.inductionOn'._proof_1","Int.inductionOn'._proof_3","Int.inductionOn'._proof_7","Int.inductionOn'._proof_9","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.pos","Int.inductionOn'.pos.eq_1","Int.inductionOn'.pos.match_1","Int.inductionOn'.pos.match_1.congr_eq_1","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instSub","Int.le_rfl","Int.negSucc","Int.toNat","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PUnit","PUnit.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","Unit","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_6","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1.splitter","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_2","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_3","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_7","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_8","cast","cast_heq","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_11","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HSub.hSub","Int","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":630,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.negSucc","Int.negSucc_eq","Int.toNat","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_12","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HSub.hSub","Int","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":960,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.negSucc","Int.negSucc_eq","Int.toNat","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_13","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","instHAdd","instHSub","instOfNat"],"value_dag_size":102,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_11","instHAdd","instHSub","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_14","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","instHAdd","instHSub","instOfNat"],"value_dag_size":98,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.negSucc","Int.toNat","LE.le","Not","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_12","instHAdd","instHSub","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_16","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":267,"type_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.inductionOn'._proof_7","Int.inductionOn'._proof_9","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.pos","Int.inductionOn'.pos.match_1","Int.instAdd","Int.instLEInt","Int.instSub","Int.le_rfl","Int.negSucc","Int.toNat","LE.le","Nat","Not","OfNat.ofNat","PUnit","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_11","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_12","cast","instAddNat","instHAdd","instHSub","instOfNat","instOfNatNat"],"value_dag_size":5551,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","HEq.refl","HEq.symm","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.inductionOn'._proof_1","Int.inductionOn'._proof_7","Int.inductionOn'._proof_9","Int.inductionOn'.match_1","Int.inductionOn'.neg","Int.inductionOn'.neg.hcongr_5","Int.inductionOn'.pos","Int.inductionOn'.pos.match_1","Int.inductionOn'.pos.match_1.congr_eq_2","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instSub","Int.le_rfl","Int.negSucc","Int.toNat","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.sub","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PUnit","PUnit.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","Unit","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'._proof_6","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'.pos.match_1.splitter","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_11","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_12","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_13","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_14","cast","cast_heq","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_2","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HSub.hSub","Int","Int.instSub","Int.negSucc","Int.toNat","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":490,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.negSucc","Int.negSucc_eq","Int.toNat","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.ofNat_toNat","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_3","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","HSub.hSub","Int","Int.instSub","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":151,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","False","HSub.hSub","Int","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.norm_eq_var","Int.instSub","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_7","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","Int.negSucc","Int.toNat","OfNat.ofNat","instHAdd","instHSub","instOfNat"],"value_dag_size":91,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instSub","Int.negSucc","Int.toNat","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_2","instHAdd","instHSub","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_8","namespace":"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":79,"value_refs":["Eq","Eq.rec","HAdd.hAdd","HSub.hSub","Int","Int.inductionOn'._proof_1","Int.instAdd","Int.instSub","OfNat.ofNat","_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_sub_one._proof_1_3","instHAdd","instHSub","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.leInduction._proof_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.leInduction","reducibility":null,"statement_dag_size":35,"type_refs":["False","HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":194,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","OfNat.ofNat","eagerReduce","id","instHAdd","instHMul","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.leInductionDown._proof_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.leInductionDown","reducibility":null,"statement_dag_size":33,"type_refs":["HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":221,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instHAdd","instHMul","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.leInductionDown._proof_3","namespace":"_private.Mathlib.Data.Int.Init.0.Int.leInductionDown","reducibility":null,"statement_dag_size":35,"type_refs":["False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","LE.le","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":185,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","OfNat.ofNat","eagerReduce","id","instHAdd","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.leInduction_add_one._proof_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.leInduction_add_one","reducibility":null,"statement_dag_size":33,"type_refs":["HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","LE.le","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":212,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instHAdd","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.lt_succ_self._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.lt_succ_self","reducibility":null,"statement_dag_size":27,"type_refs":["HAdd.hAdd","Int","Int.instAdd","Int.instLTInt","LT.lt","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":116,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.le_eq_true","Int.instAdd","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHAdd","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.natCast_pred_of_pos._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.natCast_pred_of_pos","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","HSub.hSub","Int","Int.instSub","LT.lt","Nat","NatCast.natCast","OfNat.ofNat","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":672,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instSub","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.natMod_lt._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.natMod_lt","reducibility":null,"statement_dag_size":33,"type_refs":["Int","Int.instLTInt","LT.lt","Nat","NatCast.natCast","Ne","OfNat.ofNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":249,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instHMul","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.pred_self_lt._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.pred_self_lt","reducibility":null,"statement_dag_size":27,"type_refs":["HSub.hSub","Int","Int.instLTInt","Int.instSub","LT.lt","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":130,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.le_eq_true","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instSub","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHAdd","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.sign_add_eq_of_sign_eq._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.sign_add_eq_of_sign_eq","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Int.sign","instHAdd"],"value_dag_size":1787,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.decLe","Int.decLt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.sign","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.Int.sign_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.strongRec._proof_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.strongRec","reducibility":null,"statement_dag_size":21,"type_refs":["Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Not"],"value_dag_size":271,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.strongRec._proof_3","namespace":"_private.Mathlib.Data.Int.Init.0.Int.strongRec","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","Int","Int.instAdd","Int.instLTInt","LT.lt","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":363,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.strongRec._proof_5","namespace":"_private.Mathlib.Data.Int.Init.0.Int.strongRec","reducibility":null,"statement_dag_size":33,"type_refs":["HSub.hSub","Int","Int.instLTInt","Int.instSub","LT.lt","OfNat.ofNat","instHSub","instOfNat"],"value_dag_size":314,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instHMul","instHSub","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.toNat_lt_of_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.toNat_lt_of_ne_zero","reducibility":null,"statement_dag_size":40,"type_refs":["Iff","Int","Int.instLTInt","Int.toNat","LT.lt","Nat","NatCast.natCast","Ne","OfNat.ofNat","instLTNat","instNatCastInt","instOfNatNat"],"value_dag_size":905,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","Int.toNat","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Init","name":"_private.Mathlib.Data.Int.Init.0.Int.toNat_pred_coe_of_pos._simp_1_1","namespace":"_private.Mathlib.Data.Int.Init.0.Int.toNat_pred_coe_of_pos","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Int","Int.instLTInt","Int.toNat","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":31,"value_refs":["Int","Int.instLTInt","Int.lt_toNat","Int.toNat","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ._proof_1_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ","reducibility":null,"statement_dag_size":85,"type_refs":["And","Eq","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instNegInt","LE.le","Lattice.toSemilatticeInf","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instHAdd","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":2192,"value_refs":["And","And.left","And.right","Bool","Bool.true","Classical.propDecidable","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Decidable.and_not_or_not_and_of_not_iff","Lean.Omega.Decidable.or_not_not_of_not_and","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.neg_congr","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instNeg","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.neg_eval","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.and_not_not_of_not_or","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","id","instDecidableEqBool","instHAdd","instHSub","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ._simp_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Icc","Finset.instSetLike","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ._simp_1_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Icc_succ_succ","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ._proof_1_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ","reducibility":null,"statement_dag_size":91,"type_refs":["And","Eq","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instHAdd","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":2065,"value_refs":["And","And.left","And.right","Bool","Bool.true","Classical.propDecidable","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Decidable.and_not_or_not_and_of_not_iff","Lean.Omega.Decidable.or_not_not_of_not_and","Lean.Omega.Int.add_congr","Lean.Omega.Int.le_of_not_lt","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.neg_congr","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instNeg","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.neg_eval","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.and_not_not_of_not_or","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Nat.cast","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","id","instDecidableEqBool","instHAdd","instHSub","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ._simp_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ._simp_1_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ico_succ_succ","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ._proof_1_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","instHAdd","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":2350,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ._simp_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ioc","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ioc","Finset.instSetLike","Finset.mem_Ioc","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ._simp_1_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ._proof_1_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ","reducibility":null,"statement_dag_size":81,"type_refs":["And","Eq","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instNegInt","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","instHAdd","instLatticeInt","instNatCastInt","instOfNat"],"value_dag_size":1880,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","True","congr","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ._simp_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Ioo","Finset.instSetLike","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLT","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Ioo","Finset.instSetLike","Finset.mem_Ioo","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ._simp_1_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Finset.Ioo_succ_succ","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.Icc_eq_pair._proof_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.Icc_eq_pair","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","False","HAdd.hAdd","Iff","Int","Int.instAdd","LE.le","Lattice.toSemilatticeInf","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instHAdd","instLatticeInt","instOfNat"],"value_dag_size":1053,"value_refs":["And","And.left","And.right","Bool","Bool.true","Classical.propDecidable","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","Int.instSub","Int.lt_or_gt_of_ne","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Decidable.and_not_or_not_and_of_not_iff","Lean.Omega.Decidable.or_not_not_of_not_and","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.and_not_not_of_not_or","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List.cons","List.nil","Nat","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","id","instDecidableEqBool","instHAdd","instHSub","instLatticeInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod._proof_1_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Int","Int.instAdd","Int.instDiv","Int.instMul","OfNat.ofNat","instHAdd","instHDiv","instHMul","instOfNat"],"value_dag_size":233,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.instAdd","Int.instDiv","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instHAdd","instHDiv","instHMul","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod._simp_1_1","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod._simp_1_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod._simp_1_4","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.image_Ico_emod","reducibility":null,"statement_dag_size":74,"type_refs":["AddRightMono","AddRightReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":81,"value_refs":["AddRightMono","AddRightReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd","le_add_iff_nonneg_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_10","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":101,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","Exists","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":1088,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.not_le_eq","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","congr","congrArg","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_11","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":100,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":2187,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_13","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":97,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","Exists","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":1461,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.not_le_eq","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_14","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":96,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":2453,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_4","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":96,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","Exists","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":1044,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.not_le_eq","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","congr","congrArg","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_5","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":95,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt","instOfNat"],"value_dag_size":1591,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_7","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":92,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","Exists","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt"],"value_dag_size":1073,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.not_le_eq","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","congr","congrArg","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_8","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":91,"type_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Nat","NatCast.natCast","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","instHAdd","instHSub","instLTNat","instLatticeInt"],"value_dag_size":1630,"value_refs":["AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.instRing","Int.instSub","Int.toNat","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Int.lt_eq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.ofNat_toNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Ring.toAddGroupWithOne","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._simp_2","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Interval","name":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._simp_3","namespace":"_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.coe_greatestOfBdd_eq._proof_1_2","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.coe_greatestOfBdd_eq","reducibility":null,"statement_dag_size":66,"type_refs":["And","DecidablePred","Eq","Exists","Int","Int.greatestOfBdd","Int.instLEInt","LE.le","Subtype.val"],"value_dag_size":1026,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.greatestOfBdd","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Subtype.property","Subtype.val","True","congrArg","eagerReduce","eq_true","forall_congr","id","implies_congr","instHAdd","instHMul","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.coe_leastOfBdd_eq._proof_1_2","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.coe_leastOfBdd_eq","reducibility":null,"statement_dag_size":67,"type_refs":["And","DecidablePred","Eq","Exists","Int","Int.instLEInt","Int.leastOfBdd","LE.le","Subtype.val"],"value_dag_size":1043,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.leastOfBdd","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Subtype.property","Subtype.val","True","congrArg","eagerReduce","eq_true","forall_congr","id","implies_congr","instHAdd","instHMul","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_greatest_of_bdd.match_1_1","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_greatest_of_bdd","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists","Exists.intro","Int","Int.instLEInt","LE.le"],"value_dag_size":64,"value_refs":["Exists","Exists.casesOn","Exists.intro","Int","Int.instLEInt","LE.le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_greatest_of_bdd.match_1_3","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_greatest_of_bdd","reducibility":"abbrev","statement_dag_size":60,"type_refs":["And","Int","Int.instLEInt","LE.le","Subtype","Subtype.mk"],"value_dag_size":76,"value_refs":["And","Int","Int.instLEInt","LE.le","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_least_of_bdd.match_1_1","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_least_of_bdd","reducibility":"abbrev","statement_dag_size":48,"type_refs":["Exists","Exists.intro","Int","Int.instLEInt","LE.le"],"value_dag_size":64,"value_refs":["Exists","Exists.casesOn","Exists.intro","Int","Int.instLEInt","LE.le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.LeastGreatest","name":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_least_of_bdd.match_1_3","namespace":"_private.Mathlib.Data.Int.LeastGreatest.0.Int.exists_least_of_bdd","reducibility":"abbrev","statement_dag_size":60,"type_refs":["And","Int","Int.instLEInt","LE.le","Subtype","Subtype.mk"],"value_dag_size":76,"value_refs":["And","Int","Int.instLEInt","LE.le","Subtype","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Lemmas","name":"_private.Mathlib.Data.Int.Lemmas.0.Int.ediv_emod_unique''.match_1_1","namespace":"_private.Mathlib.Data.Int.Lemmas.0.Int.ediv_emod_unique''","reducibility":"abbrev","statement_dag_size":87,"type_refs":["And","And.intro","Eq","Eq.refl","HDiv.hDiv","HMod.hMod","Int","Int.instDiv","Int.instMod","Unit","instHDiv","instHMod"],"value_dag_size":348,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HDiv.hDiv","HEq","HEq.refl","HMod.hMod","Int","Int.instDiv","Int.instMod","Unit","Unit.unit","eq_of_heq","instHDiv","instHMod"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Lemmas","name":"_private.Mathlib.Data.Int.Lemmas.0.Int.ediv_emod_unique''.match_1_3","namespace":"_private.Mathlib.Data.Int.Lemmas.0.Int.ediv_emod_unique''","reducibility":"abbrev","statement_dag_size":125,"type_refs":["And","And.intro","Eq","Eq.refl","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instAddGroup","Int.instLEInt","Int.instLTInt","Int.instMul","LE.le","LT.lt","OfNat.ofNat","abs","instHAdd","instHMul","instLatticeInt","instOfNat"],"value_dag_size":304,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HAdd.hAdd","HEq","HEq.refl","HMul.hMul","Int","Int.instAdd","Int.instAddGroup","Int.instLEInt","Int.instLTInt","Int.instMul","LE.le","LT.lt","OfNat.ofNat","abs","eq_of_heq","instHAdd","instHMul","instLatticeInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Lemmas","name":"_private.Mathlib.Data.Int.Lemmas.0.Int.le_natCast_sub._proof_1_1","namespace":"_private.Mathlib.Data.Int.Lemmas.0.Int.le_natCast_sub","reducibility":null,"statement_dag_size":39,"type_refs":["HSub.hSub","Int","Int.instLEInt","Int.instSub","LE.le","Nat","NatCast.natCast","instHSub","instNatCastInt","instSubNat"],"value_dag_size":514,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.not_le_eq","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Lemmas","name":"_private.Mathlib.Data.Int.Lemmas.0.Int.natAbs_inj_of_nonpos_of_nonpos._simp_1_1","namespace":"_private.Mathlib.Data.Int.Lemmas.0.Int.natAbs_inj_of_nonpos_of_nonpos","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","InvolutiveNeg","InvolutiveNeg.toNeg","Neg.neg"],"value_dag_size":34,"value_refs":["Eq","InvolutiveNeg","InvolutiveNeg.toNeg","Neg.neg","neg_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq","reducibility":null,"statement_dag_size":73,"type_refs":["AddCommGroup","AddCommGroup.ModEq","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","Exists","HSMul.hSMul","HSub.hSub","Int","SubNegMonoid.toSub","SubNegMonoid.toZSMul","ZSMul.toSMul","instHSMul","instHSub"],"value_dag_size":78,"value_refs":["AddCommGroup","AddCommGroup.ModEq","AddCommGroup.modEq_iff_zsmul'","AddCommGroup.toAddCommMonoid","AddCommGroup.toAddGroup","AddGroup.toSubNegMonoid","Eq","Exists","HSMul.hSMul","HSub.hSub","Int","SubNegMonoid.toSub","SubNegMonoid.toZSMul","ZSMul.toSMul","instHSMul","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq._simp_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq","reducibility":null,"statement_dag_size":52,"type_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","instHMul","semigroupDvd"],"value_dag_size":56,"value_refs":["CommMagma.toMul","CommSemigroup","CommSemigroup.toCommMagma","CommSemigroup.toSemigroup","Dvd.dvd","Eq","Exists","HMul.hMul","dvd_iff_exists_eq_mul_left","instHMul","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq._simp_1_4","namespace":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HMod.hMod","HSub.hSub","Int","Int.instMod","Int.instSub","OfNat.ofNat","instHMod","instHSub","instOfNat"],"value_dag_size":54,"value_refs":["Eq","HMod.hMod","HSub.hSub","Int","Int.emod_eq_emod_iff_emod_sub_eq_zero","Int.instMod","Int.instSub","OfNat.ofNat","instHMod","instHSub","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq._simp_1_5","namespace":"_private.Mathlib.Data.Int.ModEq.0.AddCommGroup.modEq_iff_intModEq","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Int","Int.instDvd","Int.instMod","OfNat.ofNat","instHMod","instOfNat"],"value_dag_size":46,"value_refs":["Dvd.dvd","Eq","Eq.symm","HMod.hMod","Int","Int.dvd_iff_emod_eq_zero","Int.instDvd","Int.instMod","OfNat.ofNat","instHMod","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.add._proof_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.add","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","instHAdd","instHSub"],"value_dag_size":156,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.eq_eq_true","Int.instAdd","Int.instSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHAdd","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.add_left_cancel._proof_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.add_left_cancel","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instSub","instHAdd","instHSub"],"value_dag_size":156,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.eq_eq_true","Int.instAdd","Int.instSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHAdd","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.dvd_iff._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.dvd_iff","reducibility":null,"statement_dag_size":27,"type_refs":["Dvd.dvd","Eq","Int","Int.ModEq","Int.instDvd","OfNat.ofNat","instOfNat"],"value_dag_size":35,"value_refs":["Dvd.dvd","Eq.symm","Int","Int.ModEq","Int.instDvd","Int.modEq_zero_iff_dvd","OfNat.ofNat","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_left_cancel'._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_left_cancel'","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_left_cancel'._simp_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_left_cancel'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","instHMul","instHSub"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","Int.mul_sub","instHMul","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_right_cancel'._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_right_cancel'","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_right_cancel'._simp_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.mul_right_cancel'","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","instHMul","instHSub"],"value_dag_size":44,"value_refs":["Eq.symm","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","Int.sub_mul","instHMul","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.neg._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.ModEq.neg","reducibility":null,"statement_dag_size":57,"type_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","Neg.neg","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":63,"value_refs":["AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq.symm","HAdd.hAdd","HSub.hSub","Neg.neg","SubNegMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegMonoid.toSub","instHAdd","instHSub","sub_eq_add_neg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.abs_modEq_two._proof_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.abs_modEq_two","reducibility":null,"statement_dag_size":21,"type_refs":["Int","Int.ModEq","Int.instAddGroup","OfNat.ofNat","abs","instLatticeInt","instOfNat"],"value_dag_size":1640,"value_refs":["AddGroup.toSubtractionMonoid","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_of_core","Int.Internal.Linear.diseq_split_resolve","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.emod_nonneg","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.Internal.Linear.norm_le_coeff","Int.ModEq","Int.ModEq.eq_1","Int.decLe","Int.instAdd","Int.instAddGroup","Int.instDiv","Int.instLEInt","Int.instLinearOrder","Int.instMax","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lattice.toSemilatticeSup","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMax","LinearOrder.toPartialOrder","Max.max","Nat","Neg.neg","NegZeroClass.toNeg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toMax","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","abs","abs.eq_1","congrArg","eagerReduce","eq_false","eq_true","id","instHAdd","instHDiv","instHMod","instHMul","instLatticeInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","max_def","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.add_modEq_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.add_modEq_left_iff","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.existsUnique_equiv_nat.match_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.existsUnique_equiv_nat","reducibility":"abbrev","statement_dag_size":99,"type_refs":["And","And.intro","Exists","Exists.intro","Int","Int.ModEq","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","OfNat.ofNat","instOfNat"],"value_dag_size":186,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","Int","Int.ModEq","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","OfNat.ofNat","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_and_modEq_iff_modEq_lcm._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_and_modEq_iff_modEq_lcm","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_and_modEq_iff_modEq_lcm._simp_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_and_modEq_iff_modEq_lcm","reducibility":null,"statement_dag_size":33,"type_refs":["And","Dvd.dvd","Eq","Int","Int.instDvd","Int.lcm","Nat.cast","instNatCastInt"],"value_dag_size":36,"value_refs":["And","Dvd.dvd","Int","Int.coe_lcm_dvd_iff","Int.instDvd","Int.lcm","Nat.cast","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_dvd","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HMod.hMod","HSub.hSub","Int","Int.instMod","Int.instSub","OfNat.ofNat","instHMod","instHSub","instOfNat"],"value_dag_size":54,"value_refs":["Eq","HMod.hMod","HSub.hSub","Int","Int.emod_eq_emod_iff_emod_sub_eq_zero","Int.instMod","Int.instSub","OfNat.ofNat","instHMod","instHSub","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_dvd._simp_1_3","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_dvd","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Int","Int.instDvd","Int.instMod","OfNat.ofNat","instHMod","instOfNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Int","Int.dvd_iff_emod_eq_zero","Int.instDvd","Int.instMod","OfNat.ofNat","instHMod","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_eq_of_div_eq._proof_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_iff_eq_of_div_eq","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HDiv.hDiv","Iff","Int","Int.ModEq","Int.instDiv","instHDiv"],"value_dag_size":139,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HDiv.hDiv","Iff","Int","Int.ModEq","Int.ext_ediv_modEq_iff","Int.instDiv","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Not","congrArg","eq_true","id","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_neg._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.modEq_neg","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg._proof_1_2","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","HSub.hSub","Int","Int.instNegInt","Int.instSub","Neg.neg","instHSub"],"value_dag_size":119,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HSub.hSub","Int","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.eq_eq_true","Int.instNegInt","Int.instSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instHSub","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg._simp_1_1","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg","reducibility":null,"statement_dag_size":33,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","instHSub"],"value_dag_size":36,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.ModEq","Int.instDvd","Int.instSub","Int.modEq_iff_dvd","instHSub","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.ModEq","name":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg._simp_1_3","namespace":"_private.Mathlib.Data.Int.ModEq.0.Int.neg_modEq_neg","reducibility":null,"statement_dag_size":22,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Int.instNegInt","Neg.neg"],"value_dag_size":24,"value_refs":["Dvd.dvd","Int","Int.dvd_neg","Int.instDvd","Int.instNegInt","Neg.neg","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.NatAbs","name":"_private.Mathlib.Data.Int.NatAbs.0.Int.natAbs_natCast_sub_natCast_of_ge._proof_1_1","namespace":"_private.Mathlib.Data.Int.NatAbs.0.Int.natAbs_natCast_sub_natCast_of_ge","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HSub.hSub","Int","Int.instSub","Int.natAbs","LE.le","Nat","NatCast.natCast","instHSub","instLENat","instNatCastInt","instSubNat"],"value_dag_size":634,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.natAbs","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Omega.Int.ofNat_natAbs","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.NatAbs","name":"_private.Mathlib.Data.Int.NatAbs.0.Int.natAbs_natCast_sub_natCast_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Int.NatAbs.0.Int.natAbs_natCast_sub_natCast_of_le","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HSub.hSub","Int","Int.instSub","Int.natAbs","LE.le","Nat","NatCast.natCast","instHSub","instLENat","instNatCastInt","instSubNat"],"value_dag_size":1153,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.sub","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","Int.instSub","Int.natAbs","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Omega.Int.ofNat_natAbs","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Order.Basic","name":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_neg_iff._proof_1_1","namespace":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_neg_iff","reducibility":null,"statement_dag_size":53,"type_refs":["And","Iff","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Not","OfNat.ofNat","Or","instOfNat"],"value_dag_size":1576,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Order.Basic","name":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_nonneg_of_nonneg_or_nonpos.match_1_1","namespace":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_nonneg_of_nonneg_or_nonpos","reducibility":"abbrev","statement_dag_size":93,"type_refs":["And","And.intro","Int","Int.instLEInt","LE.le","OfNat.ofNat","Or","Or.inl","Or.inr","instOfNat"],"value_dag_size":142,"value_refs":["And","And.casesOn","And.intro","Int","Int.instLEInt","LE.le","OfNat.ofNat","Or","Or.casesOn","Or.inl","Or.inr","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Order.Basic","name":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_nonpos_iff._proof_1_1","namespace":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_nonpos_iff","reducibility":null,"statement_dag_size":53,"type_refs":["And","Iff","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Not","OfNat.ofNat","Or","instOfNat"],"value_dag_size":1395,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Order.Basic","name":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_pos_iff._proof_1_1","namespace":"_private.Mathlib.Data.Int.Order.Basic.0.Int.mul_pos_iff","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Iff","Int","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","Not","OfNat.ofNat","Or","instOfNat"],"value_dag_size":1699,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","Int.not_le_eq","LE.le","LT.lt","Lean.Grind.Int.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","Nat","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHMul","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Order.Basic","name":"_private.Mathlib.Data.Int.Order.Basic.0.Int.nonneg_or_nonpos_of_mul_nonneg._proof_1_1","namespace":"_private.Mathlib.Data.Int.Order.Basic.0.Int.nonneg_or_nonpos_of_mul_nonneg","reducibility":null,"statement_dag_size":45,"type_refs":["And","HMul.hMul","Int","Int.instLEInt","Int.instMul","LE.le","OfNat.ofNat","Or","instHMul","instOfNat"],"value_dag_size":927,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instMul","Int.instNegInt","Int.mul_nonneg_iff_of_pos_right","Int.not_le_eq","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Int.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_eq_of_eq_true_left","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","implies_congr","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELE._simp_1","namespace":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELE","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","LE.le","LT.lt","OfNat.ofNat","instHAdd","instOfNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.lt_add_one_iff","LE.le","LT.lt","OfNat.ofNat","instHAdd","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT._simp_1","namespace":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Int","Int.instLEInt","Int.instLTInt","Int.range","LE.le","LT.lt","List","List.instMembership","Membership.mem"],"value_dag_size":43,"value_refs":["And","Int","Int.instLEInt","Int.instLTInt","Int.mem_range_iff","Int.range","LE.le","LT.lt","List","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT._simp_2","namespace":"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff._simp_1_2","namespace":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff._simp_1_3","namespace":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","List","List.instMembership","List.range","Membership.mem","Nat","instLTNat"],"value_dag_size":30,"value_refs":["LT.lt","List","List.instMembership","List.mem_range","List.range","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff._simp_1_4","namespace":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Int","Int.instLTInt","Int.toNat","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt"],"value_dag_size":31,"value_refs":["Int","Int.instLTInt","Int.lt_toNat","Int.toNat","LT.lt","Nat","Nat.cast","instLTNat","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff._simp_1_5","namespace":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff","reducibility":null,"statement_dag_size":83,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub"],"value_dag_size":90,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddMonoid.toAddZeroClass","AddRightStrictMono","AddZero.toAdd","AddZeroClass.toAddZero","HAdd.hAdd","HSub.hSub","LT","LT.lt","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","instHAdd","instHSub","lt_sub_iff_add_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Range","name":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff.match_1_6","namespace":"_private.Mathlib.Data.Int.Range.0.Int.mem_range_iff","reducibility":"abbrev","statement_dag_size":104,"type_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","And","Eq","Exists","Exists.intro","HAdd.hAdd","Int","Int.instAdd","Int.instAddCommSemigroup","Int.instLTInt","LT.lt","Nat","Nat.cast","instHAdd","instNatCastInt"],"value_dag_size":127,"value_refs":["AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","And","Eq","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","Int","Int.instAdd","Int.instAddCommSemigroup","Int.instLTInt","LT.lt","Nat","Nat.cast","instHAdd","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Int.Sqrt","name":"_private.Mathlib.Data.Int.Sqrt.0.Int.exists_mul_self.match_1_1","namespace":"_private.Mathlib.Data.Int.Sqrt.0.Int.exists_mul_self","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Eq","Exists","Exists.intro","HMul.hMul","Int","Int.instMul","instHMul"],"value_dag_size":61,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HMul.hMul","Int","Int.instMul","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.Star","name":"_private.Mathlib.Data.Int.Star.0.Int.instStarOrderedRing._simp_1","namespace":"_private.Mathlib.Data.Int.Star.0.Int.instStarOrderedRing","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.WithZero","name":"_private.Mathlib.Data.Int.WithZero.0.WithZeroMulInt.toNNReal_eq_one_iff._simp_1_1","namespace":"_private.Mathlib.Data.Int.WithZero.0.WithZeroMulInt.toNNReal_eq_one_iff","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["Eq","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","eq_false","zero_ne_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Int.WithZero","name":"_private.Mathlib.Data.Int.WithZero.0.WithZeroMulInt.toNNReal_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Int.WithZero.0.WithZeroMulInt.toNNReal_ne_zero","reducibility":null,"statement_dag_size":98,"type_refs":["DFunLike.coe","Eq","FunLike","GroupWithZero","GroupWithZero.toMonoidWithZero","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHomClass","MulZeroClass.toZero","MulZeroOneClass","MulZeroOneClass.toMulZeroClass","Nontrivial","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":108,"value_refs":["DFunLike.coe","Eq","FunLike","GroupWithZero","GroupWithZero.toMonoidWithZero","MonoidWithZero.toMulZeroOneClass","MonoidWithZeroHomClass","MulZeroClass.toZero","MulZeroOneClass","MulZeroOneClass.toMulZeroClass","Nontrivial","OfNat.ofNat","Zero.toOfNat0","map_eq_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.ext.match_1_1","namespace":"_private.Mathlib.Data.List.AList.0.AList.ext","reducibility":"abbrev","statement_dag_size":103,"type_refs":["AList","AList.entries","AList.mk","Eq","List","List.NodupKeys","Sigma"],"value_dag_size":197,"value_refs":["AList","AList.casesOn","AList.entries","AList.mk","Eq","List","List.NodupKeys","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1","reducibility":null,"statement_dag_size":179,"type_refs":["AList","AList.insertRec.match_1","AList.mk","Eq","List","List.NodupKeys","List.cons","List.nil","Sigma"],"value_dag_size":507,"value_refs":["AList","AList.insertRec.match_1","AList.mk","Eq","Eq.ndrec","Eq.refl","Eq.symm","List","List.NodupKeys","List.cons","List.nil","Sigma","_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1.eq_1","namespace":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1","reducibility":null,"statement_dag_size":91,"type_refs":["AList","AList.insertRec.match_1","AList.mk","Eq","List","List.NodupKeys","List.cons","List.nil","Sigma"],"value_dag_size":89,"value_refs":["AList","AList.insertRec.match_1","AList.mk","Eq.refl","List","List.NodupKeys","List.cons","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1.eq_2","namespace":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1","reducibility":null,"statement_dag_size":106,"type_refs":["AList","AList.insertRec.match_1","AList.mk","Eq","List","List.NodupKeys","List.cons","List.nil","Sigma"],"value_dag_size":102,"value_refs":["AList","AList.insertRec.match_1","AList.mk","Eq.refl","List","List.NodupKeys","List.cons","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1.splitter","namespace":"_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["AList","AList.mk","List","List.NodupKeys","List.cons","List.nil","Sigma"],"value_dag_size":1,"value_refs":["AList.insertRec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_assoc._simp_1_1","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_assoc","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_assoc._simp_1_2","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_assoc","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","or_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_assoc._simp_1_3","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_assoc","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":25,"value_refs":["And","Or","and_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_assoc._simp_1_4","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_assoc","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_comm_of_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_comm_of_disjoint","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.AList","name":"_private.Mathlib.Data.List.AList.0.AList.union_comm_of_disjoint._simp_1_2","namespace":"_private.Mathlib.Data.List.AList.0.AList.union_comm_of_disjoint","reducibility":null,"statement_dag_size":83,"type_refs":["And","DecidableEq","Eq","List","List.dlookup","List.instMembership","List.keys","List.kunion","Membership.mem","Not","Option","Option.some","Or","Sigma"],"value_dag_size":90,"value_refs":["And","DecidableEq","Eq","List","List.dlookup","List.dlookup_kunion_eq_some","List.instMembership","List.keys","List.kunion","Membership.mem","Not","Option","Option.some","Or","Sigma","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.Function.Injective.list_map.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.Function.Injective.list_map","reducibility":"abbrev","statement_dag_size":102,"type_refs":["Eq","List","List.cons","List.map","List.nil"],"value_dag_size":383,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.casesOn","List.cons","List.ctorIdx","List.map","List.nil","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.Function.Surjective.list_map.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.Function.Surjective.list_map","reducibility":"abbrev","statement_dag_size":47,"type_refs":["Exists.intro","Function.HasRightInverse","Function.RightInverse"],"value_dag_size":67,"value_refs":["Exists.casesOn","Exists.intro","Function.HasRightInverse","Function.RightInverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.Forall.imp._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.Forall.imp","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsPrefix.idxOf_le._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsPrefix.idxOf_le","reducibility":null,"statement_dag_size":47,"type_refs":["BEq","HAppend.hAppend","LE.le","LawfulBEq","List","List.idxOf","List.instAppend","Nat","instHAppendOfAppend","instLENat"],"value_dag_size":827,"value_refs":["BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","LawfulBEq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_append","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsPrefix.mem_iff_idxOf_lt_length._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsPrefix.mem_iff_idxOf_lt_length","reducibility":null,"statement_dag_size":61,"type_refs":["BEq","LE.le","LT.lt","LawfulBEq","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","instLENat","instLTNat"],"value_dag_size":451,"value_refs":["BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le","reducibility":null,"statement_dag_size":105,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":121,"value_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le","reducibility":null,"statement_dag_size":105,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":121,"value_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le","reducibility":null,"statement_dag_size":105,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":121,"value_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le","reducibility":null,"statement_dag_size":105,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":121,"value_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_add_length_le","reducibility":null,"statement_dag_size":64,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","LE.le","LawfulBEq","List","List.idxOf","List.instAppend","List.length","Nat","instAddNat","instHAdd","instHAppendOfAppend","instLENat"],"value_dag_size":1288,"value_refs":["BEq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","LawfulBEq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_append","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","List.length_append","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_le._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.IsSuffix.idxOf_le","reducibility":null,"statement_dag_size":73,"type_refs":["BEq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LawfulBEq","List","List.idxOf","List.instAppend","List.length","Nat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instSubNat"],"value_dag_size":1979,"value_refs":["And","And.casesOn","BEq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","LawfulBEq","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_append","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","List.length_append","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.Perm.disjoint_left._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.Perm.disjoint_left","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.Disjoint","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["List","List.Disjoint","List.disjoint_left","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.Perm.disjoint_right._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.Perm.disjoint_right","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.Disjoint","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["List","List.Disjoint","List.disjoint_right","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.Sublist.of_cons_of_ne.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.Sublist.of_cons_of_ne","reducibility":"abbrev","statement_dag_size":79,"type_refs":["List","List.Sublist","List.Sublist.cons","List.cons","Ne"],"value_dag_size":805,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Sublist","List.Sublist.casesOn","List.Sublist.cons","List.Sublist.cons_cons","List.Sublist.slnil","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Ne","absurd","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem","reducibility":null,"statement_dag_size":79,"type_refs":["And","Eq","Exists","HAppend.hAppend","List","List.instAppend","Or","instHAppendOfAppend"],"value_dag_size":84,"value_refs":["And","Eq","Exists","HAppend.hAppend","List","List.append_eq_append_iff","List.instAppend","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem._simp_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem","reducibility":null,"statement_dag_size":78,"type_refs":["And","Eq","Exists","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Or","instHAppendOfAppend"],"value_dag_size":83,"value_refs":["And","Eq","Exists","HAppend.hAppend","List","List.cons","List.cons_eq_append_iff","List.instAppend","List.nil","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem._simp_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.append_cons_inj_of_notMem","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","List","List.cons"],"value_dag_size":43,"value_refs":["And","Eq","List","List.cons","List.cons_eq_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.concat_eq_reverse_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.concat_eq_reverse_cons","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.concat","List.cons","List.reverse"],"value_dag_size":169,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.nil","List.reverse","List.reverse_cons","List.reverse_reverse","Not","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.cons_head?_tail.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.cons_head?_tail","reducibility":"abbrev","statement_dag_size":91,"type_refs":["List","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":134,"value_refs":["List","List.casesOn","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.cons_sublist_cons'._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.cons_sublist_cons'","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","Iff","List","List.Sublist","List.cons","Or"],"value_dag_size":1016,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HAppend.hAppend","HEq","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.Sublist","List.Sublist.of_cons_cons","List.cons","List.cons.noConfusion","List.cons_sublist_cons","List.cons_sublist_iff","List.instAppend","List.instMembership","List.sublist_cons_iff","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_true","heq_eq_eq","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.disjoint_pmap._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.disjoint_pmap","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Exists","List","List.instMembership","List.pmap","Membership.mem"],"value_dag_size":88,"value_refs":["Eq","Exists","List","List.instMembership","List.mem_pmap","List.pmap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.dropLast_append_getLast.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.dropLast_append_getLast","reducibility":"abbrev","statement_dag_size":85,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":156,"value_refs":["List","List.casesOn","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.dropLast_append_getLast?.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.dropLast_append_getLast?","reducibility":"abbrev","statement_dag_size":121,"type_refs":["Eq.refl","List","List.cons","List.getLast","List.getLast._proof_2","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":443,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.casesOn","List.cons","List.getLast","List.getLast._proof_2","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership","Option.some","Option.some.noConfusion","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":212,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_unsat","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":117,"value_refs":["Eq","Eq.mpr_prop","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_2","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":114,"value_refs":["Eq","Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_2","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.eq_cons_of_length_one._proof_2","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":50,"value_refs":["Eq","Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.eq_cons_of_length_one._proof_2","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","Fin.mk","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":198,"value_refs":["Eq","Fin.mk","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","Fin.mk","LT.lt","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":796,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.isLt","Fin.mk","Fin.mk.hcongr_3","Fin.val","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.intro_with_eq'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.eq_cons_of_length_one._proof_2","List.get","List.getElem_cons","List.getElem_cons.match_1","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_2","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_3","_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_6","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?._simp_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?._simp_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Option","Option.some"],"value_dag_size":28,"value_refs":["Eq","Option","Option.some","Option.some_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_mem_head?","reducibility":"abbrev","statement_dag_size":84,"type_refs":["List","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":126,"value_refs":["List","List.casesOn","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_10","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":132,"type_refs":["BEq","GetElem.getElem","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":145,"value_refs":["BEq","Eq.substr","GetElem.getElem","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_11","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":132,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","GetElem.getElem","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":778,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HSub.hSub","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.erase","List.erase_cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_10","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_3","congrArg","dite","dite_cond_eq_false","eagerReduce","eq_true","id","implies_congr","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_12","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":124,"type_refs":["BEq","GetElem.getElem","HAdd.hAdd","LT.lt","LawfulBEq","List","List.Perm","List.cons","List.erase","List.eraseIdx","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":10266,"value_refs":["BEq","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_true_of_eq","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_of_beq_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Perm","List.Perm.count","List.boole_getElem_le_count","List.cons","List.count","List.count_cons","List.count_erase","List.erase","List.eraseIdx","List.eraseIdx_cons_succ","List.erase_cons","List.getElem_cons","List.getElem_cons.match_1","List.instGetElemNatLtLength","List.length","List.length_cons","List.perm_iff_count","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_3","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_7","congrArg","dite","dite_cond_eq_false","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","heq_of_eq","id","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":76,"type_refs":["BEq","GetElem.getElem","LT.lt","LawfulBEq","List","List.Perm","List.cons","List.erase","List.eraseIdx","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":533,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff","Iff.mp","LT.lt","LawfulBEq","Lean.Grind.beq_eq_true_of_eq","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","List","List.Perm","List.cons","List.count","List.erase","List.eraseIdx","List.eraseIdx_cons_zero","List.erase_cons","List.getElem_cons","List.getElem_cons.match_1","List.instGetElemNatLtLength","List.length","List.perm_iff_count","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","True","True.intro","congrArg","dite","dite_cond_eq_true","eq_false","eq_self","eq_true","id","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":196,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":143,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":146,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_4","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":128,"type_refs":["BEq","GetElem.getElem","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":142,"value_refs":["BEq","Eq.substr","GetElem.getElem","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":128,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","GetElem.getElem","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.erase","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":604,"value_refs":["BEq","BEq.beq","Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","GetElem.getElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.erase","List.erase_cons","List.instGetElemNatLtLength","List.length","List.length_cons","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_6","congrArg","eagerReduce","eq_true","id","instAddNat","instDecidableEqBool","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":35,"value_refs":["LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_1","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_9","namespace":"_private.Mathlib.Data.List.Basic.0.List.erase_getElem","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":470,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_3","_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_8","congrArg","dite","dite_cond_eq_false","eq_true","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_cons_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_cons_iff","reducibility":null,"statement_dag_size":48,"type_refs":["And","Exists","Iff","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":884,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_cons_of_exists.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_cons_of_exists","reducibility":"abbrev","statement_dag_size":93,"type_refs":["And","And.intro","Exists","Exists.intro","List","List.instMembership","Membership.mem"],"value_dag_size":148,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_get.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_get","reducibility":"abbrev","statement_dag_size":160,"type_refs":["Exists","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":239,"value_refs":["Exists","Exists.casesOn","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_get.match_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_get","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Exists","Exists.intro","Fin","List","List.get","List.length"],"value_dag_size":89,"value_refs":["Exists","Exists.casesOn","Exists.intro","Fin","List","List.get","List.length"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":68,"value_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_iff_getElem","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem.match_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem","reducibility":"abbrev","statement_dag_size":234,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":475,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem.match_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_mem_iff_getElem","reducibility":"abbrev","statement_dag_size":160,"type_refs":["Exists","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":239,"value_refs":["Exists","Exists.casesOn","Exists.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.exists_of_length_succ.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.exists_of_length_succ","reducibility":"abbrev","statement_dag_size":88,"type_refs":["Eq","HAdd.hAdd","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":124,"value_refs":["Eq","HAdd.hAdd","List","List.casesOn","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem!._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem!","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","GetElem.getElem","GetElem?","GetElem?.getElem!","GetElem?.toGetElem","Inhabited","LawfulGetElem"],"value_dag_size":81,"value_refs":["Eq.symm","GetElem.getElem","GetElem?","GetElem?.getElem!","GetElem?.toGetElem","Inhabited","LawfulGetElem","getElem!_pos"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":640,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.none","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.ext_getElem?'","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","Max.max","Nat","Nat.instMax","Option","instLTNat"],"value_dag_size":1669,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Max.max","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instMax","Nat.max_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.none","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","eagerReduce","eq_false","eq_true","forall_congr","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.ext_get_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.ext_get_iff","reducibility":"abbrev","statement_dag_size":157,"type_refs":["And","And.intro","Eq","Fin.mk","LT.lt","List","List.get","List.length","Nat","instLTNat"],"value_dag_size":172,"value_refs":["And","And.casesOn","And.intro","Eq","Fin.mk","LT.lt","List","List.get","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Basic.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List.filterMap.match_1","Option","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":34,"value_refs":["Eq.refl","List.filterMap.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List.filterMap.match_1","Option","Option.none","Option.some","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","List.filterMap.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1.splitter","namespace":"_private.Mathlib.Data.List.Basic.0.List.filterMap.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["List.filterMap.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filterMap_eq_map_iff_forall_eq_some._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.filterMap_eq_map_iff_forall_eq_some","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","HAdd.hAdd","List","List.cons","List.filterMap","List.length","List.map","Nat","OfNat.ofNat","Option","Option.none","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":491,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HEq","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.filterMap","List.filterMap.match_1","List.filterMap.match_1.congr_eq_1","List.filterMap_cons","List.length","List.length_cons","List.length_filterMap_le","List.length_map","List.map","List.map_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.none","PUnit","Unit","congrArg","eagerReduce","heq_eq_eq","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filterMap_eq_map_iff_forall_eq_some._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.filterMap_eq_map_iff_forall_eq_some","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","HAdd.hAdd","List","List.cons","List.filterMap","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":321,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Exists","Exists.casesOn","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.filterMap","List.instMembership","List.length","List.length_filterMap_le","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","eagerReduce","eq_false","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.filter_attach._simp_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.filter_attach","reducibility":null,"statement_dag_size":43,"type_refs":["Bool","Eq","Function.comp","List","List.filter","List.map"],"value_dag_size":50,"value_refs":["Bool","Eq.symm","Function.comp","List","List.filter","List.filter_map","List.map"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext._simp_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext._simp_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext._simp_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.foldr_ext","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.forall_append._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.forall_append","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.forall_mem_iff_getElem._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.forall_mem_iff_getElem","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":68,"value_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_iff_getElem","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getElem_fin_surjective_iff._proof_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getElem_fin_surjective_iff","reducibility":null,"statement_dag_size":30,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail","reducibility":null,"statement_dag_size":64,"type_refs":["GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.nil","List.tail","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":331,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","GetElem.getElem","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_nil","List.nil","List.tail","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":135,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail","reducibility":null,"statement_dag_size":73,"type_refs":["GetElem.getElem","LT.lt","List","List.cons","List.instGetElemNatLtLength","List.instMembership","List.length","List.tail","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":455,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.dite_cond_eq_false'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","List.tail","List.tail_cons","Membership.mem","Nat","Nat.succ","Nat.succ_lt_succ_iff","Ne","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.getElem_mem_tail._proof_1_2","congrArg","dite","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1.splitter","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.getLast?.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?_append_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?_append_cons","reducibility":"abbrev","statement_dag_size":68,"type_refs":["List","List.cons","List.nil"],"value_dag_size":102,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?_append_of_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?_append_of_ne_nil","reducibility":"abbrev","statement_dag_size":61,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":91,"value_refs":["List","List.casesOn","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast?_eq_getLast_of_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast?_eq_getLast_of_ne_nil","reducibility":"abbrev","statement_dag_size":85,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":156,"value_refs":["List","List.casesOn","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","List","List.cons","List.getLastI.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":62,"value_refs":["Eq.refl","List","List.cons","List.getLastI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","List","List.cons","List.getLastI.match_1","List.nil","Unit"],"value_dag_size":66,"value_refs":["Eq.refl","List","List.cons","List.getLastI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","List","List.cons","List.getLastI.match_1","List.nil","Unit"],"value_dag_size":70,"value_refs":["Eq.refl","List","List.cons","List.getLastI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.eq_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","False","List","List.cons","List.getLastI.match_1","List.nil","Unit"],"value_dag_size":395,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","List","List.casesOn","List.cons","List.ctorIdx","List.getLastI._sparseCasesOn_1","List.getLastI._sparseCasesOn_1.else_eq","List.getLastI.match_1","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.splitter._sparseCasesOn_4","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.splitter","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1","reducibility":"abbrev","statement_dag_size":64,"type_refs":["Eq","False","List","List.cons","List.nil","Unit"],"value_dag_size":186,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","List","List.casesOn","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.splitter._sparseCasesOn_4","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.splitter._sparseCasesOn_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI.match_1.splitter","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD","reducibility":"abbrev","statement_dag_size":72,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":150,"value_refs":["List","List.casesOn","List.cons","List.ctorIdx","List.nil","Nat.hasNotBit","Unit","Unit.unit","_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD._sparseCasesOn_1_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":33,"type_refs":["HAppend.hAppend","List","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":22,"value_refs":["List","List.append_ne_nil_of_right_ne_nil","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_10","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":86,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":98,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_11","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":100,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":233,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_7","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_12","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":107,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_13","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":109,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":246,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.getElem_append._proof_1","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_5","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_14","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":260,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instAppend","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_5","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_15","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":21,"type_refs":["List","List.nil","Ne"],"value_dag_size":70,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Lean.Grind.eq_false_of_imp_eq_true","List","List.head_append._proof_2","List.isEmpty","List.nil","List.nil_of_isEmpty","Ne","eq_false","eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_16","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","HAppend.hAppend","List","List.append_ne_nil_of_right_ne_nil","List.cons","List.getLast","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":391,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.append_ne_nil_of_right_ne_nil","List.cons","List.getLast","List.getLast_append","List.getLast_append._proof_1","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_15","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_4","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_8","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_9","dite","eq_false","eq_true","id","instDecidableEqBool","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.append_ne_nil_of_right_ne_nil","List.getLast","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":290,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_ne_nil_of_right_ne_nil","List.getLast","List.getLast.hcongr_3","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_1","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":42,"type_refs":["HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":30,"value_refs":["List","List.append_ne_nil_of_right_ne_nil","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":66,"type_refs":["HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":58,"value_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.instAppend","List.nil","Ne","Not","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_4","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":60,"type_refs":["HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":51,"value_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.append_ne_nil_of_right_ne_nil","List.getLast_eq_getElem._proof_3","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":41,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":71,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_4","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil._proof_1_9","namespace":"_private.Mathlib.Data.List.Basic.0.List.getLast_append_of_right_ne_nil","reducibility":null,"statement_dag_size":35,"type_refs":["Bool","Bool.true","Eq","List","List.isEmpty","List.nil","Ne"],"value_dag_size":64,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.append_ne_nil_of_right_ne_nil","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.get_tail._proof_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.get_tail","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":923,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.head!_mem_head?.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.head!_mem_head?","reducibility":"abbrev","statement_dag_size":61,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":91,"value_refs":["List","List.casesOn","List.cons","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.head?_append_of_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.head?_append_of_ne_nil","reducibility":"abbrev","statement_dag_size":59,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":109,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.casesOn","List.cons","List.nil","Ne","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.idxOf_append_of_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.idxOf_append_of_mem","reducibility":null,"statement_dag_size":56,"type_refs":["BEq","Eq","HAppend.hAppend","LawfulBEq","List","List.idxOf","List.instAppend","List.instMembership","Membership.mem","Nat","instHAppendOfAppend"],"value_dag_size":267,"value_refs":["BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LawfulBEq","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_append","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.idxOf_append_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.idxOf_append_of_notMem","reducibility":null,"statement_dag_size":72,"type_refs":["BEq","Eq","HAdd.hAdd","HAppend.hAppend","LawfulBEq","List","List.idxOf","List.instAppend","List.instMembership","List.length","Membership.mem","Nat","Not","instAddNat","instHAdd","instHAppendOfAppend"],"value_dag_size":272,"value_refs":["BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LawfulBEq","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_append","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat","ite","ite_cond_eq_false","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_length_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_length_iff","reducibility":null,"statement_dag_size":45,"type_refs":["BEq","Eq","Iff","LawfulBEq","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","Not"],"value_dag_size":830,"value_refs":["And","And.casesOn","BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_zero_iff_eq_nil_or_head_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_zero_iff_eq_nil_or_head_eq","reducibility":null,"statement_dag_size":65,"type_refs":["BEq","Eq","Iff","LawfulBEq","List","List.cons","List.head?","List.idxOf","List.nil","Nat","OfNat.ofNat","Option","Option.some","Or","instOfNatNat"],"value_dag_size":802,"value_refs":["And","And.casesOn","BEq","BEq.beq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LawfulBEq","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_true_of_eq","Lean.Grind.cond_eq_ite","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_of_beq_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.head?","List.head?_cons","List.idxOf","List.idxOf_cons","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Option.some.inj","Or","Or.casesOn","True","True.intro","cond","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_true","false_or","id","instAddNat","instDecidableEqBool","instHAdd","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_zero_iff_head_eq._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.idxOf_eq_zero_iff_head_eq","reducibility":null,"statement_dag_size":60,"type_refs":["BEq","Eq","LawfulBEq","List","List.head?","List.idxOf","List.nil","Nat","OfNat.ofNat","Option","Option.some","Or","instOfNatNat"],"value_dag_size":66,"value_refs":["BEq","Eq","LawfulBEq","List","List.head?","List.idxOf","List.idxOf_eq_zero_iff_eq_nil_or_head_eq","List.nil","Nat","OfNat.ofNat","Option","Option.some","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_four.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_four","reducibility":"abbrev","statement_dag_size":75,"type_refs":["Eq","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":895,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_four.match_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_four","reducibility":"abbrev","statement_dag_size":191,"type_refs":["Eq","Exists","Exists.intro","List","List.cons","List.nil"],"value_dag_size":401,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","List","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_length_filter_add._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_length_filter_add","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Eq","List","List.countP","List.filter","List.length","Nat"],"value_dag_size":32,"value_refs":["Bool","Eq.symm","List","List.countP","List.countP_eq_length_filter","List.filter","List.length","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_succ_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_succ_iff","reducibility":null,"statement_dag_size":64,"type_refs":["And","Eq","Exists","HAdd.hAdd","Iff","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1093,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.casesOn","List.cons","List.length","List.length_cons","List.length_nil","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","false_or","forall_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_three.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_three","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Eq","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":660,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_three.match_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_three","reducibility":"abbrev","statement_dag_size":144,"type_refs":["Eq","Exists","Exists.intro","List","List.cons","List.nil"],"value_dag_size":257,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","List","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_11","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head","List.nil","Ne","Not"],"value_dag_size":111,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.getLast","List.head","List.nil","Ne","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_12","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head","List.nil","Ne","Not"],"value_dag_size":40,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast","List.getLast_cons_cons._proof_1","List.head","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_13","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.nil","Ne","Not"],"value_dag_size":35,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast","List.getLast_cons_cons._proof_2","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_14","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":144,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":631,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getLast","List.head","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_15","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":157,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":784,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons.match_1","List.getLast","List.head","List.length","List.nil","Nat","Nat.ToInt.lt_eq","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_16","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":132,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":366,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.getLast","List.head","List.length","List.nil","Nat","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_17","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Exists","Iff","List","List.cons","List.getLast","List.head","List.nil","Ne"],"value_dag_size":719,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","List","List.cons","List.ctorIdx","List.getLast","List.getLast.hcongr_3","List.getLast_cons_cons","List.getLast_cons_cons._proof_1","List.getLast_cons_cons._proof_2","List.getLast_singleton","List.head","List.head.hcongr_3","List.head_cons","List.nil","Ne","Not","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_3","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_4","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_5","cast","congr","congrArg","eq_false","eq_of_heq","eq_true","forall_congr","heq_of_eq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.cons","List.nil","Ne","Not"],"value_dag_size":95,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.nil","Ne","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":21,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":14,"value_refs":["List.getLast_cons_cons._proof_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":17,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":11,"value_refs":["List.getLast_cons_cons._proof_2","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":121,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":611,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":138,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":742,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.ToInt.lt_eq","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two'","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","List.nil","Nat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":345,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.length","List.nil","Nat","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.length_eq_two'._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHMul","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two","reducibility":"abbrev","statement_dag_size":63,"type_refs":["Eq","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":465,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.Internal.elimOffset","Nat.add","Nat.ctorIdx","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two.match_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eq_two","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Eq","Exists","Exists.intro","List","List.cons","List.nil"],"value_dag_size":165,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","List","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eraseIdx_add_one._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eraseIdx_add_one","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HAdd.hAdd","LT.lt","List","List.eraseIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":755,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.eraseIdx","List.length","List.length_eraseIdx","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.length_eraseP_add_one._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.length_eraseP_add_one","reducibility":null,"statement_dag_size":62,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","List","List.eraseP","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1014,"value_refs":["And","Bool","Bool.ctorIdx","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","False.elim","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.bool_eq_to_prop","Lean.Grind.em","Lean.Grind.forall_forall_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.any","List.any_eq","List.decidableBEx","List.eraseP","List.instMembership","List.length","List.length_eraseP","List.length_pos_of_mem","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","instAddNat","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.lookup_graph._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.lookup_graph","reducibility":null,"statement_dag_size":62,"type_refs":["BEq","Eq","List","List.instMembership","List.lookup","List.map","List.nil","Membership.mem","Option","Option.some","Prod","Prod.mk"],"value_dag_size":117,"value_refs":["BEq","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.instMembership","List.lookup","List.map","List.nil","List.not_mem_nil","Membership.mem","Not","Option","Option.some","Prod","Prod.mk","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.lookup_graph._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.lookup_graph","reducibility":null,"statement_dag_size":110,"type_refs":["BEq","Eq","LawfulBEq","List","List.cons","List.instMembership","List.lookup","List.map","Membership.mem","Option","Option.some","Prod","Prod.mk"],"value_dag_size":765,"value_refs":["BEq","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Iff","LawfulBEq","Lean.Grind._simp_2","Lean.Grind.beq_eq_true_of_eq","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.instMembership","List.lookup","List.lookup_cons","List.map","List.map_cons","List.mem_cons","Membership.mem","Not","Option","Option.some","Or","Or.casesOn","PUnit","PUnit.casesOn","Prod","Prod.mk","True","True.intro","Unit","_private.Mathlib.Data.List.Basic.0.List.filter.match_1.splitter","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.map_surjective_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.map_surjective_iff","reducibility":"abbrev","statement_dag_size":105,"type_refs":["Eq","Exists","Exists.intro","List","List.cons","List.map","List.nil"],"value_dag_size":673,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","False","False.elim","HEq","HEq.refl","List","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.map","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":48,"type_refs":["HSub.hSub","LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":41,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_10","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":59,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.getLast_eq_getElem._proof_3","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_9"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_11","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":45,"type_refs":["List","List.dropLast","List.getLast","List.instMembership","List.ne_nil_of_mem","Membership.mem","Ne"],"value_dag_size":300,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.ne_nil_of_mem","List.nil","List.not_mem_nil","Membership.mem","Ne","Not","Or","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":398,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":77,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":107,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":539,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not","instHAppendOfAppend"],"value_dag_size":173,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.instAppend","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not","True","cast","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":65,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.isEmpty","List.ne_nil_of_mem","List.nil","Membership.mem","Ne","Not"],"value_dag_size":207,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_concat_getLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.instMembership","List.isEmpty","List.ne_nil_of_mem","List.nil","Membership.mem","Not","True","cast","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":79,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instMembership","List.isEmpty","List.ne_nil_of_mem","List.nil","Membership.mem","Ne","Not"],"value_dag_size":79,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.instMembership","List.isEmpty","List.ne_nil_of_mem","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":262,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instMembership","List.length","List.length_dropLast","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_4","eagerReduce","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_9","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Ne","Not"],"value_dag_size":150,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.ctorIdx","List.getLast","List.instMembership","List.isEmpty","List.ne_nil_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Not","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_7","eq_false'","implies_congr","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?","reducibility":null,"statement_dag_size":48,"type_refs":["HSub.hSub","LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":41,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List","List.getLast","List.getLast?","List.instMembership","List.ne_nil_of_mem","Membership.mem","Ne","Not","Option","Option.some"],"value_dag_size":962,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray.branch","Lean.RArray.leaf","List","List.getLast","List.getLast?","List.getLast?_eq_getElem?","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_pos_of_mem","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast?._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD","reducibility":null,"statement_dag_size":48,"type_refs":["HSub.hSub","LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":41,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","List","List.getLast","List.getLastD","List.instMembership","List.ne_nil_of_mem","Membership.mem","Ne","Not"],"value_dag_size":1013,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_not","Lean.RArray.branch","Lean.RArray.leaf","List","List.getLast","List.getLast?","List.getLast?_eq_getElem?","List.getLastD","List.getLastD_eq_getLast?","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_pos_of_mem","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Option.getD_some","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLastD._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":84,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":100,"value_refs":["Eq.substr","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":87,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":532,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_1","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":103,"type_refs":["HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instAppend","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1086,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getLast?","List.getLast?_append","List.getLast?_eq_getElem?","List.instAppend","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.getD","Option.none","Option.or","Option.or_some","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_2","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":86,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":98,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":140,"type_refs":["HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instAppend","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":271,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_4","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?","reducibility":null,"statement_dag_size":49,"type_refs":["HAppend.hAppend","List","List.getLast?","List.instAppend","Membership.mem","Option","Option.instMembership","instHAppendOfAppend"],"value_dag_size":1155,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getLast?","List.getLast?_append","List.getLast?_eq_getElem?","List.instAppend","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.instMembership","Option.none","Option.not_mem_none","Option.or","Option.some","Option.some_or","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_1","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_append_of_mem_getLast?._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_cons","reducibility":"abbrev","statement_dag_size":84,"type_refs":["List","List.cons","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":126,"value_refs":["List","List.casesOn","List.cons","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_10","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":77,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_11","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":45,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":38,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Not","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_10"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_12","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_cons_cons._proof_2","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_13","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":89,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_14","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":206,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_11","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_15","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":67,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":83,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_16","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":192,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_12","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_17","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_18","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":97,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":750,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_13","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_19","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":108,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":738,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_15","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_20","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Exists","List","List.cons","List.getLast","List.getLast?","List.nil","Membership.mem","Not","Option","Option.instMembership"],"value_dag_size":2457,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.forall_true","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_exists","Lean.Grind.not_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.getLast","List.getLast?","List.getLast?_cons","List.getLast?_eq_getElem?","List.getLast_cons_cons","List.getLast_cons_cons._proof_1","List.getLast_cons_cons._proof_2","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_cons","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Option.getD_some","Option.instMembership","Option.mem_some","Option.some","Option.some.inj","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_10","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_11","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_12","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_13","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_15","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_18","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_19","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_pos","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":57,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":73,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","List","List.getLast","List.getLast?","List.nil","Membership.mem","Not","Option","Option.instMembership"],"value_dag_size":228,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","Lean.Grind.intro_with_eq","Lean.Grind.not_exists","Lean.Grind.not_true","List","List.getLast","List.getLast?","List.getLast?_nil","List.nil","Membership.mem","Not","Option","Option.instMembership","Option.none","Option.not_mem_none","True","True.casesOn","True.intro","congrArg","eq_false","eq_self","eq_true","forall_false","forall_prop_domain_congr","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_5","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":68,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_6","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":39,"type_refs":["HSub.hSub","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":29,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Not","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_7","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":66,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":82,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_8","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HSub.hSub","LT.lt","List.cons","List.length","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":194,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_6","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_9","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Exists","List","List.cons","List.getLast","List.getLast?","List.nil","Membership.mem","Not","Option","Option.instMembership"],"value_dag_size":388,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","False.elim","Iff","Lean.Grind.forall_true","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.getLast","List.getLast?","List.getLast?_cons","List.getLast?_nil","List.getLast_singleton","List.nil","Membership.mem","Not","Option","Option.getD","Option.getD_none","Option.instMembership","Option.mem_some","Option.none","Option.some","True","True.intro","_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast._proof_1_5","congrArg","eq_false","eq_false'","eq_true","forall_prop_domain_congr","id","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_getLast?_eq_getLast","reducibility":"abbrev","statement_dag_size":122,"type_refs":["List","List.cons","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":218,"value_refs":["List","List.casesOn","List.cons","List.getLast?","List.nil","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_head?_append_of_mem_head?._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_head?_append_of_mem_head?","reducibility":null,"statement_dag_size":49,"type_refs":["HAppend.hAppend","List","List.head?","List.instAppend","Membership.mem","Option","Option.instMembership","instHAppendOfAppend"],"value_dag_size":221,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.iff_eq","List","List.head?","List.head?_append","List.instAppend","Membership.mem","Not","Option","Option.instMembership","Option.mem_def","Option.or","Option.some","Option.some_or","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_map_of_injective.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_map_of_injective","reducibility":"abbrev","statement_dag_size":120,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List","List.instMembership","Membership.mem"],"value_dag_size":184,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.mem_take_iff_idxOf_lt._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.mem_take_iff_idxOf_lt","reducibility":null,"statement_dag_size":54,"type_refs":["BEq","Iff","LT.lt","LawfulBEq","List","List.idxOf","List.instMembership","List.length","List.take","Membership.mem","Nat","instLTNat"],"value_dag_size":1417,"value_refs":["And","And.casesOn","BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_take","List.take","Membership.mem","Min.min","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right","reducibility":null,"statement_dag_size":22,"type_refs":["Bool","List.Sublist","List.filter","List.nil"],"value_dag_size":134,"value_refs":["Bool","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Sublist","List.Sublist.refl","List.filter","List.filter_nil","List.nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right._proof_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right","reducibility":null,"statement_dag_size":53,"type_refs":["Bool","Bool.true","Eq","List","List.Sublist","List.cons","List.filter"],"value_dag_size":976,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","List","List.Sublist","List.Sublist.cons","List.cons","List.filter","List.filter_cons","List.sublist_cons_iff","List.sublist_filter_iff","Not","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","instDecidableEqBool","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.or_exists_of_exists_mem_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.or_exists_of_exists_mem_cons","reducibility":null,"statement_dag_size":54,"type_refs":["And","Exists","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":420,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Not","Or","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.replicate_right_inj'.match_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.replicate_right_inj'","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","List","List.instMembership","List.length","List.replicate","Membership.mem","Nat"],"value_dag_size":56,"value_refs":["And","Eq","List","List.eq_replicate_iff","List.instMembership","List.length","List.replicate","Membership.mem","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","List","List.instHasSubset","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["HasSubset.Subset","List","List.instHasSubset","List.instMembership","List.subset_def","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Basic.0.List.subset_singleton_iff","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.succ_idxOf_lt_length_of_mem_dropLast._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.succ_idxOf_lt_length_of_mem_dropLast","reducibility":null,"statement_dag_size":78,"type_refs":["BEq","HAdd.hAdd","LT.lt","LawfulBEq","List","List.dropLast","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1236,"value_refs":["BEq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsPrefix","List.IsPrefix.idxOf_eq_of_mem","List.IsPrefix.mem","List.dropLast","List.dropLast_prefix","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_dropLast","List.length_pos_of_mem","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Basic","name":"_private.Mathlib.Data.List.Basic.0.List.tail_append_singleton_of_ne_nil._proof_1_1","namespace":"_private.Mathlib.Data.List.Basic.0.List.tail_append_singleton_of_ne_nil","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.tail","Ne","instHAppendOfAppend"],"value_dag_size":185,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedDecidable","List","List.cons","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","List.tail","List.tail_append","Ne","Not","True","True.intro","eq_false","eq_true","id","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.backwards_induction._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.backwards_induction","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.nil","List.reverse","Ne","Not"],"value_dag_size":36,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.head_reverse._proof_1","List.nil","List.reverse","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.backwards_induction._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.backwards_induction","reducibility":null,"statement_dag_size":65,"type_refs":["List","List.getLast","List.head","List.instMembership","List.nil","List.reverse","Membership.mem","Ne"],"value_dag_size":420,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","List","List.getLast","List.head","List.head_reverse","List.head_reverse._proof_1","List.instMembership","List.mem_reverse","List.nil","List.reverse","Membership.mem","Ne","Not","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.IsChain.backwards_induction._proof_1_1","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons","reducibility":"abbrev","statement_dag_size":125,"type_refs":["List","List.IsChain","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"],"value_dag_size":196,"value_refs":["List","List.IsChain","List.casesOn","List.cons","List.head?","List.nil","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le","reducibility":null,"statement_dag_size":37,"type_refs":["LT.lt","LinearOrder","LinearOrder.toPartialOrder","List.IsChain","List.cons","List.nil","PartialOrder.toPreorder","Preorder.toLT"],"value_dag_size":104,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","LT.lt","LinearOrder","LinearOrder.toPartialOrder","List.IsChain","List.IsChain.singleton","List.cons","List.nil","Not","PartialOrder.toPreorder","Preorder.toLT","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le._simp_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","le_iff_lt_or_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le._simp_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_le","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","List","List.cons","List.nil","Ne","Not"],"value_dag_size":89,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.nil","Ne","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List","List.cons","List.nil","Ne","Not"],"value_dag_size":98,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.nil","Ne","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil","reducibility":null,"statement_dag_size":44,"type_refs":["List","List.IsChain","List.cons","List.head","List.nil","Ne"],"value_dag_size":727,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.IsChain","List.IsChain.casesOn","List.IsChain.cons_cons","List.IsChain.nil","List.IsChain.singleton","List.cons","List.ctorIdx","List.head","List.head.hcongr_3","List.head_cons","List.isChain_cons_cons","List.nil","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_2","_private.Mathlib.Data.List.Chain.0.List.IsChain.cons_of_ne_nil._proof_1_3","cast","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iff_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iff_mem","reducibility":null,"statement_dag_size":54,"type_refs":["And","Iff","List","List.instMembership","Membership.mem"],"value_dag_size":205,"value_refs":["And","Classical.byContradiction","Eq","Eq.symm","Eq.trans","False","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","List","List.instMembership","Membership.mem","Not","Or","True","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iff_mem_mem_tail._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iff_mem_mem_tail","reducibility":null,"statement_dag_size":60,"type_refs":["And","Iff","List","List.instMembership","List.tail","Membership.mem"],"value_dag_size":214,"value_refs":["And","Classical.byContradiction","Eq","Eq.symm","Eq.trans","False","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","List","List.instMembership","List.tail","Membership.mem","Not","Or","True","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp","reducibility":null,"statement_dag_size":14,"type_refs":["List.IsChain","List.nil"],"value_dag_size":64,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.IsChain","List.IsChain.nil","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp","reducibility":null,"statement_dag_size":20,"type_refs":["List.IsChain","List.cons","List.nil"],"value_dag_size":74,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.IsChain","List.IsChain.singleton","List.cons","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.imp_of_mem_tail_imp","reducibility":null,"statement_dag_size":105,"type_refs":["List","List.IsChain","List.cons","List.instMembership","List.tail","Membership.mem"],"value_dag_size":720,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.IsChain","List.cons","List.instMembership","List.isChain_cons_cons","List.mem_cons","List.tail","List.tail_cons","Membership.mem","Not","Or","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":23,"type_refs":["List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":78,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":68,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":28,"type_refs":["LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":50,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_2","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":50,"type_refs":["List","List.cons","List.head","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":353,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.forall_true","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.not_false","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.ctorIdx","List.head","List.head_cons","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Ne","Not","Or","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_2","congrArg","eq_false","eq_false'","eq_of_heq","eq_true","forall_prop_domain_congr","id","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_5","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":71,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_6","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":77,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_7","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":34,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_6","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_8","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":30,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":54,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_5","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_9","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.induction","reducibility":null,"statement_dag_size":107,"type_refs":["List","List.IsChain","List.cons","List.head","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":921,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_false","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.cons","List.ctorIdx","List.head","List.head_cons","List.instMembership","List.isChain_cons_cons","List.mem_cons","List.nil","Membership.mem","Ne","Not","Or","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_5","_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_6","congrArg","eq_false","eq_false'","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons","reducibility":null,"statement_dag_size":20,"type_refs":["List.IsChain","List.cons","List.nil"],"value_dag_size":74,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.IsChain","List.IsChain.singleton","List.cons","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":71,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons","reducibility":null,"statement_dag_size":30,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":54,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_2","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons","reducibility":null,"statement_dag_size":53,"type_refs":["List","List.IsChain","List.cons","List.head","List.nil","Ne"],"value_dag_size":330,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.forall_true","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.not_false","List","List.IsChain","List.cons","List.ctorIdx","List.head","List.head_cons","List.isChain_cons_cons","List.nil","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.IsChain.isChain_cons._proof_1_2","congrArg","eq_false","eq_false'","eq_of_heq","eq_true","forall_prop_domain_congr","id","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq._proof_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq","reducibility":null,"statement_dag_size":36,"type_refs":["False","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":399,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_nonneg","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq","reducibility":null,"statement_dag_size":51,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.IsChain.iterate_eq_of_apply_eq._proof_2","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.iterate_eq_of_apply_eq","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_dropLast._proof_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_dropLast","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.dropLast","List.nil","Ne","Not"],"value_dag_size":104,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.intro_with_eq","Lean.Grind.not_not","List","List.dropLast","List.dropLast_nil","List.nil","Ne","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_dropLast.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_dropLast","reducibility":"abbrev","statement_dag_size":134,"type_refs":["List","List.IsChain","List.cons","List.dropLast","List.nil","Ne"],"value_dag_size":377,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.IsChain","List.casesOn","List.cons","List.dropLast","List.nil","Ne","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_head_of_append.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.rel_getLast_head_of_append","reducibility":"abbrev","statement_dag_size":200,"type_refs":["HAppend.hAppend","List","List.IsChain","List.cons","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":555,"value_refs":["Eq","Eq.refl","False","False.elim","HAppend.hAppend","List","List.IsChain","List.casesOn","List.cons","List.instAppend","List.nil","Ne","absurd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.IsChain.tail._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.IsChain.tail","reducibility":null,"statement_dag_size":24,"type_refs":["List","List.IsChain","List.tail"],"value_dag_size":403,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.nestedProof","List","List.IsChain","List.IsChain.casesOn","List.IsChain.cons_cons","List.IsChain.nil","List.IsChain.singleton","List.cons","List.nil","List.tail","List.tail_cons","List.tail_nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","List","List.cons","List.nil","Not"],"value_dag_size":71,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":192,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_1","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen","reducibility":null,"statement_dag_size":30,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":54,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_2","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_5","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen","reducibility":null,"statement_dag_size":79,"type_refs":["And","Eq","Exists","List","List.IsChain","List.cons","List.cons_ne_nil","List.getLast","List.head","List.nil","Not"],"value_dag_size":661,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","False.elim","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.exists_and_left","Lean.Grind.forall_forall_or","Lean.Grind.forall_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_false","List","List.IsChain","List.cons","List.cons_ne_nil","List.ctorIdx","List.getLast","List.head","List.head_cons","List.nil","Ne","Not","Or","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_2","congrArg","eq_false'","eq_of_heq","eq_true","false_or","forall_congr","forall_prop_domain_congr","id","implies_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_not_getElem_of_not_isChain._proof_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_not_getElem_of_not_isChain","reducibility":null,"statement_dag_size":47,"type_refs":["False","HAdd.hAdd","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":411,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.natCast_add","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.exists_not_getElem_of_not_isChain._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.exists_not_getElem_of_not_isChain","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.IsChain","List.instGetElemNatLtLength","List.isChain_iff_getElem._proof_2","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["GetElem.getElem","HAdd.hAdd","LT.lt","List","List.IsChain","List.instGetElemNatLtLength","List.isChain_iff_getElem","List.isChain_iff_getElem._proof_2","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_append._simp_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_append","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","List","List.IsChain","List.cons","List.head?","Membership.mem","Option","Option.instMembership"],"value_dag_size":53,"value_refs":["And","List","List.IsChain","List.cons","List.head?","List.isChain_cons","Membership.mem","Option","Option.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_append._simp_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_append","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_append.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_append","reducibility":"abbrev","statement_dag_size":56,"type_refs":["List","List.cons","List.nil"],"value_dag_size":85,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":81,"type_refs":["Exists","Iff","List","List.IsChain","List.attachWith","List.instMembership","List.nil","Membership.mem","Subtype","Subtype.mk"],"value_dag_size":289,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.nil","List.attachWith","List.attachWith_nil","List.instMembership","List.nil","Membership.mem","Not","Subtype","Subtype.mk","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_10","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":186,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_self","List.nil","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_11","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":200,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_of_mem","List.nil","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_13","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":109,"type_refs":["Exists","Lean.Grind.nestedProof","List","List.IsChain","List.cons","Subtype","Subtype.mk"],"value_dag_size":142,"value_refs":["Exists","Exists.intro","Lean.Grind.nestedProof","List","List.IsChain","List.IsChain.cons_cons","List.cons","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_14","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":187,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_15","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":193,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_self","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_16","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":209,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_of_mem","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_17","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":88,"type_refs":["Lean.Grind.nestedProof","List","List.IsChain","List.cons","Subtype","Subtype.mk"],"value_dag_size":88,"value_refs":["Lean.Grind.nestedProof","List","List.IsChain","List.IsChain.cons_cons","List.cons","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_18","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":152,"type_refs":["Eq","Exists","Lean.Grind.nestedProof","List","List.IsChain","List.attachWith","List.cons","List.instMembership","Membership.mem","Not","Subtype","Subtype.mk"],"value_dag_size":198,"value_refs":["Eq","Eq.symm","Eq.trans","Exists","False","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.nestedProof","List","List.IsChain","List.attachWith","List.cons","List.instMembership","Membership.mem","Not","Subtype","Subtype.mk","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_19","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":179,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":42,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":67,"value_refs":["Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_of_mem","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_20","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":185,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_self","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_21","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":198,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.mem_cons_of_mem","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_22","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":135,"type_refs":["Exists","Iff","List","List.IsChain","List.attachWith","List.cons","List.instMembership","Membership.mem","Subtype","Subtype.mk"],"value_dag_size":13100,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","False.casesOn","False.elim","HEq","HEq.refl","HEq.trans","Iff","Lean.Grind.abstractFn","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","List","List.IsChain","List.IsChain.casesOn","List.IsChain.cons_cons","List.IsChain.nil","List.IsChain.singleton","List.attachWith","List.attachWith.hcongr_4","List.attachWith_cons","List.attachWith_nil","List.cons","List.cons.inj","List.cons.noConfusion","List.ctorIdx","List.instMembership","List.isChain_cons_cons","List.mem_cons_of_mem","List.mem_cons_self","List.nil","Membership.mem","Not","Or","Or.casesOn","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_10","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_11","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_13","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_14","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_15","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_16","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_17","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_18","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_19","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_20","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_21","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_3","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_4","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_5","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_6","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_7","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_8","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_9","cast","congrArg","eq_false","eq_false'","eq_of_heq","eq_true","forall_congr","forall_not_of_not_exists","heq_eq_eq","heq_of_eq","id","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":27,"type_refs":["List.IsChain","List.nil","Subtype"],"value_dag_size":24,"value_refs":["List.IsChain.nil","Subtype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":41,"type_refs":["List.IsChain","List.cons","List.nil","Subtype","Subtype.mk"],"value_dag_size":35,"value_refs":["List.IsChain.singleton","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_5","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":151,"type_refs":["Exists","Iff","Lean.Grind.nestedProof","List","List.IsChain","List.attachWith","List.cons","List.instMembership","Membership.mem","Subtype","Subtype.mk","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2"],"value_dag_size":299,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Iff","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.nestedProof","List","List.IsChain","List.attachWith","List.cons","List.instMembership","Membership.mem","Subtype","Subtype.mk","True","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","eq_true","forall_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_6","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":50,"type_refs":["Exists","List.IsChain","List.nil","Subtype","Subtype.mk"],"value_dag_size":47,"value_refs":["Exists","List.IsChain.nil","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_7","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":168,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.nil","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_8","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":56,"type_refs":["Exists","List.IsChain","List.cons","List.nil","Subtype","Subtype.mk"],"value_dag_size":50,"value_refs":["Exists","List.IsChain.singleton","Subtype","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_9","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":180,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Lean.Grind.abstractFn","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.nil","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2","cast","congrArg","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons","reducibility":"abbrev","statement_dag_size":106,"type_refs":["And","And.intro","List","List.IsChain","List.head?","Membership.mem","Option","Option.instMembership"],"value_dag_size":132,"value_refs":["And","And.casesOn","And.intro","List","List.IsChain","List.head?","Membership.mem","Option","Option.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_append_singleton_iff_forall₂._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_append_singleton_iff_forall₂","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.Forall₂","List.IsChain","List.dropLast","List.tail"],"value_dag_size":36,"value_refs":["List","List.Forall₂","List.IsChain","List.dropLast","List.isChain_iff_forall₂","List.tail","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_eq_iff_eq_replicate._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_eq_iff_eq_replicate","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.IsChain","List.head?","List.length","List.replicate","Membership.mem","Option","Option.instMembership"],"value_dag_size":52,"value_refs":["Eq","List","List.IsChain","List.head?","List.isChain_eq_iff_eq_replicate","List.length","List.replicate","Membership.mem","Option","Option.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._proof_1_6","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Exists","Iff","List","List.IsChain","List.cons","List.nil","Or"],"value_dag_size":1569,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","List","List.IsChain","List.cons","List.nil","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","False","List","List.cons","List.nil"],"value_dag_size":27,"value_refs":["Eq","List","List.cons","List.cons_ne_nil","List.nil","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":38,"type_refs":["And","Eq","List","List.cons"],"value_dag_size":43,"value_refs":["And","Eq","List","List.cons","List.cons_eq_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","True"],"value_dag_size":20,"value_refs":["Eq","Exists","eq_true","exists_eq'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff._simp_1_5","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff_forall₂._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_iff_forall₂","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.Forall₂","List.IsChain","List.dropLast","List.tail"],"value_dag_size":36,"value_refs":["List","List.Forall₂","List.IsChain","List.dropLast","List.isChain_iff_forall₂","List.tail","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_of_isChain_cons_pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_of_isChain_cons_pmap","reducibility":null,"statement_dag_size":59,"type_refs":["Exists"],"value_dag_size":196,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedProof","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap","reducibility":null,"statement_dag_size":45,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":210,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Not","Or","True","True.intro","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons","reducibility":null,"statement_dag_size":20,"type_refs":["Eq"],"value_dag_size":80,"value_refs":["Eq","Eq.rec","Eq.trans","HEq","HEq.refl","True","eq_of_heq","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.instMembership","Membership.mem"],"value_dag_size":82,"value_refs":["Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","List","List.instMembership","Membership.mem","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons","reducibility":null,"statement_dag_size":107,"type_refs":["Exists","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":1103,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","False","HEq","HEq.refl","Iff","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons._proof_1_1","_private.Mathlib.Data.List.Chain.0.List.isChain_cons_pmap_of_isChain_cons._proof_1_2","eq_of_heq","eq_true","forall_congr","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_split._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_cons_split","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","instHAppendOfAppend"],"value_dag_size":42,"value_refs":["Eq.symm","HAppend.hAppend","List","List.cons","List.cons_append","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_eq_iff_eq_replicate._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_eq_iff_eq_replicate","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.IsChain","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.IsChain","List.cons","List.isChain_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_eq_iff_eq_replicate._simp_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_eq_iff_eq_replicate","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten._simp_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":47,"value_refs":["And","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten._simp_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_flatten","reducibility":"abbrev","statement_dag_size":119,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Not"],"value_dag_size":215,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_iff_forall_rel_of_append_cons_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_iff_forall_rel_of_append_cons_cons","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","HAppend.hAppend","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":102,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.IsChain","List.IsChain.nil","List.cons","List.instAppend","List.nil","Not","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_iff_forall_rel_of_append_cons_cons._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_iff_forall_rel_of_append_cons_cons","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","HAppend.hAppend","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":113,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.IsChain","List.IsChain.singleton","List.cons","List.instAppend","List.nil","Not","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_isInfix.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_isInfix","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":74,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_map._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_map","reducibility":null,"statement_dag_size":38,"type_refs":["Iff","List.IsChain","List.map","List.nil"],"value_dag_size":181,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.nil","List.map","List.map_nil","List.nil","Not","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_map._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_map","reducibility":null,"statement_dag_size":44,"type_refs":["Iff","List.IsChain","List.cons","List.map","List.nil"],"value_dag_size":229,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.singleton","List.cons","List.map","List.map_cons","List.map_nil","List.nil","Not","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_map._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_map","reducibility":null,"statement_dag_size":60,"type_refs":["Iff","List","List.IsChain","List.cons","List.map"],"value_dag_size":323,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.IsChain","List.cons","List.isChain_cons_cons","List.map","List.map_cons","Not","congrArg","forall_congr","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_of_isChain_pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_of_isChain_pmap","reducibility":null,"statement_dag_size":59,"type_refs":["Exists"],"value_dag_size":196,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedProof","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pair._simp_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pair","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","List.IsChain","List.cons","List.nil","True"],"value_dag_size":27,"value_refs":["List.IsChain","List.IsChain.singleton","List.cons","List.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pair._simp_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pair","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.IsChain","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.IsChain","List.cons","List.isChain_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":73,"type_refs":["Exists","Iff","List","List.IsChain","List.instMembership","List.nil","List.pmap","Membership.mem"],"value_dag_size":289,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.nil","List.instMembership","List.nil","List.pmap","List.pmap_nil","List.pmap_nil._proof_1","Membership.mem","Not","True","True.intro","congrArg","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":31,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":70,"value_refs":["And","And.left","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":42,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":70,"value_refs":["And","And.right","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_4","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":79,"type_refs":["Exists","Iff","List","List.IsChain","List.cons","List.instMembership","List.nil","List.pmap","Membership.mem"],"value_dag_size":420,"value_refs":["And","And.left","And.right","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","HEq.trans","Iff","Iff.mp","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.singleton","List.cons","List.forall_mem_cons","List.instMembership","List.nil","List.pmap","List.pmap_cons","List.pmap_nil","List.pmap_nil._proof_1","Membership.mem","Not","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_2","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_3","congrArg","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_5","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":76,"value_refs":["And","And.left","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_6","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":49,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":76,"value_refs":["And","And.right","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_7","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":81,"value_refs":["And","And.left","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_6"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_8","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":46,"type_refs":["List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":81,"value_refs":["And","And.right","Iff.mp","Lean.Grind.nestedProof","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_6"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_9","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap","reducibility":null,"statement_dag_size":142,"type_refs":["Exists","Iff","List","List.IsChain","List.cons","List.instMembership","List.pmap","Membership.mem"],"value_dag_size":1924,"value_refs":["And","And.casesOn","And.left","And.right","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","HEq.trans","Iff","Iff.mp","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","List","List.IsChain","List.cons","List.forall_mem_cons","List.instMembership","List.isChain_cons_cons","List.pmap","List.pmap_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_5","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_6","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_7","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap._proof_1_8","congrArg","eq_false","eq_of_heq","eq_true","forall_congr","forall_not_of_not_exists","id","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap_of_isChain._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap_of_isChain","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.instMembership","Membership.mem"],"value_dag_size":82,"value_refs":["Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","List","List.instMembership","Membership.mem","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap_of_isChain._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_pmap_of_isChain","reducibility":null,"statement_dag_size":96,"type_refs":["Exists","List","List.instMembership","Membership.mem"],"value_dag_size":376,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","List","List.instMembership","Membership.mem","Not","True","True.intro","_private.Mathlib.Data.List.Chain.0.List.isChain_pmap_of_isChain._proof_1_1","eq_true","forall_congr","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel","reducibility":null,"statement_dag_size":26,"type_refs":["List.IsChain","List.replicate","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":111,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.IsChain","List.IsChain.nil","List.nil","List.replicate","List.replicate_zero","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel","reducibility":null,"statement_dag_size":26,"type_refs":["List.IsChain","List.replicate","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":166,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","List","List.IsChain","List.IsChain.singleton","List.cons","List.nil","List.replicate","List.replicate_succ","List.replicate_zero","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_replicate_of_rel","reducibility":null,"statement_dag_size":57,"type_refs":["HAdd.hAdd","List.IsChain","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":299,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.iff_eq","Lean.RArray.leaf","List","List.IsChain","List.cons","List.isChain_cons_cons","List.replicate","List.replicate_succ","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_reverse","reducibility":null,"statement_dag_size":27,"type_refs":["Iff","List.IsChain","List.nil","List.reverse"],"value_dag_size":159,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","List","List.IsChain","List.IsChain.nil","List.nil","List.reverse","List.reverse_nil","Not","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_reverse._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_reverse","reducibility":null,"statement_dag_size":33,"type_refs":["Iff","List.IsChain","List.cons","List.nil","List.reverse"],"value_dag_size":374,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.singleton","List.cons","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.reverse","List.reverse_cons","List.reverse_nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","True.intro","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_split._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_split","reducibility":null,"statement_dag_size":47,"type_refs":["And","HAppend.hAppend","Iff","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":309,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.singleton","List.cons","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Not","OfNat.ofNat","Or","PLift","PLift.up","True","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_split._proof_1_2","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_split","reducibility":null,"statement_dag_size":51,"type_refs":["And","HAppend.hAppend","Iff","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":720,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Iff","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsChain","List.IsChain.singleton","List.cons","List.cons_append","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isChain_cons_cons","List.nil","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.List.isChain_split._proof_1_3","namespace":"_private.Mathlib.Data.List.Chain.0.List.isChain_split","reducibility":null,"statement_dag_size":73,"type_refs":["And","HAppend.hAppend","Iff","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":767,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.cons","List.cons_append","List.instAppend","List.isChain_cons_cons","List.nil","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_true","forall_congr","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.WellFounded.listPairwise_reverse_compl._proof_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.WellFounded.listPairwise_reverse_compl","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LT.lt","List","List.length","List.nil","List.reverse","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":254,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","List","List.length","List.length_nil","List.length_reverse","List.nil","List.reverse","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Chain","name":"_private.Mathlib.Data.List.Chain.0.WellFoundedRelation.asymmetricₙ.match_1_1","namespace":"_private.Mathlib.Data.List.Chain.0.WellFoundedRelation.asymmetricₙ","reducibility":"abbrev","statement_dag_size":118,"type_refs":["List","List.IsChain","List.cons","List.nil","Ne","WellFoundedRelation","WellFoundedRelation.rel"],"value_dag_size":253,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.IsChain","List.casesOn","List.cons","List.nil","Ne","WellFoundedRelation","WellFoundedRelation.rel","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ChainOfFn","name":"_private.Mathlib.Data.List.ChainOfFn.0.List.isChain_ofFn._simp_1_1","namespace":"_private.Mathlib.Data.List.ChainOfFn.0.List.isChain_ofFn","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.IsChain","List.instGetElemNatLtLength","List.isChain_iff_getElem._proof_2","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["GetElem.getElem","HAdd.hAdd","LT.lt","List","List.IsChain","List.instGetElemNatLtLength","List.isChain_iff_getElem","List.isChain_iff_getElem._proof_2","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Count","name":"_private.Mathlib.Data.List.Count.0.List.countP_erase._proof_1_1","namespace":"_private.Mathlib.Data.List.Count.0.List.countP_erase","reducibility":null,"statement_dag_size":96,"type_refs":["And","BEq","Bool","Bool.true","Eq","HSub.hSub","LawfulBEq","List","List.countP","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","Membership.mem","Nat","OfNat.ofNat","instDecidableAnd","instDecidableEqBool","instHSub","instOfNatNat","instSubNat","ite"],"value_dag_size":1908,"value_refs":["And","And.casesOn","BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.countP","List.countP_eq_length_filter","List.erase","List.erase_filter","List.filter","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","List.length_erase","List.length_pos_of_mem","List.mem_filter","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instDecidableAnd","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Count","name":"_private.Mathlib.Data.List.Count.0.List.countP_lt_length_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Count.0.List.countP_lt_length_iff","reducibility":null,"statement_dag_size":29,"type_refs":["And","Eq","LE.le","LT.lt","Nat","Ne","instLENat","instLTNat"],"value_dag_size":31,"value_refs":["And","LE.le","LT.lt","Nat","Nat.lt_iff_le_and_ne","Ne","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Count","name":"_private.Mathlib.Data.List.Count.0.List.countP_lt_length_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Count.0.List.countP_lt_length_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Bool","Eq","LE.le","List","List.countP","List.length","Nat","True","instLENat"],"value_dag_size":32,"value_refs":["Bool","LE.le","List","List.countP","List.countP_le_length","List.length","Nat","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Count","name":"_private.Mathlib.Data.List.Count.0.List.count_diff._simp_1_3","namespace":"_private.Mathlib.Data.List.Count.0.List.count_diff","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Count","name":"_private.Mathlib.Data.List.Count.0.List.count_diff.match_1_1","namespace":"_private.Mathlib.Data.List.Count.0.List.count_diff","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Chain._simp_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Chain","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Nodup.nontrivial_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Nodup.nontrivial_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.succ","Nat.succ_le_iff","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":32,"type_refs":["Cycle","Cycle.Subsingleton","Cycle.length","Eq","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":34,"value_refs":["Cycle","Cycle.Subsingleton","Cycle.length","Cycle.length_subsingleton_iff","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["Eq","LE.le","LT.lt","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","le_iff_lt_or_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.lt_add_one_iff","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["Eq","List","List.length","List.length_eq_zero_iff","List.nil","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Exists","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":45,"value_refs":["Eq","Exists","List","List.cons","List.length","List.length_eq_one_iff","List.nil","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr._simp_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.congr","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","False","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":21,"value_refs":["LT.lt","Nat","Nat.not_lt_zero","OfNat.ofNat","eq_false","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.nodup._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.nodup","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["Eq","List","List.length","List.length_eq_zero_iff","List.nil","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.nodup._simp_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.Subsingleton.nodup","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","Membership.mem","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["And","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","List.pairwise_append","Membership.mem","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","IsEmpty","True"],"value_dag_size":22,"value_refs":["IsEmpty","IsEmpty.forall_iff","True","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","List.Pairwise","List.nil","True"],"value_dag_size":20,"value_refs":["List.Pairwise","List.Pairwise.nil","List.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise._simp_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_iff_pairwise","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_map._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_map","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HAppend.hAppend","List","List.concat","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":41,"value_refs":["Eq.symm","HAppend.hAppend","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.nil","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_map._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_map","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.concat","List.map"],"value_dag_size":43,"value_refs":["Eq.symm","List","List.concat","List.map","List.map_concat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_of_pairwise._proof_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_of_pairwise","reducibility":null,"statement_dag_size":103,"type_refs":["Cycle","Cycle.instMembership","Cycle.ofList","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","instHAppendOfAppend"],"value_dag_size":417,"value_refs":["Classical.byContradiction","Cycle","Cycle.instMembership","Cycle.ofList","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Not","Or","True","True.intro","eq_false","eq_of_heq","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_of_pairwise._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.chain_of_pairwise","reducibility":null,"statement_dag_size":104,"type_refs":["Cycle","Cycle.instMembership","Cycle.ofList","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":351,"value_refs":["Classical.byContradiction","Cycle","Cycle.instMembership","Cycle.ofList","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Iff","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Not","Or","True","True.intro","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1","reducibility":null,"statement_dag_size":146,"type_refs":["Cycle.decidableNontrivialCoe.match_1","Eq","List","List.cons","List.nil","Unit"],"value_dag_size":471,"value_refs":["Cycle.decidableNontrivialCoe.match_1","Eq","Eq.ndrec","Eq.refl","Eq.symm","List","List.cons","List.nil","Unit","Unit.unit","_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Cycle.decidableNontrivialCoe.match_1","Eq","List","List.cons","List.nil","Unit","Unit.unit"],"value_dag_size":51,"value_refs":["Cycle.decidableNontrivialCoe.match_1","Eq.refl","List","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1","reducibility":null,"statement_dag_size":58,"type_refs":["Cycle.decidableNontrivialCoe.match_1","Eq","List","List.cons","List.nil","Unit"],"value_dag_size":56,"value_refs":["Cycle.decidableNontrivialCoe.match_1","Eq.refl","List","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1","reducibility":null,"statement_dag_size":66,"type_refs":["Cycle.decidableNontrivialCoe.match_1","Eq","List","List.cons","List.nil","Unit"],"value_dag_size":62,"value_refs":["Cycle.decidableNontrivialCoe.match_1","Eq.refl","List","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1.splitter","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.decidableNontrivialCoe.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["Cycle.decidableNontrivialCoe.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.length_nontrivial._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.length_nontrivial","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.length_nontrivial._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.length_nontrivial","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.next_reverse_eq_prev'._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.next_reverse_eq_prev'","reducibility":null,"statement_dag_size":78,"type_refs":["Cycle","Cycle.Nodup","Cycle.instMembership","Cycle.mem_reverse_iff","Cycle.next","Cycle.nodup_reverse_iff","Cycle.prev","Cycle.reverse","DecidableEq","Eq","Iff.mpr","Membership.mem"],"value_dag_size":86,"value_refs":["Cycle","Cycle.Nodup","Cycle.instMembership","Cycle.mem_reverse_iff","Cycle.next","Cycle.nodup_reverse_iff","Cycle.prev","Cycle.prev_reverse_eq_next","Cycle.reverse","DecidableEq","Eq.symm","Iff.mpr","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.next_reverse_eq_prev._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.next_reverse_eq_prev","reducibility":null,"statement_dag_size":78,"type_refs":["Cycle","Cycle.Nodup","Cycle.instMembership","Cycle.mem_reverse_iff","Cycle.next","Cycle.nodup_reverse_iff","Cycle.prev","Cycle.reverse","DecidableEq","Eq","Iff.mpr","Membership.mem"],"value_dag_size":86,"value_refs":["Cycle","Cycle.Nodup","Cycle.instMembership","Cycle.mem_reverse_iff","Cycle.next","Cycle.nodup_reverse_iff","Cycle.prev","Cycle.prev_reverse_eq_next","Cycle.reverse","DecidableEq","Eq.symm","Iff.mpr","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","True","instLENat","instOfNatNat"],"value_dag_size":21,"value_refs":["LE.le","Nat","Nat.zero_le","OfNat.ofNat","eq_true","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff._simp_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff._simp_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.nontrivial_coe_nodup_iff","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.Cycle.subsingleton_reverse_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.Cycle.subsingleton_reverse_iff","reducibility":null,"statement_dag_size":32,"type_refs":["Cycle","Cycle.Subsingleton","Cycle.length","Eq","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":34,"value_refs":["Cycle","Cycle.Subsingleton","Cycle.length","Cycle.length_subsingleton_iff","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","List","List.cons","List.nextOr.match_1","List.nil"],"value_dag_size":73,"value_refs":["Eq.refl","List","List.cons","List.nextOr.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","List","List.cons","List.nextOr.match_1","List.nil"],"value_dag_size":78,"value_refs":["Eq.refl","List","List.cons","List.nextOr.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","List","List.cons","List.nextOr.match_1","List.nil"],"value_dag_size":84,"value_refs":["Eq.refl","List","List.cons","List.nextOr.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1.splitter","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr.match_1","reducibility":"abbrev","statement_dag_size":63,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.nextOr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","reducibility":null,"statement_dag_size":80,"type_refs":["DecidableEq","HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":96,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","GetElem?.getElem?","LT.lt","List","List.cons","List.idxOf","List.instGetElem?NatLtLength","List.length","Nat","Option","Option.some","instBEqOfDecidableEq","instLTNat"],"value_dag_size":392,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.nestedDecidable","List","List.cons","List.getElem?_cons","List.idxOf","List.idxOf_cons","List.instGetElem?NatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.some","True","True.intro","cond","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instDecidableEqNat","instHAdd","instHSub","instLTNat","instLawfulBEq","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","List","List.cons","List.dropLast","List.instMembership","Membership.mem","Not"],"value_dag_size":183,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.dropLast","List.dropLast_cons_cons","List.instMembership","List.mem_cons","Membership.mem","Not","Or","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast.match_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","reducibility":"abbrev","statement_dag_size":111,"type_refs":["List","List.cons","List.dropLast","List.instMembership","List.nil","Membership.mem"],"value_dag_size":205,"value_refs":["List","List.casesOn","List.cons","List.dropLast","List.instMembership","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast","reducibility":null,"statement_dag_size":59,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":46,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":230,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_true_left","List","List.cons","List.dropLast","List.dropLast_cons_cons","List.getLast","List.instMembership","List.mem_cons","List.nil","Membership.mem","Ne","Not","Or","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":106,"value_refs":["Eq","False","HEq","Lean.Grind.nestedProof","List","List.cons","List.getLast._proof_2","List.getLast_eq_getElem._proof_3","List.nil","List.rec"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","List","List.cons","List.dropLast","List.getLast","List.getLast._proof_2","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":533,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.trans","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.dropLast","List.dropLast_cons_cons","List.getLast","List.getLast._proof_2","List.getLast_cons_cons","List.getLast_cons_cons._proof_1","List.getLast_cons_cons._proof_2","List.instMembership","List.mem_cons","List.nil","List.rec","Membership.mem","Ne","Not","Or","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast.match_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_getLast_of_notMem_dropLast","reducibility":"abbrev","statement_dag_size":174,"type_refs":["List","List.cons","List.dropLast","List.getLast","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":330,"value_refs":["List","List.casesOn","List.cons","List.dropLast","List.getLast","List.instMembership","List.nil","Membership.mem","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableEq","Eq","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":426,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.nextOr","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_succ_lt_succ","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_11","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","HAdd.hAdd","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":152,"value_refs":["Bool","Bool.false","Bool.true","DecidableEq","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_12","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","HAdd.hAdd","LT.lt","List","List.dropLast","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":612,"value_refs":["Bool","Bool.false","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.idxOf","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.nextOr","List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_11","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_13","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":84,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":100,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_14","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","HAdd.hAdd","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":418,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","List.nextOr","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_15","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableEq","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","instLTNat"],"value_dag_size":422,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","List.nextOr","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_succ_lt_succ","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_16","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":137,"type_refs":["DecidableEq","Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.cons","List.dropLast","List.idxOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instMembership","List.length","List.nextOr","List.nil","Membership.mem","Nat","OfNat.ofNat","Option","Option.some","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":2267,"value_refs":["And","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HSub.hSub","Iff","Iff.mp","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_cons","List.getElem_cons.match_1","List.getElem_cons_succ","List.idxOf","List.idxOf_add_mem_idxsOf","List.idxsOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.mem_idxsOf_iff_getElem_sub_pos","List.nextOr","List.nextOr_eq_getElem?_idxOf_succ_of_mem_dropLast","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.lt_of_succ_lt_succ","Nat.not_le_eq","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_10","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_12","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_13","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_9","cast","congr","congrArg","congrFun'","decide_eq_true_eq","dite","dite_cond_eq_true","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","exists_prop_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","heq_of_eq","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_17","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":65,"type_refs":["DecidableEq","HAdd.hAdd","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":81,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_18","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","LT.lt","List","List.dropLast","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","instBEqOfDecidableEq","instLTNat"],"value_dag_size":596,"value_refs":["Bool","Bool.false","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem?_idxOf","List.idxOf","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.mem_of_mem_dropLast","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_17","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_19","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","Eq","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":110,"value_refs":["DecidableEq","Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","cast","congrArg","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_20","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":80,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":96,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_21","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":100,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":236,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_22","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","Eq","HSub.hSub","LT.lt","List","List.dropLast","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1564,"value_refs":["And","BEq.beq","Bool","Bool.false","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Iff.mpr","Iff.of_eq","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem?_idxOf","List.idxOf","List.idxsOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_nil","List.mem_idxsOf_getElem","List.mem_idxsOf_iff_getElem_sub_pos","List.mem_of_mem_dropLast","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_18","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_20","congr","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","exists_prop_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_23","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":96,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":231,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_24","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":97,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","List","List.dropLast","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1820,"value_refs":["And","BEq.beq","Bool","Bool.false","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Iff.mpr","Iff.of_eq","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.getElem?_idxOf","List.idxOf","List.idxsOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_nil","List.mem_idxsOf_getElem","List.mem_idxsOf_iff_getElem_sub_pos","List.mem_of_mem_dropLast","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_18","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_20","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_21","congr","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","exists_prop_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_25","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":100,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":246,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_26","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":96,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":240,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_27","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":103,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":795,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_25","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_28","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":100,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":246,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_29","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":139,"type_refs":["DecidableEq","Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.cons","List.dropLast","List.idxOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instMembership","List.length","List.nextOr","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","Option","Option.some","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":9165,"value_refs":["And","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mp","Iff.mpr","Iff.of_eq","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem?_idxOf","List.getElem_cons","List.getElem_cons.match_1","List.idxOf","List.idxOf?","List.idxOf_add_mem_idxsOf","List.idxOf_eq_getD_idxOf?","List.idxsOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.length_nil","List.mem_idxsOf_getElem","List.mem_idxsOf_iff_getElem_sub_pos","List.mem_of_mem_dropLast","List.nextOr","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.getD","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_13","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_18","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_20","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_21","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_22","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_23","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_24","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_25","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_26","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_27","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_28","_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_8","congr","congrArg","congrFun'","decide_eq_true_eq","dite","eagerReduce","eq_false","eq_of_heq","eq_true","exists_prop_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqNat","instEquivBEqOfLawfulBEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true","optParam","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":111,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.idxOf","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":127,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.idxOf","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":98,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HAppend.hAppend","LE.le","List","List.cons","List.dropLast","List.idxOf","List.instAppend","List.instMembership","List.length","List.nextOr","List.nil","Membership.mem","Nat","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instLENat"],"value_dag_size":1527,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_true_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.idxOf","List.idxOf_append","List.idxOf_lt_length_iff","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.length","List.length_append","List.length_cons","List.length_dropLast","List.length_nil","List.length_pos_of_mem","List.mem_append","List.nextOr","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","HAdd.hAdd","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":87,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":86,"type_refs":["DecidableEq","Eq","HSub.hSub","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":177,"value_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nextOr","List.nil","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":null,"statement_dag_size":86,"type_refs":["DecidableEq","Eq","HAdd.hAdd","LT.lt","List","List.cons","List.length","List.nextOr","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.nextOr","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast.match_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.nextOr_infix_of_mem_dropLast","reducibility":"abbrev","statement_dag_size":75,"type_refs":["Eq","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.dropLast","List.instAppend","instHAppendOfAppend"],"value_dag_size":104,"value_refs":["Eq","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.dropLast","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":37,"type_refs":["LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":327,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","List","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":72,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_11","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":35,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_12","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":823,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_13","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":77,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_14","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":114,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":948,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_15","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":276,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instMembership","List.length","List.length_dropLast","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_14","eagerReduce","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_16","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":142,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.ctorIdx","List.getLast","List.isEmpty","List.nil","List.nil_of_isEmpty","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_10","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","eq_false'","implies_congr","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":103,"value_refs":["Eq","Eq.substr","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_false","List","List.cons","List.ctorIdx","List.getLast","List.nil","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","congrArg","eq_false'","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_18","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.dropLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":309,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_cons.match_1","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_15","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_19","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":52,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_16","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_20","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":138,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":154,"value_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_21","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast","List.instMembership","List.nil","Membership.mem","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":35,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_mem","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_22","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":87,"type_refs":["DecidableEq","Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instBEqOfDecidableEq","instLTNat"],"value_dag_size":569,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.idxOf","List.idxOf_lt_length_iff","List.instAppend","List.instMembership","List.length","List.mem_append","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_15","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_23","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","LT.lt","List","List.idxOf","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","instBEqOfDecidableEq","instLTNat"],"value_dag_size":390,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_11","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_24","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":122,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":134,"value_refs":["Eq","Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_25","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":152,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":338,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_append._proof_1","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_15","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_26","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":129,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1883,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.dropLast_singleton","List.getLast","List.idxOf","List.idxOf_cons","List.instAppend","List.instMembership","List.length","List.length_dropLast","List.length_nil","List.length_pos_of_mem","List.mem_append","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_25","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_27","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instLTNat","instOfNatNat"],"value_dag_size":545,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_15","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_28","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":86,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":106,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.getLast_append._proof_1","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_16","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_29","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":96,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":97,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","HAdd.hAdd","HMod.hMod","LT.lt","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["DecidableEq","HAdd.hAdd","List","List.idxOf","List.instMembership","List.length","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.mod_lt","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_30","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instMembership","List.nil","Membership.mem","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":619,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","HEq.trans","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.dropLast","List.dropLast_append_getLast","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.head_append._proof_2","List.instAppend","List.instMembership","List.isEmpty","List.nil","List.nil_of_isEmpty","Membership.mem","Ne","Not","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_10","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_16","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_29","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_8","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_9","cast","congrArg","dite","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","implies_congr","instDecidableEqBool","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_31","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":86,"type_refs":["DecidableEq","HAdd.hAdd","HMod.hMod","LE.le","LT.lt","List","List.dropLast","List.idxOf","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLENat","instLTNat","instOfNatNat"],"value_dag_size":152,"value_refs":["DecidableEq","Eq","Eq.rec","Eq.symm","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.idxOf","List.length","List.length_dropLast","Nat","Nat.instMod","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_6","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_32","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":157,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HAppend.hAppend","HMod.hMod","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.instMod","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHMod","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1275,"value_refs":["BEq.beq","Bool","Bool.false","Bool.not_eq_true","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HAppend.hAppend","HMod.hMod","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_append_getLast","List.dropLast_singleton","List.getLast","List.idxOf","List.idxOf_append","List.idxOf_cons","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.isEmpty","List.length","List.length_append","List.length_dropLast","List.length_nil","List.mem_append","List.mem_cons","List.nil","List.nil_of_isEmpty","List.not_mem_nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_6","cast","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_false'","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHAppendOfAppend","instHMod","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_33","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":179,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.instMod","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1312,"value_refs":["BEq.beq","Bool","Bool.false","Bool.not_eq_true","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HAppend.hAppend","HMod.hMod","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_append_getLast","List.dropLast_singleton","List.getElem_append._proof_1","List.getLast","List.idxOf","List.idxOf_append","List.idxOf_cons","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instMembership","List.isEmpty","List.length","List.length_append","List.length_dropLast","List.length_nil","List.mem_append","List.mem_cons","List.nil","List.nil_of_isEmpty","List.not_mem_nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.instMod","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_6","cast","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_false'","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHAppendOfAppend","instHMod","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_34","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":140,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":156,"value_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_35","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":56,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":113,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.getLast","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_8","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_36","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":32,"type_refs":["Bool","Bool.true","Eq","List","List.dropLast","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":29,"value_refs":["Bool","Bool.true","Eq","List","List.dropLast","List.head_append._proof_2","List.isEmpty","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_37","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":56,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_39","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":131,"type_refs":["DecidableEq","Eq","GetElem.getElem","HAdd.hAdd","HMod.hMod","LT.lt","List","List.dropLast","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next","List.next_eq_getElem._proof_2","List.nil","Membership.mem","Nat","Nat.instMod","Nat.mod_lt","Ne","Not","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":1967,"value_refs":["BEq.beq","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HAppend.hAppend","HEq.refl","HEq.trans","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Iff.mpr","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_append_getLast","List.dropLast_singleton","List.getLast","List.getLast_mem","List.head","List.head_eq_getElem","List.idxOf","List.idxOf_append","List.idxOf_cons","List.idxOf_lt_length_iff","List.instAppend","List.instDecidableMemOfLawfulBEq","List.instGetElemNatLtLength","List.instMembership","List.isEmpty","List.length","List.length_append","List.length_dropLast","List.length_nil","List.length_pos_iff","List.length_pos_of_mem","List.mem_append","List.mem_cons","List.next","List.next.hcongr_5","List.next_eq_getElem._proof_2","List.next_getLast_eq_head_of_notMem_dropLast","List.nil","List.nil_of_isEmpty","List.not_mem_nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instMod","Nat.mod_lt","Nat.mod_self","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_21","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_37","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHAppendOfAppend","instHMod","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","List","List.nil","Ne","Not"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.not_eq_of_eq_false","List","List.nil","Ne","Not","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":119,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HAppend.hAppend","HMod.hMod","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.instMod","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHMod","instLTNat","instOfNatNat"],"value_dag_size":465,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMod.hMod","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","IntCast.intCast","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.idxOf","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.instMod","NatCast.natCast","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHMod","instIntCastInt","instIsPreorder_mathlib","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":89,"type_refs":["DecidableEq","HAdd.hAdd","HMod.hMod","LE.le","LT.lt","List","List.dropLast","List.idxOf","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLENat","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["DecidableEq","Eq.mpr_prop","HAdd.hAdd","HMod.hMod","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.idxOf","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":145,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.idxOf","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.instMod","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":512,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMod.hMod","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMod","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getElem_append._proof_1","List.getLast","List.idxOf","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.instMod","NatCast.natCast","Ne","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHAppendOfAppend","instHMod","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","instHAppendOfAppend"],"value_dag_size":167,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.instAppend","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","eq_false","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem","reducibility":null,"statement_dag_size":58,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4"],"value_dag_size":200,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dropLast","List.dropLast_append_getLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_4","cast","eq_false","eq_true","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem","reducibility":null,"statement_dag_size":40,"type_refs":["Fin.mk","LT.lt","List","List.get","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":31,"value_refs":["Fin.mk","LT.lt","List","List.get_mem","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","HMod.hMod","LT.lt","List","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["HAdd.hAdd","LE.le.trans_lt","LT.lt","List","List.length","Nat","Nat.instPreorder","Nat.mod_lt","Nat.zero_le","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem","reducibility":null,"statement_dag_size":89,"type_refs":["DecidableEq","GetElem.getElem","HAdd.hAdd","HMod.hMod","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":108,"value_refs":["DecidableEq","Fin.mk","GetElem.getElem","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.get","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.mod_lt","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_2","instAddNat","instBEqOfDecidableEq","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem","reducibility":null,"statement_dag_size":37,"type_refs":["Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"],"value_dag_size":35,"value_refs":["Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getElem","reducibility":null,"statement_dag_size":118,"type_refs":["DecidableEq","Eq","Fin.mk","GetElem.getElem","HAdd.hAdd","HMod.hMod","LE.le.trans_lt","LT.lt","List","List.Nodup","List.get_mem","List.instGetElemNatLtLength","List.length","List.next","Nat","Nat.instMod","Nat.instPreorder","Nat.mod_lt","Nat.zero_le","OfNat.ofNat","instAddNat","instHAdd","instHMod","instLTNat","instOfNatNat"],"value_dag_size":720,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin.mk","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HMod.hMod","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le.trans_lt","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.Nodup","List.Nodup.idxOf_getElem","List.get","List.get_mem","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next","List.next_eq_getElem","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.instMod","Nat.instPreorder","Nat.mod_lt","Nat.zero_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_2","_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.next_getElem._proof_1_4","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":45,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":38,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Not","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_5"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_11","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":137,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_12","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_cons_cons._proof_2","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_13","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":241,"type_refs":["Eq","Eq.mp","Eq.mpr","Eq.trans","Fin.mk","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.cons","List.cons_ne_nil","List.dropLast","List.dropLast_cons_cons","List.get","List.getLast","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_dropLast","Membership.mem","Nat","Nat.add_lt_add_iff_right._simp_1","Nat.lt_add_one._simp_1","Nat.lt_of_succ_lt","Nat.succ","OfNat.ofNat","congrArg","congrFun'","id","instAddNat","instHAdd","instLTNat","instOfNatNat","of_eq_true"],"value_dag_size":1710,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","Fin.isLt","Fin.mk","Fin.val","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.cons","List.cons_ne_nil","List.dropLast","List.dropLast_cons_cons","List.get","List.getElem_cons","List.getElem_cons.match_1","List.getElem_dropLast","List.getLast","List.getLast_cons_cons","List.getLast_cons_cons._proof_1","List.getLast_cons_cons._proof_2","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.get_eq_getElem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.length_dropLast","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.add_lt_add_iff_right._simp_1","Nat.decLe","Nat.decLt","Nat.lt_add_one._simp_1","Nat.lt_of_lt_of_le","Nat.lt_of_succ_lt","Nat.pred_le","Nat.sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_12","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_5","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_6","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_7","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_8","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_9","congrArg","congrFun'","dite","dite_cond_eq_false","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":41,"type_refs":["LT.lt","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":114,"value_refs":["Eq","Eq.rec","Eq.symm","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.length","List.length_dropLast","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","False","GetElem.getElem","LT.lt","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instGetElemNatLtLength","List.length","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":410,"value_refs":["Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getElem_cons","List.getElem_cons.match_1","List.getElem_dropLast","List.getLast","List.instGetElemNatLtLength","List.length","List.length_dropLast","List.nil","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","Nat.succ","Nat.succ_lt_succ_iff","Ne","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_3","congrArg","dite","dite_cond_eq_true","eq_false","eq_self","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":24,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":19,"value_refs":["List","List.cons","List.cons_ne_nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":156,"value_refs":["Eq","Eq.mp","Eq.mpr","Eq.trans","HAdd.hAdd","LT.lt","List","List.cons","List.dropLast","List.dropLast_cons_cons","List.length","List.length_dropLast","Nat","Nat.add_lt_add_iff_right._simp_1","Nat.lt_of_succ_lt","Nat.succ","OfNat.ofNat","congrArg","congrFun'","id","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":35,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":40,"value_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","Nat.lt_add_one._simp_1","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":57,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_7","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":55,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_7","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons","reducibility":null,"statement_dag_size":78,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_6","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":76,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_cons._proof_1_6","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head._proof_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":693,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_pos_iff","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","congrFun'","eagerReduce","eq_false","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":309,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":29,"value_refs":["List","List.getLast","List.getLast_mem","List.length_pos_of_mem","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast","reducibility":null,"statement_dag_size":49,"type_refs":["Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_1","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_1","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Fin.mk","List","List.get","List.getLast","List.getLast_mem","List.head","List.length","List.length_pos_of_mem","List.nil","Nat","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":284,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin.isLt","Fin.mk","Fin.val","GetElem.getElem","HEq.trans","Iff.mpr","LT.lt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","List","List.get","List.getLast","List.getLast_mem","List.get_eq_getElem","List.head","List.head_eq_getElem","List.instGetElemNatLtLength","List.length","List.length_pos_iff","List.length_pos_of_mem","List.nil","Nat","Ne","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_1","_private.Mathlib.Data.List.Cycle.0.List.next_getLast_eq_head_of_notMem_dropLast._proof_1_3","congrArg","eq_false","eq_of_heq","eq_true","id","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"],"value_dag_size":115,"value_refs":["Eq.refl","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1","reducibility":null,"statement_dag_size":131,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"],"value_dag_size":127,"value_refs":["Eq.refl","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1","reducibility":null,"statement_dag_size":141,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"],"value_dag_size":135,"value_refs":["Eq.refl","List","List.cons","List.instMembership","List.nil","List.prev.match_1","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1.splitter","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev.match_1","reducibility":"abbrev","statement_dag_size":110,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":1,"value_refs":["List.prev.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":46,"type_refs":["LE.le","List","List.cons","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":328,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","List","List.cons","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":82,"type_refs":["DecidableEq","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.idxOf","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","List","List.idxOf","List.instMembership","List.length","List.next_eq_getElem._proof_2","List.nil","Membership.mem","Nat","Nat.mod_lt","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":118,"type_refs":["DecidableEq","Eq","GetElem.getElem","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","List.nil","List.prev","Membership.mem","Nat","Nat.instMod","Nat.mod_lt","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":196,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","List.nil","List.not_mem_nil","List.prev","Membership.mem","Nat","Nat.instMod","Nat.mod_lt","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_2","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","LT.lt","List","List.cons","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":210,"value_refs":["AddMonoid.toAddZeroClass","DecidableEq","Eq","Eq.rec","Eq.trans","EquivBEq.toReflBEq","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.cons","List.idxOf","List.idxOf_cons_self","List.instMembership","List.length","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.instAddMonoid","Nat.instMod","Nat.mod_lt","Nat.mod_succ","OfNat.ofNat","congrArg","congrFun'","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMod","instHSub","instLTNat","instLawfulBEq","instOfNatNat","instSubNat","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","HSub.hSub","LT.lt","List","List.cons","List.instMembership","List.length","Membership.mem","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":151,"value_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instMembership","List.length","Membership.mem","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_4","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":239,"type_refs":["AddMonoid.toAddZeroClass","DecidableEq","Eq","Eq.rec","Eq.trans","EquivBEq.toReflBEq","GetElem.getElem","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.cons","List.cons_ne_nil","List.getLast","List.idxOf","List.idxOf_cons_self","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.instAddMonoid","Nat.instMod","Nat.mod_lt","Nat.mod_succ","OfNat.ofNat","congrArg","congrFun'","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMod","instHSub","instLTNat","instLawfulBEq","instOfNatNat","instSubNat","zero_add"],"value_dag_size":1115,"value_refs":["AddMonoid.toAddZeroClass","Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","EquivBEq.toReflBEq","False","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.cons","List.cons_ne_nil","List.getLast","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.idxOf","List.idxOf_cons_self","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.length_pos_of_mem","List.next_eq_getElem._proof_2","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instAddMonoid","Nat.instMod","Nat.mod_lt","Nat.mod_succ","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_5","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMod","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true","zero_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":77,"type_refs":["DecidableEq","Eq","HSub.hSub","LT.lt","List","List.cons","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","Not","OfNat.ofNat","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1115,"value_refs":["BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf_cons","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","LE.le","List","List.cons","List.idxOf","Nat","Not","OfNat.ofNat","instBEqOfDecidableEq","instLENat","instOfNatNat"],"value_dag_size":453,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr'","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf_cons","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHSub","instLENat","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":42,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":40,"value_refs":["List","List.cons","List.instMembership","List.ne_nil_of_mem","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_15","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":34,"value_refs":["List","List.cons","List.instMembership","List.ne_nil_of_mem","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_16","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":52,"type_refs":["LT.lt","List","List.cons","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":79,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.length","List.length_pos_iff","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_17","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":59,"type_refs":["List","List.cons","List.head","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Ne"],"value_dag_size":194,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.head","List.head_cons","List.instMembership","List.mem_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Ne","Not","Or","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_15","eq_false","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_18","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":60,"type_refs":["List","List.cons","List.head","List.instMembership","List.ne_nil_of_mem","Membership.mem","Ne"],"value_dag_size":188,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.head","List.head_cons","List.instMembership","List.mem_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Ne","Not","Or","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","eq_false","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_19","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":61,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.prev._proof_3","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_20","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":93,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":109,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_21","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":70,"type_refs":["LT.lt","List","List.cons","List.head","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":98,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.head","List.instMembership","List.length","List.length_pos_iff","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_17","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_22","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":87,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":103,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_23","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":154,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1043,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.idxOf_cons","List.idxOf_le_length","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_20","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_24","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":152,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1107,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.idxOf_cons","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_22","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_25","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":178,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":314,"value_refs":["DecidableEq","Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_24","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_26","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":182,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":325,"value_refs":["DecidableEq","Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_23","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_27","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":91,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":107,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_28","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":156,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1168,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.idxOf_cons","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_27","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_29","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":154,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":789,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.instMembership","List.length","List.length_pos_of_mem","List.mem_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_22","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":25,"type_refs":["List","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":25,"value_refs":["List","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_30","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":179,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":315,"value_refs":["DecidableEq","Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_29","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_31","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":175,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1072,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.idxOf_cons","List.idxOf_le_length","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_20","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_32","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","LT.lt","List","List.cons","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Ne","instBEqOfDecidableEq","instLTNat"],"value_dag_size":810,"value_refs":["BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.head","List.head_cons","List.idxOf","List.idxOf_cons","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_21","cast","cond","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_33","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":187,"type_refs":["DecidableEq","Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.cons","List.head","List.idxOf","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ne_nil_of_mem","List.prev","Membership.mem","Nat","Ne","OfNat.ofNat","Option","Option.some","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":11416,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.mpr_not","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mp","Iff.mpr","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.cond_eq_ite","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_ne_nil","List.getElem?_cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_idxOf","List.getLast","List.head","List.head_cons","List.head_eq_getElem","List.idxOf","List.idxOf_cons","List.idxOf_le_length","List.idxOf_lt_length_iff","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.length_pos_iff","List.mem_cons","List.ne_nil_of_mem","List.nil","List.prev","List.prev._proof_3","List.prev.eq_3","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_15","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_17","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_18","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_19","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_20","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_21","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_22","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_23","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_24","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_26","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_27","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_28","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_32","cast","cond","congrArg","congrFun'","decide_eq_true_eq","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_pos","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.idxOf","List.instGetElem?NatLtLength","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","OfNat.ofNat","Option","Option.some","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":134,"value_refs":["DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HSub.hSub","LT.lt","Lean.Grind.eq_false_of_not_eq_true","List","List.idxOf","List.instGetElem?NatLtLength","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","Not","OfNat.ofNat","Option","Option.some","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_3","eq_true","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":34,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":34,"value_refs":["List","List.cons","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":46,"type_refs":["LT.lt","List","List.cons","List.instMembership","List.length","List.nil","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":69,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.length","List.length_pos_iff","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_5","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":86,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.cons","List.idxOf","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":102,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.idxOf","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":118,"type_refs":["DecidableEq","Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.cons","List.head","List.idxOf","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","List.prev","Membership.mem","Nat","Ne","OfNat.ofNat","Option","Option.some","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":285,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HSub.hSub","Iff","LT.lt","Lean.Grind.eq_congr","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.head","List.head_cons","List.idxOf","List.instGetElem?NatLtLength","List.instMembership","List.length","List.mem_cons","List.ne_nil_of_mem","List.nil","List.not_mem_nil","List.prev","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Option","Option.some","Or","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_5","eq_false","eq_true","id","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head.match_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head","reducibility":"abbrev","statement_dag_size":173,"type_refs":["List","List.cons","List.head","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Ne"],"value_dag_size":332,"value_refs":["List","List.casesOn","List.cons","List.head","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem_idxOf_pred_of_ne_head._proof_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem_idxOf_pred_of_ne_head","reducibility":null,"statement_dag_size":60,"type_refs":["DecidableEq","HSub.hSub","LT.lt","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1124,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":32,"type_refs":["LT.lt","List","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":318,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":40,"type_refs":["Fin.mk","LT.lt","List","List.get","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":31,"value_refs":["Fin.mk","LT.lt","List","List.get_mem","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":61,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","List.prev_getElem._proof_2","Nat","Nat.mod_lt","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":100,"type_refs":["DecidableEq","GetElem.getElem","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":119,"value_refs":["DecidableEq","Fin.mk","GetElem.getElem","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.get","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","Membership.mem","Nat","Nat.mod_lt","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_2","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":37,"type_refs":["Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"],"value_dag_size":35,"value_refs":["Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_getElem","reducibility":null,"statement_dag_size":119,"type_refs":["DecidableEq","Eq","Fin.mk","GetElem.getElem","HAdd.hAdd","HMod.hMod","HSub.hSub","LT.lt","List","List.Nodup","List.get_mem","List.instGetElemNatLtLength","List.length","List.prev","List.prev_getElem._proof_2","Nat","Nat.instMod","Nat.mod_lt","OfNat.ofNat","instAddNat","instHAdd","instHMod","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":476,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin.mk","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HMod.hMod","HSub.hSub","LT.lt","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","List","List.Nodup","List.Nodup.idxOf_getElem","List.get","List.get_mem","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.next_eq_getElem._proof_2","List.prev","List.prev_eq_getElem","List.prev_getElem._proof_2","Membership.mem","Nat","Nat.instMod","Nat.mod_lt","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_2","_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.prev_getElem._proof_1_4","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMod","instHSub","instLTNat","instLawfulBEq","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_10","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":89,"type_refs":["DecidableEq","Eq","HSub.hSub","LT.lt","List","List.cons","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":199,"value_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_11","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":94,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_12","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":75,"type_refs":["DecidableEq","HSub.hSub","LT.lt","List","List.head","List.idxOf","List.instMembership","List.length","List.ne_nil_of_mem","Membership.mem","Nat","Ne","OfNat.ofNat","instBEqOfDecidableEq","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":675,"value_refs":["Bool","Bool.false","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.head","List.idxOf","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","List.prev","List.prev_eq_getElem?_idxOf_pred_of_ne_head","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_8","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","getElem?_neg","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":89,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":105,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_14","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":137,"value_refs":["DecidableEq","Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","OfNat.ofNat","cast","congrArg","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_15","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":91,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":110,"value_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.idxOf","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_16","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":142,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.idxOf","List.instMembership","List.length","List.tail","Membership.mem","Nat","Nat.succ","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instSubNat"],"value_dag_size":1429,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_pos_of_mem","List.length_tail","List.tail","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_17","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":94,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.instMembership","List.length","List.tail","Membership.mem","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":414,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.tail","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_15","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_18","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":105,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":245,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_19","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":107,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":126,"value_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.idxOf","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_18","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_2","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":104,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HSub.hSub","LE.le","List","List.cons","List.idxOf","List.instMembership","List.length","List.nil","List.prev","List.tail","Membership.mem","Nat","Nat.succ","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":1226,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","List.length_cons","List.length_nil","List.nil","List.prev","List.tail","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_20","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":241,"type_refs":["DecidableEq","Eq","GetElem.getElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.idxOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.tail","Membership.mem","Nat","Nat.succ","NatCast.natCast","Neg.neg","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":2624,"value_refs":["And","BEq.beq","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mpr","Iff.of_eq","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.idxsOf","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_nil","List.length_pos_of_mem","List.length_tail","List.mem_idxsOf_getElem","List.mem_idxsOf_iff_getElem_sub_pos","List.ne_nil_of_mem","List.nil","List.tail","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_16","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_18","congr","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_of_heq","eq_true","exists_prop_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instBEqOfDecidableEq","instEquivBEqOfLawfulBEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_21","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":105,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":255,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_22","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":107,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":126,"value_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.idxOf","List.length","List.tail","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_21","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_23","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":105,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":255,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.leaf","List","List.idxOf","List.length","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.sub_sub","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_24","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":176,"type_refs":["DecidableEq","Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.head","List.idxOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","List.prev","List.tail","Membership.mem","Nat","Nat.succ","Ne","Not","OfNat.ofNat","Option","Option.some","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":8241,"value_refs":["And","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mp","Iff.mpr","Iff.of_eq","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.head","List.idxOf","List.idxOf?","List.idxOf_add_mem_idxsOf","List.idxOf_eq_getD_idxOf?","List.idxOf_lt_length_iff","List.idxsOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.length_nil","List.length_pos_of_mem","List.length_tail","List.mem_idxsOf_getElem","List.mem_idxsOf_iff_getElem_sub_pos","List.ne_nil_of_mem","List.nil","List.prev","List.prev_eq_getElem?_idxOf_pred_of_ne_head","List.tail","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","Nat.sub_sub","Nat.succ","Nat.succ_eq_add_one","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.getD","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_10","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_11","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_12","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_13","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_16","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_18","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_20","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_21","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_23","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_8","congr","congrArg","congrFun'","decide_eq_true_eq","dite","eagerReduce","eq_false","eq_of_heq","eq_true","exists_prop_congr","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqNat","instEquivBEqOfLawfulBEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true","optParam","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_3","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":84,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Bool.true","DecidableEq","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_4","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","LT.lt","List","List.cons","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":238,"value_refs":["DecidableEq","Eq","Eq.rec","False","False.elim","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instMembership","List.length","List.nil","List.prev","Membership.mem","Nat","Nat.ctorIdx","Nat.sub_self","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","eq_false'","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_5","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":125,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":711,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_3","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_6","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":100,"type_refs":["DecidableEq","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.idxOf","List.instMembership","List.length","Membership.mem","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instBEqOfDecidableEq","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":410,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.idxOf","List.idxOf_lt_length_iff","List.instMembership","List.length","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_5","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_7","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":154,"type_refs":["DecidableEq","Eq","GetElem.getElem","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.idxOf","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instMembership","List.length","List.nil","List.prev","List.tail","Membership.mem","Nat","Nat.succ","OfNat.ofNat","Option","Option.some","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":2090,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_idxOf","List.idxOf","List.idxOf_lt_length_iff","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.ne_nil_of_mem","List.nil","List.prev","List.tail","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.ctorIdx","Nat.sub_self","Nat.succ","Nat.succ_eq_add_one","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_3","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_4","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_5","_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_6","cast","congrArg","congrFun'","dite","dite_cond_eq_false","dite_cond_eq_true","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_self","eq_true","forall_prop_domain_congr","getElem?_pos","heq_of_eq","id","instAddNat","instBEqOfDecidableEq","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_8","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":27,"type_refs":["List","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":35,"value_refs":["Lean.Grind.nestedProof","List","List.instMembership","List.ne_nil_of_mem","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_9","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail","reducibility":null,"statement_dag_size":84,"type_refs":["DecidableEq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":100,"value_refs":["DecidableEq","Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.idxOf","List.length","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Cycle","name":"_private.Mathlib.Data.List.Cycle.0.List.prev_reverse_eq_next._proof_1_1","namespace":"_private.Mathlib.Data.List.Cycle.0.List.prev_reverse_eq_next","reducibility":null,"statement_dag_size":45,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1202,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.Perm.dedup._simp_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.Perm.dedup","reducibility":null,"statement_dag_size":24,"type_refs":["DecidableEq","Eq","List","List.Nodup","List.dedup","True"],"value_dag_size":25,"value_refs":["DecidableEq","List","List.Nodup","List.dedup","List.nodup_dedup","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_mem'._simp_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_mem'","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["Eq","List","List.forall_mem_ne","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_mem'._simp_1_2","namespace":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_mem'","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_notMem'._simp_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_notMem'","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["Eq","List","List.forall_mem_ne","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.dedup_eq_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.dedup_eq_cons","reducibility":null,"statement_dag_size":66,"type_refs":["DecidableEq","False","HAdd.hAdd","LE.le","LT.lt","List","List.count","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":257,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray","Lean.RArray.leaf","List","List.count","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","NatCast.natCast","Neg.neg","OfNat.ofNat","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.dedup_eq_nil._simp_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.dedup_eq_nil","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","False","List","List.cons","List.nil"],"value_dag_size":27,"value_refs":["Eq","List","List.cons","List.cons_ne_nil","List.nil","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.headI_dedup.match_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.headI_dedup","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.mem_dedup._simp_1_2","namespace":"_private.Mathlib.Data.List.Dedup.0.List.mem_dedup","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["Eq","List","List.forall_mem_ne","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.mem_dedup._simp_1_3","namespace":"_private.Mathlib.Data.List.Dedup.0.List.mem_dedup","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.replicate_dedup.match_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.replicate_dedup","reducibility":"abbrev","statement_dag_size":67,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":107,"value_refs":["HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Dedup","name":"_private.Mathlib.Data.List.Dedup.0.List.tail_dedup.match_1_1","namespace":"_private.Mathlib.Data.List.Dedup.0.List.tail_dedup","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.Forall.match_1","List.cons","List.nil","Unit","Unit.unit"],"value_dag_size":47,"value_refs":["Eq.refl","List","List.Forall.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","List","List.Forall.match_1","List.cons","List.nil","Unit"],"value_dag_size":52,"value_refs":["Eq.refl","List","List.Forall.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","False","List","List.Forall.match_1","List.cons","List.nil","Unit"],"value_dag_size":337,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","List","List.Forall.match_1","List.casesOn","List.cons","List.ctorIdx","List.getLastI._sparseCasesOn_1","List.getLastI._sparseCasesOn_1.else_eq","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.splitter._sparseCasesOn_3","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.splitter","namespace":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Eq","False","List","List.cons","List.nil","Unit"],"value_dag_size":153,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","List","List.casesOn","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Data.List.Defs.0.List.Forall.match_1.splitter","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.headI.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.headI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.headI.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.headI.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1.splitter","namespace":"_private.Mathlib.Data.List.Defs.0.List.headI.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.headI.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","List.iterate.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","List.iterate.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List.iterate.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","List.iterate.match_1","Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1.splitter","namespace":"_private.Mathlib.Data.List.Defs.0.List.iterate.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["List.iterate.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.length_mapAccumr.match_1_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.length_mapAccumr","reducibility":"abbrev","statement_dag_size":69,"type_refs":["List","List.cons","List.nil","Prod"],"value_dag_size":85,"value_refs":["List","List.casesOn","List.cons","List.nil","Prod"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.length_mapAccumr₂.match_1_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.length_mapAccumr₂","reducibility":"abbrev","statement_dag_size":129,"type_refs":["List","List.cons","List.nil","Prod"],"value_dag_size":187,"value_refs":["List","List.casesOn","List.cons","List.nil","Prod"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","List.cons","List.map₂Left'.match_1","List.nil"],"value_dag_size":73,"value_refs":["Eq.refl","List","List.cons","List.map₂Left'.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","List","List.cons","List.map₂Left'.match_1","List.nil"],"value_dag_size":77,"value_refs":["Eq.refl","List","List.cons","List.map₂Left'.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","List","List.cons","List.map₂Left'.match_1","List.nil"],"value_dag_size":85,"value_refs":["Eq.refl","List","List.cons","List.map₂Left'.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1.splitter","namespace":"_private.Mathlib.Data.List.Defs.0.List.map₂Left'.match_1","reducibility":"abbrev","statement_dag_size":64,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.map₂Left'.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1","reducibility":null,"statement_dag_size":136,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux.rec.match_1"],"value_dag_size":442,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","List","List.cons","List.nil","List.permutationsAux.rec.match_1","_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux.rec.match_1"],"value_dag_size":49,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux.rec.match_1"],"value_dag_size":57,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1.splitter","namespace":"_private.Mathlib.Data.List.Defs.0.List.permutationsAux.rec.match_1","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Defs","name":"_private.Mathlib.Data.List.Defs.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.List.Defs.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter._simp_1_5","namespace":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter","reducibility":"abbrev","statement_dag_size":209,"type_refs":["List","List.IsChain","List.Sublist","List.Sublist.cons","List.Sublist.cons_cons","List.cons","List.nil"],"value_dag_size":2253,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.IsChain","List.Sublist","List.Sublist.casesOn","List.Sublist.cons","List.Sublist.cons_cons","List.Sublist.slnil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.Destutter.0.List.IsChain.length_le_length_destutter._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup._simp_1_4","namespace":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup._simp_1_5","namespace":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup._simp_1_6","namespace":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.Pairwise.destutter_eq_dedup","reducibility":"abbrev","statement_dag_size":82,"type_refs":["List","List.Pairwise","List.cons","List.nil"],"value_dag_size":148,"value_refs":["List","List.Pairwise","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.destutter'.match_1","List.nil"],"value_dag_size":46,"value_refs":["Eq.refl","List","List.cons","List.destutter'.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","List","List.cons","List.destutter'.match_1","List.nil"],"value_dag_size":53,"value_refs":["Eq.refl","List","List.cons","List.destutter'.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1.splitter","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter'.match_1","reducibility":"abbrev","statement_dag_size":38,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.destutter'.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","List","List.cons","List.destutter.match_1","List.nil","Unit"],"value_dag_size":43,"value_refs":["Eq.refl","List","List.cons","List.destutter.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.destutter.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":35,"value_refs":["Eq.refl","List","List.cons","List.destutter.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter.match_1","reducibility":"abbrev","statement_dag_size":30,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.destutter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_nil","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Eq","List","List.cons","List.nil"],"value_dag_size":118,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.cons","List.ctorIdx","List.nil","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_nil.match_1_3","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_nil","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_self_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter_eq_self_iff","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter_of_isChain.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter_of_isChain","reducibility":"abbrev","statement_dag_size":59,"type_refs":["List","List.IsChain","List.cons","List.nil"],"value_dag_size":87,"value_refs":["List","List.IsChain","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.destutter_sublist.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.destutter_sublist","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'._simp_1_2","namespace":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'","reducibility":null,"statement_dag_size":21,"type_refs":["Decidable","Eq","True","ite"],"value_dag_size":25,"value_refs":["Decidable","True","if_true_right","ite","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'._simp_1_3","namespace":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.IsChain","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.IsChain","List.cons","List.isChain_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'._simp_1_4","namespace":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'","reducibility":null,"statement_dag_size":28,"type_refs":["And","Decidable","Eq","Not","ite"],"value_dag_size":33,"value_refs":["And","Decidable","Not","ite","ite_prop_iff_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'._simp_1_5","namespace":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter'","reducibility":null,"statement_dag_size":20,"type_refs":["And","Eq"],"value_dag_size":25,"value_refs":["And","imp_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.isChain_destutter","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.le_length_destutter'_cons._simp_1_3","namespace":"_private.Mathlib.Data.List.Destutter.0.List.le_length_destutter'_cons","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","LE.le","Nat","Nat.succ","True","instLENat"],"value_dag_size":16,"value_refs":["LE.le","Nat","Nat.le_succ","Nat.succ","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.le_length_destutter'_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.le_length_destutter'_cons","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter'_cotrans_ge._simp_1_7","namespace":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter'_cotrans_ge","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Preorder","Preorder.toLE","True"],"value_dag_size":24,"value_refs":["LE.le","Preorder","Preorder.toLE","eq_true","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter'_cotrans_ge.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter'_cotrans_ge","reducibility":"abbrev","statement_dag_size":65,"type_refs":["List","List.cons","List.nil","Not"],"value_dag_size":79,"value_refs":["List","List.casesOn","List.cons","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter_le_length_destutter_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.length_destutter_le_length_destutter_cons","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.map_destutter._simp_1_5","namespace":"_private.Mathlib.Data.List.Destutter.0.List.map_destutter","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableRel","Eq","List","List.cons","List.destutter","List.destutter'"],"value_dag_size":47,"value_refs":["DecidableRel","Eq.symm","List","List.cons","List.destutter","List.destutter'","List.destutter_cons'"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Destutter","name":"_private.Mathlib.Data.List.Destutter.0.List.map_destutter.match_1_1","namespace":"_private.Mathlib.Data.List.Destutter.0.List.map_destutter","reducibility":"abbrev","statement_dag_size":196,"type_refs":["Iff","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":360,"value_refs":["Iff","List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.dropWhile_idempotent._simp_1_1","namespace":"_private.Mathlib.Data.List.DropRight.0.List.dropWhile_idempotent","reducibility":null,"statement_dag_size":70,"type_refs":["Bool","Bool.true","Eq","GetElem.getElem","LT.lt","List","List.dropWhile","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["Bool","Bool.true","Eq","GetElem.getElem","LT.lt","List","List.dropWhile","List.dropWhile_eq_self_iff","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.DropRight.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.rdropWhile_eq_self_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.DropRight.0.List.rdropWhile_eq_self_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.reverse"],"value_dag_size":29,"value_refs":["Eq","List","List.reverse","List.reverse_eq_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.rdropWhile_eq_self_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.DropRight.0.List.rdropWhile_eq_self_iff","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":26,"value_refs":["LT.lt","Nat","Nat.pos_iff_ne_zero","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.DropRight","name":"_private.Mathlib.Data.List.DropRight.0.List.rtakeWhile_eq_self_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.DropRight.0.List.rtakeWhile_eq_self_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List","List.reverse"],"value_dag_size":29,"value_refs":["Eq","List","List.reverse","List.reverse_eq_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.Duplicate.of_duplicate_cons._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.Duplicate.of_duplicate_cons","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Duplicate","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":48,"value_refs":["And","Eq","List","List.Duplicate","List.cons","List.duplicate_cons_iff","List.instMembership","Membership.mem","Or","propext"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List._aux_Mathlib_Data_List_Duplicate___unexpand_List_Duplicate_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":250,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.decidableDuplicate._simp_5","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.decidableDuplicate","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Duplicate","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":48,"value_refs":["And","Eq","List","List.Duplicate","List.cons","List.duplicate_cons_iff","List.instMembership","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_cons_iff_of_ne._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_cons_iff_of_ne","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Duplicate","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":48,"value_refs":["And","Eq","List","List.Duplicate","List.cons","List.duplicate_cons_iff","List.instMembership","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_sublist._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_sublist","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","List","List.Sublist","List.cons"],"value_dag_size":32,"value_refs":["List","List.Sublist","List.cons","List.cons_sublist_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_sublist._simp_1_2","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_sublist","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.Sublist","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":36,"value_refs":["List","List.Sublist","List.cons","List.instMembership","List.nil","List.singleton_sublist","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_two_le_count._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_two_le_count","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Duplicate","List.Sublist","List.cons","List.nil"],"value_dag_size":32,"value_refs":["List","List.Duplicate","List.Sublist","List.cons","List.duplicate_iff_sublist","List.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_two_le_count._simp_1_2","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.duplicate_iff_two_le_count","reducibility":null,"statement_dag_size":45,"type_refs":["BEq","Eq","LE.le","LawfulBEq","List","List.Sublist","List.count","List.replicate","Nat","instLENat"],"value_dag_size":57,"value_refs":["BEq","Eq.symm","LE.le","LawfulBEq","List","List.Sublist","List.count","List.replicate","List.replicate_sublist_iff","Nat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.exists_duplicate_iff_not_nodup._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.exists_duplicate_iff_not_nodup","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","List","List.Duplicate","List.Nodup","Not"],"value_dag_size":25,"value_refs":["List","List.Duplicate","List.Nodup","List.nodup_iff_forall_not_duplicate","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate._simp_1_1","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","List","List.Nodup","List.Sublist","List.cons","List.nil","Not"],"value_dag_size":32,"value_refs":["List","List.Nodup","List.Sublist","List.cons","List.nil","List.nodup_iff_sublist","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate._simp_1_2","namespace":"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Duplicate","List.Sublist","List.cons","List.nil"],"value_dag_size":32,"value_refs":["List","List.Duplicate","List.Sublist","List.cons","List.duplicate_iff_sublist","List.nil","propext"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.«_aux_Mathlib_Data_List_Duplicate___macroRules__private_Mathlib_Data_List_Duplicate_0_List_term_∈+__1»","namespace":"_private.Mathlib.Data.List.Duplicate.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":237,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Duplicate","name":"_private.Mathlib.Data.List.Duplicate.0.List.«term_∈+_»","namespace":"_private.Mathlib.Data.List.Duplicate.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":61,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Enum","name":"_private.Mathlib.Data.List.Enum.0.List.exists_mem_zipIdx._simp_1_1","namespace":"_private.Mathlib.Data.List.Enum.0.List.exists_mem_zipIdx","reducibility":null,"statement_dag_size":71,"type_refs":["And","Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":75,"value_refs":["And","Exists","GetElem.getElem","LT.lt","List","List.exists_mem_iff_getElem","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Enum","name":"_private.Mathlib.Data.List.Enum.0.List.forall_mem_zipIdx._simp_1_1","namespace":"_private.Mathlib.Data.List.Enum.0.List.forall_mem_zipIdx","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":64,"value_refs":["GetElem.getElem","LT.lt","List","List.forall_mem_iff_getElem","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.Equiv.Perm.map_finRange_perm._simp_1_1","namespace":"_private.Mathlib.Data.List.FinRange.0.Equiv.Perm.map_finRange_perm","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.Equiv.Perm.map_finRange_perm._simp_1_2","namespace":"_private.Mathlib.Data.List.FinRange.0.Equiv.Perm.map_finRange_perm","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","List","List.finRange","List.instMembership","Membership.mem","Nat","True"],"value_dag_size":26,"value_refs":["Fin","List","List.finRange","List.instMembership","List.mem_finRange","Membership.mem","Nat","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.nodup_ofFn._simp_1_1","namespace":"_private.Mathlib.Data.List.FinRange.0.List.nodup_ofFn","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.nodup_ofFn._simp_1_2","namespace":"_private.Mathlib.Data.List.FinRange.0.List.nodup_ofFn","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Fin","List","List.instMembership","List.ofFn","Membership.mem","Nat"],"value_dag_size":47,"value_refs":["Eq","Exists","Fin","List","List.instMembership","List.mem_ofFn","List.ofFn","Membership.mem","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","List","List.instMembership","List.range","Membership.mem","Nat","instLTNat"],"value_dag_size":30,"value_refs":["Iff.mp","LT.lt","List","List.instMembership","List.mem_range","List.range","Membership.mem","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_10","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Fin","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.ofFn","Nat","Option","Option.some","instLTNat"],"value_dag_size":523,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_ofFn","List.ofFn","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_11","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","Fin","GetElem.getElem","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.ofFn","List.range","Nat","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_7","instLTNat"],"value_dag_size":702,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","Fin","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_ofFn","List.length_range","List.ofFn","List.range","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_5","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_7","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_12","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Not","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instLTNat"],"value_dag_size":663,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_pmap","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_13","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":155,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Not","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instLTNat"],"value_dag_size":630,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_14","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Not","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instLTNat"],"value_dag_size":710,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_ofFn","List.length_pmap","List.length_range","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_3","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_15","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":131,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Not","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instLTNat"],"value_dag_size":684,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_pmap","List.length_range","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_16","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":162,"type_refs":["Eq","Fin","Fin.mk","GetElem.getElem","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Not","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_12","instLTNat"],"value_dag_size":815,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_pmap","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_12","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_5","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_17","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","Iff","Iff.mp","LT.lt","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.mem_range","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Option","Option.some","instLTNat"],"value_dag_size":2138,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","Fin.mk.hcongr_3","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq","HEq.refl","HEq.trans","Iff","Iff.mp","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.dite_cond_eq_true'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem?_ofFn","List.getElem?_pmap","List.getElem_range","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_ofFn","List.length_pmap","List.length_range","List.mem_of_getElem?","List.mem_range","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.pmap","Option.pmap_congr","Option.pmap_pred_congr","Option.pmap_some'","Option.some","Option.some.inj","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_10","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_11","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_12","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_13","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_14","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_15","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_16","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_2","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_3","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_5","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_7","congrArg","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_2","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":111,"type_refs":["Fin","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instMembership","List.length","List.pmap","List.range","Membership.mem","Nat","OfNat.ofNat","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":127,"value_refs":["Eq.substr","Fin","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.instMembership","List.length","List.pmap","List.range","Membership.mem","Nat","OfNat.ofNat","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_3","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":57,"type_refs":["Fin","HAdd.hAdd","LE.le","LT.lt","List.length","List.ofFn","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":73,"value_refs":["Eq.substr","Fin","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.ofFn","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_4","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":49,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_5","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.range","Nat","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":122,"value_refs":["Eq","Eq.refl","GetElem?.getElem?","HAdd.hAdd","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.mem_of_getElem?","List.range","Membership.mem","Nat","OfNat.ofNat","Option","Option.pmap_pred_congr","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":44,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","List.range","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.range","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_7","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","Fin","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.ofFn","List.range","Nat","Option","Option.some","instLTNat"],"value_dag_size":546,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_ofFn","List.length_range","List.ofFn","List.range","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_6","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_8","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Fin","Fin.mk","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Option","Option.some","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","instLTNat"],"value_dag_size":608,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","Fin.mk","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.instMembership","List.length","List.length_ofFn","List.length_pmap","List.length_range","List.ofFn","List.pmap","List.range","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_1","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.FinRange","name":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_9","namespace":"_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Fin","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.ofFn","Nat","Option","Option.some","instLTNat"],"value_dag_size":495,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Fin","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.ofFn","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","_private.Mathlib.Data.List.FinRange.0.List.ofFn_eq_pmap._proof_1_3","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Find.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Find.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Find.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_congr._proof_1_1","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_congr","reducibility":null,"statement_dag_size":24,"type_refs":["Bool","Eq","List.find?","List.nil","Option"],"value_dag_size":104,"value_refs":["Bool","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.find?","List.find?_nil","List.nil","Not","Option","Option.none","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_congr._proof_1_4","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_congr","reducibility":null,"statement_dag_size":75,"type_refs":["Bool","Eq","List","List.cons","List.find?","List.instMembership","Membership.mem","Option"],"value_dag_size":614,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","List.instMembership","List.mem_cons","Membership.mem","Not","Option","Option.some","Or","Or.casesOn","PUnit","PUnit.casesOn","True","True.intro","Unit","_private.Mathlib.Data.List.Find.0.List.filter.match_1.splitter","congrArg","congrFun'","eq_false","eq_self","eq_true","heq_eq_eq","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_3","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":87,"type_refs":["And","Bool","Bool.true","Eq","List","List.cons","List.find?","List.instMembership","Membership.mem","Option","Set.Subsingleton","Set.ofPred"],"value_dag_size":1225,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.Bool.ne_of_eq_true_of_eq_false","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","List.instMembership","List.mem_cons","Membership.mem","Not","Option","Option.some","Or","Or.casesOn","PUnit","PUnit.casesOn","Set.Subsingleton","Set.ofPred","True","True.intro","Unit","_private.Mathlib.Data.List.Find.0.List.filter.match_1.splitter","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","funext","heq_eq_eq","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_4","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":89,"type_refs":["And","Bool","Bool.true","Eq","List","List.cons","List.find?","List.instMembership","Membership.mem","Option"],"value_dag_size":494,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.find?","List.find?_cons","List.instMembership","List.mem_cons","List.mem_of_find?_eq_some","Membership.mem","Not","Option","Option.some","Or","PUnit","True","True.intro","Unit","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","heq_eq_eq","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_5","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":49,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.find?","Not","Option"],"value_dag_size":285,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","Not","Option","Option.some","PUnit","True","True.intro","Unit","eq_false","eq_true","heq_eq_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_6","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":49,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.find?","Not","Option"],"value_dag_size":291,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","Not","Option","Option.some","PUnit","True","True.intro","Unit","eq_false","eq_true","heq_eq_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_7","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":50,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.find?","Not","Option"],"value_dag_size":335,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","Not","Option","Option.some","PUnit","True","True.intro","Unit","eq_false","eq_true","heq_eq_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_8","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":56,"type_refs":["And","Bool","Bool.true","Eq","List","List.instMembership","Membership.mem","Set.Subsingleton","Set.ofPred"],"value_dag_size":110,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","List","List.instMembership","Membership.mem","Not","Set.Subsingleton","Set.ofPred","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Find","name":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm._proof_1_9","namespace":"_private.Mathlib.Data.List.Find.0.List.find?_eq_find?_of_perm","reducibility":null,"statement_dag_size":65,"type_refs":["And","Bool","Bool.true","Eq","List","List.Perm","List.instMembership","Membership.mem","Set.Subsingleton","Set.ofPred"],"value_dag_size":844,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.not_eq_false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Lean.Grind.Bool.ne_of_eq_true_of_eq_false","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.Perm","List.Perm.mem_iff","List.instMembership","Membership.mem","Not","Or","Or.casesOn","Set.Subsingleton","Set.ofPred","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","funext","id","implies_congr","noConfusion_of_Nat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right","reducibility":null,"statement_dag_size":28,"type_refs":["List","List.Sublist","List.flatMap","List.nil"],"value_dag_size":142,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","List","List.Sublist","List.flatMap","List.flatMap_nil","List.nil","List.sublist_nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right","reducibility":null,"statement_dag_size":78,"type_refs":["List","List.Sublist","List.cons","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":526,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.Sublist","List.Sublist.append","List.cons","List.flatMap","List.flatMap_cons","List.instAppend","List.instMembership","List.mem_cons","Membership.mem","Not","Or","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_self","eq_true","id","instHAppendOfAppend","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten","reducibility":null,"statement_dag_size":14,"type_refs":["List","List.Sublist","List.flatten","List.nil"],"value_dag_size":68,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Sublist","List.Sublist.refl","List.flatten","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten","reducibility":null,"statement_dag_size":36,"type_refs":["List","List.Sublist","List.cons","List.flatten"],"value_dag_size":169,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.imp_eq_of_eq_true_left","List","List.Sublist","List.cons","List.flatten","List.flatten_cons","List.instAppend","List.sublist_append_of_sublist_right","Not","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten._proof_1_3","namespace":"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatten","reducibility":null,"statement_dag_size":37,"type_refs":["List","List.Sublist","List.cons","List.flatten"],"value_dag_size":182,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.iff_eq","List","List.Sublist","List.append_sublist_append_left","List.cons","List.flatten","List.flatten_cons","List.instAppend","Not","True","True.intro","congr","congrArg","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.append_flatten_map_append._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.append_flatten_map_append","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HAppend.hAppend","List","List.flatten","List.instAppend","List.map","List.nil","instHAppendOfAppend"],"value_dag_size":403,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_lhs_suffix","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_lhs_exact","Lean.RArray.branch","Lean.RArray.leaf","List","List.flatten","List.flatten_nil","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.map","List.map_nil","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","congrArg","eagerReduce","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.append_flatten_map_append._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.append_flatten_map_append","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.flatten","List.instAppend","List.map","instHAppendOfAppend"],"value_dag_size":546,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.flatten","List.flatten_cons","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.map","List.map_cons","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","congrArg","eagerReduce","id","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.cons","List.drop","List.instGetElemNatLtLength","List.length","List.nil","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":342,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","GetElem.getElem","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.instGetElemNatLtLength","List.length","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_10","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":482,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.length","List.length_cons","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_8","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_11","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":72,"type_refs":["HAdd.hAdd","HMul.hMul","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":568,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.getElem_drop._proof_1","List.length","List.length_cons","List.length_nil","List.nil","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_8","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_12","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":434,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.length","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_6","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_13","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":520,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.getElem_drop._proof_1","List.length","List.length_nil","List.nil","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_6","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_14","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":164,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.drop","List.getElem_cons.match_1","List.length","List.take","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_8","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_15","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.cons","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":701,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_4","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_16","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":117,"type_refs":["Eq","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.cons","List.drop","List.instGetElemNatLtLength","List.length","List.nil","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":2487,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HAppend.hAppend","HEq.trans","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_append_of_le_length","List.drop_succ_cons","List.drop_take_self","List.drop_zero","List.eq_nil_of_length_eq_zero","List.getElem_cons","List.getElem_cons.match_1","List.instAppend","List.instGetElemNatLtLength","List.length","List.length_cons","List.length_nil","List.length_take","List.nil","List.take","List.take_add","List.take_succ_cons","List.take_zero","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_15","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_2","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_3","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_4","congr","congrArg","congrFun'","dite","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","instAddNat","instDecidableEqNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":136,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":57,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_2","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":395,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.length","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_3","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":401,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.getElem_drop._proof_1","List.length","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_3","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_7","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":45,"type_refs":["LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","instLTNat"],"value_dag_size":490,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.length","List.length_cons","List.length_nil","List.nil","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_8","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":559,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.drop","List.drop_take_self","List.drop_zero","List.getElem_drop._proof_1","List.length","List.length_cons","List.length_nil","List.nil","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_9","namespace":"_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem","reducibility":null,"statement_dag_size":89,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":87,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.cons","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Flatten.0.List.drop_take_succ_eq_cons_getElem._proof_1_2","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":114,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.flatten","List.flatten_ne_nil_iff","List.getLast","List.getLast_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":148,"value_refs":["And","And.intro","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.intro","False","False.elim","Iff.mpr","List","List.flatten","List.flatten_ne_nil_iff","List.getLast","List.getLast_mem","List.instMembership","List.nil","Membership.mem","Ne","Not","True","True.intro","eq_false","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_10","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":60,"type_refs":["Bool","Bool.true","Eq","List","List.concat","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":171,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_11","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":37,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":36,"value_refs":["Bool","Bool.true","Eq","List","List.cons","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_12","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.concat","List.cons","List.flatten","List.getLast","List.instAppend","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":422,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.concat","List.concat_eq_append","List.cons","List.flatten","List.flatten_append","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Ne","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_3","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_13","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":72,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.flatten","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":84,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.flatten","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_14","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.concat","List.cons","List.flatten","List.getLast","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":557,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.concat","List.concat_eq_append","List.cons","List.flatten","List.flatten_append","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Ne","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_3","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_15","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAppend.hAppend","List","List.concat","List.cons","List.flatten","List.getLast","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":211,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.flatten","List.flatten_append","List.getLast","List.instAppend","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_2","cast","congrArg","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_16","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":75,"type_refs":["Bool","Bool.true","Eq","List","List.concat","List.cons","List.flatten","List.getLast","List.isEmpty","List.nil","Ne"],"value_dag_size":234,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.flatten","List.flatten_append","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_2","cast","congrArg","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_17","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":42,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.flatten","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":41,"value_refs":["Bool","Bool.true","Eq","List","List.cons","List.flatten","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_18","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":19,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":110,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","List","List.cons","List.ctorIdx","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_11","eq_false'","implies_congr","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_19","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":42,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Not","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_18"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","List","List.flatten","List.getLast","List.nil","Ne","Not"],"value_dag_size":98,"value_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.flatten","List.flatten_ne_nil_iff","List.getLast","List.getLast_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_21","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.concat","List.cons","List.flatten","List.getLast","List.nil","Ne"],"value_dag_size":561,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.ctorIdx","List.flatten","List.flatten_singleton","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_singleton","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Ne","Not","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_10","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_11","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_17","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_18","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_9","cast","dite","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","implies_congr","instDecidableEqBool","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_22","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":122,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.concat","List.flatten","List.flatten_ne_nil_iff","List.getLast","List.getLast_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":1169,"value_refs":["And","And.intro","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","False.elim","HAppend.hAppend","HEq.trans","Iff.mpr","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.ctorIdx","List.flatten","List.flatten_append","List.flatten_ne_nil_iff","List.flatten_singleton","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_mem","List.getLast_singleton","List.head_append._proof_2","List.instAppend","List.instMembership","List.isEmpty","List.nil","List.nil_of_isEmpty","Membership.mem","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_10","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_11","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_15","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_16","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_17","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_18","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_2","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_21","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_9","cast","congrArg","dite","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_3","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":60,"type_refs":["HSub.hSub","LT.lt","List","List.flatten","List.getLast","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":52,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.flatten","List.getLast","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_2"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_4","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getLast","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":55,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_5","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":47,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":34,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_6","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.concat","List.cons","List.instAppend","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":366,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Ne","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_5","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_7","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":67,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":79,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_8","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.concat","List.cons","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":497,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.concat","List.concat_eq_append","List.cons","List.getElem_append._proof_1","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Ne","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_5","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten._proof_1_9","namespace":"_private.Mathlib.Data.List.Flatten.0.List.getLast_getLast_eq_getLast_flatten","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HAppend.hAppend","List","List.concat","List.cons","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":150,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.concat","List.concat_eq_append","List.cons","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_flatten_eq_head_head._proof_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_flatten_eq_head_head","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.flatten","List.nil","Ne","Not"],"value_dag_size":108,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.intro_with_eq","Lean.Grind.not_not","List","List.flatten","List.flatten_nil","List.nil","Ne","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_1","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":105,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.flatten","List.flatten_ne_nil_iff","List.head","List.head_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":155,"value_refs":["And","And.intro","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.intro","False","False.elim","Iff.mpr","Lean.Grind.not_true","List","List.flatten","List.flatten_ne_nil_iff","List.head","List.head_mem","List.instMembership","List.nil","Membership.mem","Ne","Not","True","True.intro","congrArg","eq_self","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_10","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","List","List.cons","List.head","List.nil","Ne","Not"],"value_dag_size":115,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.head","List.head_cons","List.nil","Ne","Not","eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_12","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":122,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.cons","List.flatten","List.flatten_ne_nil_iff","List.head","List.head_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":472,"value_refs":["And","And.intro","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.intro","False","HAppend.hAppend","HEq.refl","HEq.trans","Iff.mpr","Lean.Grind.eq_congr","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.flatten","List.flatten_cons","List.flatten_ne_nil_iff","List.head","List.head.hcongr_3","List.head_append_of_ne_nil","List.head_cons","List.head_mem","List.instAppend","List.instMembership","List.nil","Membership.mem","Ne","Not","True","True.intro","_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_10","_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_2","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_2","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","List","List.cons","List.flatten","List.head","List.nil","Ne","Not"],"value_dag_size":114,"value_refs":["And","And.intro","Eq","Exists","Exists.intro","Iff.mpr","List","List.cons","List.flatten","List.flatten_ne_nil_iff","List.head","List.head_mem","List.instMembership","List.nil","Membership.mem","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_3","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":63,"type_refs":["LT.lt","List","List.cons","List.flatten","List.head","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":87,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.flatten","List.head","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_2","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_4","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.head","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":89,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.head","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_5","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":46,"type_refs":["LT.lt","List","List.cons","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_6","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","Exists","List","List.cons","List.flatten","List.instMembership","List.nil","Membership.mem","Ne","Not"],"value_dag_size":47,"value_refs":["And","Eq","Exists","List","List.cons","List.head_flatten._proof_1","List.instMembership","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_7","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":59,"type_refs":["And","Bool","Bool.true","Eq","Exists","List","List.cons","List.findSome?","List.head?","List.instMembership","List.nil","Membership.mem","Not","Option.isSome"],"value_dag_size":47,"value_refs":["And","Eq","Exists","List","List.cons","List.head_flatten._proof_2","List.instMembership","List.nil","Membership.mem","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_8","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Flatten","name":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_9","namespace":"_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten","reducibility":null,"statement_dag_size":75,"type_refs":["LE.le","LT.lt","List","List.cons","List.flatten","List.head","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":152,"value_refs":["Eq","Eq.mpr_not","Eq.rec","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.cons","List.flatten","List.getElem_append._proof_1","List.head","List.length","List.nil","Nat","Nat.zero_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Flatten.0.List.head_head_eq_head_flatten._proof_1_3","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.flip.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.flip","reducibility":"abbrev","statement_dag_size":131,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","flip"],"value_dag_size":539,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq","flip"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.flip.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.flip","reducibility":"abbrev","statement_dag_size":297,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","flip"],"value_dag_size":1240,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq","flip"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.get.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.get","reducibility":"abbrev","statement_dag_size":208,"type_refs":["LT.lt","List","List.Forall₂","List.Forall₂.cons","List.cons","List.length","Nat","Nat.succ","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":817,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","LT.lt","List","List.Forall₂","List.Forall��.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.length","List.nil","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","eq_of_heq","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.get.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.get","reducibility":"abbrev","statement_dag_size":455,"type_refs":["LT.lt","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.cons","List.cons","List.length","Nat","Nat.succ","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":1729,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","LT.lt","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.length","List.nil","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","eq_of_heq","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.length_eq.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.length_eq","reducibility":"abbrev","statement_dag_size":103,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":473,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.length_eq.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.length_eq","reducibility":"abbrev","statement_dag_size":238,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1126,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.mp.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.mp","reducibility":"abbrev","statement_dag_size":140,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":2188,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.mp.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.Forall₂.mp","reducibility":"abbrev","statement_dag_size":331,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":3688,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_4","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","List","List.Forall₂","List.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","List","List.Forall₂","List.cons","List.forall₂_cons_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_5","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":47,"value_refs":["And","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_6","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_8","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left._simp_1_9","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_and_left","reducibility":"abbrev","statement_dag_size":45,"type_refs":["List","List.cons","List.nil"],"value_dag_size":60,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff","reducibility":"abbrev","statement_dag_size":85,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.cons"],"value_dag_size":970,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff.match_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff","reducibility":"abbrev","statement_dag_size":195,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","List","List.Forall₂","List.cons"],"value_dag_size":653,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.Forall₂","List.cons","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_right_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_right_iff","reducibility":"abbrev","statement_dag_size":85,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.cons"],"value_dag_size":831,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_right_iff.match_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_right_iff","reducibility":"abbrev","statement_dag_size":195,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","List","List.Forall₂","List.cons"],"value_dag_size":667,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.Forall₂","List.cons","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_drop._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_drop","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List.Forall₂","List.nil","True"],"value_dag_size":28,"value_refs":["List.Forall₂","List.Forall₂.nil","List.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_drop.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_drop","reducibility":"abbrev","statement_dag_size":137,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":531,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","eq_of_heq","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_iff_zip._simp_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_iff_zip","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_left_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_left_iff","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","List","List.Forall₂","List.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","List","List.Forall₂","List.cons","List.forall₂_cons_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_left_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_left_iff","reducibility":"abbrev","statement_dag_size":45,"type_refs":["List","List.cons","List.nil"],"value_dag_size":59,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_right_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_right_iff","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","List","List.Forall₂","List.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","List","List.Forall₂","List.cons","List.forall₂_cons_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_right_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_map_right_iff","reducibility":"abbrev","statement_dag_size":45,"type_refs":["List","List.cons","List.nil"],"value_dag_size":59,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_of_length_eq_of_get.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_of_length_eq_of_get","reducibility":"abbrev","statement_dag_size":238,"type_refs":["Eq","Fin.mk","LT.lt","List","List.cons","List.get","List.length","List.nil","Nat","instLTNat"],"value_dag_size":724,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","Fin.mk","HEq","HEq.refl","LT.lt","List","List.casesOn","List.cons","List.get","List.length","List.nil","Nat","Nat.add","Nat.ctorIdx","Nat.succ","instLTNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_same.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_same","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_take._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_take","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","List.Forall₂","List.nil","True"],"value_dag_size":28,"value_refs":["List.Forall₂","List.Forall₂.nil","List.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_take.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_take","reducibility":"abbrev","statement_dag_size":137,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":531,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","eq_of_heq","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip","reducibility":"abbrev","statement_dag_size":170,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.cons","List.instMembership","List.zip","Membership.mem","Prod","Prod.mk"],"value_dag_size":896,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","List.zip","Membership.mem","Prod","Prod.mk","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip.match_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip","reducibility":"abbrev","statement_dag_size":211,"type_refs":["Eq","Eq.refl","List","List.instMembership","List.zipWith","Membership.mem","Or","Or.inl","Or.inr","Prod","Prod.mk"],"value_dag_size":591,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.instMembership","List.zipWith","Membership.mem","Or","Or.casesOn","Or.inl","Or.inr","Prod","Prod.mk","Prod.mk.noConfusion","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip.match_1_9","namespace":"_private.Mathlib.Data.List.Forall2.0.List.forall₂_zip","reducibility":"abbrev","statement_dag_size":423,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.cons","List.cons","List.instMembership","List.zip","Membership.mem","Prod","Prod.mk"],"value_dag_size":1853,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.cons","List.ctorIdx","List.instMembership","List.nil","List.zip","Membership.mem","Prod","Prod.mk","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.left_unique_forall₂'.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.left_unique_forall₂'","reducibility":"abbrev","statement_dag_size":149,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1350,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.left_unique_forall₂'.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.left_unique_forall₂'","reducibility":"abbrev","statement_dag_size":343,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":2386,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_append._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_append","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_append.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_append","reducibility":"abbrev","statement_dag_size":159,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.cons","List.nil"],"value_dag_size":853,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.Forall2.0.List.rel_append._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_append.match_1_8","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_append","reducibility":"abbrev","statement_dag_size":368,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.cons","List.cons","List.nil"],"value_dag_size":1882,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.Forall2.0.List.rel_append._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","List","List.Forall₂","List.cons"],"value_dag_size":56,"value_refs":["And","List","List.Forall₂","List.cons","List.forall₂_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter","reducibility":"abbrev","statement_dag_size":106,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":478,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter.match_1_8","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filter","reducibility":"abbrev","statement_dag_size":259,"type_refs":["Bool","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.filter","List.nil","Unit"],"value_dag_size":1146,"value_refs":["Bool","Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.filter","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap","reducibility":"abbrev","statement_dag_size":206,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Option","Option.Rel","Relator.LiftFun"],"value_dag_size":590,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Option","Option.Rel","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap.match_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap","reducibility":"abbrev","statement_dag_size":86,"type_refs":["Option","Option.Rel","Option.Rel.none","Option.Rel.some","Option.none","Option.some","Unit"],"value_dag_size":430,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Option","Option.Rel","Option.Rel.casesOn","Option.Rel.none","Option.Rel.some","Option.none","Option.some","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap.match_1_9","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_filterMap","reducibility":"abbrev","statement_dag_size":499,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.filterMap","List.nil","Option","Option.Rel","Relator.LiftFun"],"value_dag_size":1680,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.filterMap","List.nil","Option","Option.Rel","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten","reducibility":"abbrev","statement_dag_size":135,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":974,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Forall2.0.List.rel_flatten._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten.match_1_8","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten","reducibility":"abbrev","statement_dag_size":301,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":2013,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Forall2.0.List.rel_flatten._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldl.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldl","reducibility":"abbrev","statement_dag_size":240,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun"],"value_dag_size":627,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldl.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldl","reducibility":"abbrev","statement_dag_size":569,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun"],"value_dag_size":1859,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldr.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldr","reducibility":"abbrev","statement_dag_size":240,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun"],"value_dag_size":627,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldr.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_foldr","reducibility":"abbrev","statement_dag_size":569,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun"],"value_dag_size":1859,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_map.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_map","reducibility":"abbrev","statement_dag_size":175,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Relator.LiftFun"],"value_dag_size":1436,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Relator.LiftFun","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_map.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_map","reducibility":"abbrev","statement_dag_size":428,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.map","List.nil","Relator.LiftFun"],"value_dag_size":2946,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.map","List.nil","Relator.LiftFun","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem._simp_1_3","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":23,"value_refs":["List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem._simp_1_4","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem","reducibility":"abbrev","statement_dag_size":137,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil"],"value_dag_size":1397,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem.match_1_9","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_mem","reducibility":"abbrev","statement_dag_size":357,"type_refs":["Iff","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":2714,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","Iff","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.instMembership","List.nil","Membership.mem","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse._sparseCasesOn_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse","reducibility":"abbrev","statement_dag_size":101,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":882,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Forall2.0.List.rel_reverse._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse.match_1_8","namespace":"_private.Mathlib.Data.List.Forall2.0.List.rel_reverse","reducibility":"abbrev","statement_dag_size":236,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1860,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.List.Forall2.0.List.rel_reverse._sparseCasesOn_1_1","absurd","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.right_unique_forall₂'.match_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.right_unique_forall₂'","reducibility":"abbrev","statement_dag_size":150,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1228,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.right_unique_forall₂'.match_1_7","namespace":"_private.Mathlib.Data.List.Forall2.0.List.right_unique_forall₂'","reducibility":"abbrev","statement_dag_size":342,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":2216,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","Unit","Unit.unit","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.sublistForall₂_map_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.sublistForall₂_map_left_iff","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","Exists","List","List.Forall₂","List.Sublist","List.SublistForall₂"],"value_dag_size":54,"value_refs":["And","Exists","List","List.Forall₂","List.Sublist","List.SublistForall₂","List.sublistForall₂_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Forall2","name":"_private.Mathlib.Data.List.Forall2.0.List.sublistForall₂_map_right_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Forall2.0.List.sublistForall₂_map_right_iff","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","Exists","List","List.Forall₂","List.Sublist","List.SublistForall₂"],"value_dag_size":54,"value_refs":["And","Exists","List","List.Forall₂","List.Sublist","List.SublistForall₂","List.sublistForall₂_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_append._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_append","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.getD","List.instAppend","List.length","Nat","instHAppendOfAppend","instLTNat"],"value_dag_size":332,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedDecidable","List","List.getD","List.getD_eq_getElem?_getD","List.getElem?_append","List.instAppend","List.instGetElem?NatLtLength","List.length","Nat","Nat.decLe","Nat.decLt","Not","OfNat.ofNat","Option","Option.getD","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_append_right._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_append_right","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LE.le","List","List.getD","List.instAppend","List.length","Nat","instHAppendOfAppend","instHSub","instLENat","instSubNat"],"value_dag_size":525,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.getD","List.getD_eq_getElem?_getD","List.getElem?_append","List.instAppend","List.instGetElem?NatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_default._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_default","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_default._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_default","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LE.le","List","List.getD","List.length","Nat","instLENat"],"value_dag_size":329,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.getD","List.getD_eq_getElem?_getD","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","Option","Option.getD","Option.getD_none","Option.none","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem","reducibility":null,"statement_dag_size":25,"type_refs":["LT.lt","List","List.length","Nat","instLTNat"],"value_dag_size":62,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_1","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.getD","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":376,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.forall_propagator","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","List","List.getD","List.getD_eq_getElem?_getD","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","Option.getD","Option.getD_some","Option.some","True","True.intro","_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_1","_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem._proof_1_2","congrArg","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_pos","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem?._simp_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_eq_getElem?","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Fin","Fin.val","LT.lt","Nat","True","instLTNat"],"value_dag_size":22,"value_refs":["Fin","Fin.is_lt","Fin.val","LT.lt","Nat","eq_true","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":70,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate","reducibility":null,"statement_dag_size":27,"type_refs":["LT.lt","List.length","List.replicate","Nat","instLTNat"],"value_dag_size":552,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem?_replicate","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.replicate","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_replicate","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LT.lt","List.getD","List.replicate","Nat","instLTNat"],"value_dag_size":863,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getD","List.getD_eq_getElem?_getD","List.getElem?_replicate","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.replicate","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.getD","Option.getD_some","Option.none","Option.some","Option.some.inj","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_1","_private.Mathlib.Data.List.GetD.0.List.getD_replicate._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse","reducibility":null,"statement_dag_size":52,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.reverse","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.reverse","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse","reducibility":null,"statement_dag_size":64,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":80,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse._proof_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_reverse","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.getD","List.length","List.reverse","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":491,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.forall_imp_eq_or","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray.leaf","List","List.getD","List.getD_eq_getElem?_getD","List.getElem?_reverse","List.instGetElem?NatLtLength","List.length","List.reverse","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Not","OfNat.ofNat","Option","Option.getD","Or","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._proof_1_8","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["HAdd.hAdd","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._proof_1_9","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":83,"type_refs":["And","Eq","Exists","GetElem.getElem","Iff","LE.le","LT.lt","List","List.instGetElemNatLtLength","List.length","Nat","Or","True","instLENat","instLTNat"],"value_dag_size":1216,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAdd.hAdd","Iff","Iff.mpr","Iff.of_eq","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.instGetElemNatLtLength","List.length","Nat","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._proof_1_8","congr","congrArg","congrFun'","eq_false","eq_true","exists_prop_congr","forall_congr","funext","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true","propext","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":53,"type_refs":["Decidable","Eq","Exists","Not","Or","dite"],"value_dag_size":60,"value_refs":["Decidable","Eq","Exists","Not","Or","dite","dite_eq_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Not","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.not_lt","Not","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_5","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_6","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Exists","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.instMembership","List.length","Membership.mem","Nat","Option","Option.some","instLTNat"],"value_dag_size":64,"value_refs":["Eq","Exists","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.instMembership","List.length","List.mem_iff_getElem?","Membership.mem","Nat","Option","Option.some","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_7","namespace":"_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","Exists","GetElem.getElem","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","instLTNat"],"value_dag_size":83,"value_refs":["Eq","Exists","GetElem.getElem","GetElem?.getElem?","LT.lt","List","List.getElem?_eq_some_iff","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":70,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.length","List.replicate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":92,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","LE.le","List.length","List.length_replicate","List.replicate","Nat","OfNat.ofNat","True","_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_1","congrArg","eq_true","instAddNat","instHAdd","instLENat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.replicate","Nat","Option.getD","instLTNat"],"value_dag_size":870,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem?_replicate","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_replicate","List.replicate","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.getD","Option.getD_none","Option.getD_some","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_1","_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_replicate_default_eq._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq","reducibility":null,"statement_dag_size":55,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List.cons","List.length","List.nil","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":352,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List.cons","List.length","List.length_cons","List.length_nil","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq._proof_1_1","eagerReduce","id","instAddNat","instHAdd","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.GetD","name":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq._proof_1_4","namespace":"_private.Mathlib.Data.List.GetD.0.List.getElem?_getD_singleton_default_eq","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.cons","List.instGetElem?NatLtLength","List.length","List.nil","Nat","Option.getD","instLTNat"],"value_dag_size":295,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HSub.hSub","LT.lt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","List","List.cons","List.getElem?_cons","List.getElem?_singleton","List.instGetElem?NatLtLength","List.length","List.nil","Nat","Not","OfNat.ofNat","Option","Option.getD","Option.getD_none","Option.getD_some","Option.none","Option.some","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","id","instDecidableEqNat","instHSub","instLTNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Indexes","name":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List","List.cons","List.mapIdxMAux'.match_1","List.nil","Nat"],"value_dag_size":47,"value_refs":["Eq.refl","List","List.cons","List.mapIdxMAux'.match_1","List.nil","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Indexes","name":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","List","List.cons","List.mapIdxMAux'.match_1","List.nil","Nat"],"value_dag_size":54,"value_refs":["Eq.refl","List","List.cons","List.mapIdxMAux'.match_1","List.nil","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Indexes","name":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1.splitter","namespace":"_private.Mathlib.Data.List.Indexes.0.List.mapIdxMAux'.match_1","reducibility":"abbrev","statement_dag_size":39,"type_refs":["List","List.cons","List.nil","Nat"],"value_dag_size":1,"value_refs":["List.mapIdxMAux'.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1","reducibility":null,"statement_dag_size":146,"type_refs":["Eq","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"],"value_dag_size":471,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit","Unit.unit","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit","Unit.unit"],"value_dag_size":51,"value_refs":["Eq.refl","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"],"value_dag_size":56,"value_refs":["Eq.refl","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"],"value_dag_size":62,"value_refs":["Eq.refl","List","List.bidirectionalRec.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1.splitter","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.bidirectionalRec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":36,"type_refs":["HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":34,"value_refs":["HAppend.hAppend","List","List.cons","List.cons_ne_nil","List.instAppend","List.nil","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"],"value_dag_size":34,"value_refs":["HAppend.hAppend","List","List.bidirectionalRec._proof_3","List.cons","List.instAppend","List.nil","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_13","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":187,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.ctorIdx","List.instAppend","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_14","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":47,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":207,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_15","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"],"value_dag_size":154,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.dropLast","List.getLast","List.instAppend","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_16","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":86,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"],"value_dag_size":201,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.dropLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_17","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":99,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"],"value_dag_size":99,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":60,"type_refs":["HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":50,"value_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_19","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instAppend","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend"],"value_dag_size":170,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.ctorIdx","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_17","eq_false'","implies_congr","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_20","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":379,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_21","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":116,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_22","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":525,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.getElem_append._proof_1","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_23","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":344,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_24","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":118,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_25","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":130,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":533,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_26","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":264,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instAppend","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_18","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_28","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","HAppend.hAppend","List","List.bidirectionalRec","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":1680,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","HEq","HEq.refl","HEq.trans","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eqRec_heq","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.bidirectionalRec","List.bidirectionalRec._proof_3","List.bidirectionalRec.eq_3","List.bidirectionalRec.hcongr_6","List.casesOn","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_concat","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_singleton","List.head_append._proof_2","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_12","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_13","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_14","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_7","cast","congrArg","dite","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":17,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":11,"value_refs":["List.cons_ne_nil","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_5","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":300,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","cast","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_6","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":40,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":316,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","cast","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_7","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":34,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":32,"value_refs":["Bool","Bool.true","Eq","List.cons","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_8","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":338,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.ctorIdx","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","cast","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_9","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":354,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_4","cast","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_nil._proof_1_4","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_nil","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","HAppend.hAppend","List","List.bidirectionalRec","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":138,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.bidirectionalRec","List.bidirectionalRec.eq_1","List.cons","List.instAppend","List.nil","Not","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_singleton._proof_1_4","namespace":"_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_singleton","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HAppend.hAppend","List","List.bidirectionalRec","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":149,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.bidirectionalRec","List.bidirectionalRec.eq_2","List.cons","List.instAppend","List.nil","Not","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.recNeNil_cons.match_1_1","namespace":"_private.Mathlib.Data.List.Induction.0.List.recNeNil_cons","reducibility":"abbrev","statement_dag_size":50,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":99,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.casesOn","List.cons","List.nil","Ne","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1","reducibility":null,"statement_dag_size":112,"type_refs":["Eq","List","List.cons","List.nil","List.reverseRec.match_1","Unit"],"value_dag_size":312,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","List","List.cons","List.nil","List.reverseRec.match_1","Unit","Unit.unit","_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","List.reverseRec.match_1","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","List.reverseRec.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","List.reverseRec.match_1","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","List.reverseRec.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1.splitter","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.reverseRec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":36,"type_refs":["HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":34,"value_refs":["HAppend.hAppend","List","List.cons","List.cons_ne_nil","List.instAppend","List.nil","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":34,"value_refs":["HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reverseRec._proof_3","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_12","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":141,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.getLast","List.instAppend","List.nil","List.reverseRec._proof_3","Not","True","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_13","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":58,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":176,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.reverseRec._proof_3","Not","True","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_14","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":70,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":70,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":33,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast_eq_getElem._proof_3","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_16","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":187,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.ctorIdx","List.instAppend","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_17","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":47,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":207,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_18","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":154,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.dropLast","List.getLast","List.instAppend","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_19","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":86,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":201,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.dropLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","cast","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_20","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":99,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":99,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_21","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":275,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.getLast","List.instAppend","List.nil","List.reverseRec._proof_3","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_22","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":86,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":321,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.reverseRec._proof_3","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_23","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":97,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":97,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":60,"type_refs":["HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":50,"value_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_25","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.nil","Ne","Not"],"value_dag_size":140,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.getLast","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_14","eq_false'","implies_congr","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_26","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":335,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","List.reverseRec._proof_3","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_27","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":86,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_28","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":486,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_ne_nil","List.dropLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","List.reverseRec._proof_3","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_29","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":192,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":17,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":11,"value_refs":["List.cons_ne_nil","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_30","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.length","List.nil","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":48,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.getLast_eq_getElem._proof_3","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_25"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_31","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":169,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedProof","List","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_23","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_32","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.getLast","List.instAppend","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":170,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.ctorIdx","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_20","eq_false'","implies_congr","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_33","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":409,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.dropLast","List.dropLast_concat","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_34","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":475,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.dropLast","List.dropLast_concat","List.instAppend","List.length","List.length_dropLast","List.nil","Nat","Nat.ToInt.lt_eq","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_35","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":76,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":379,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_36","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":116,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_37","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":526,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.getElem_append._proof_1","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_38","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":344,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_39","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":118,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_4","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":300,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","cast","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_40","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":130,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":533,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_41","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":445,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","List.reverseRec._proof_3","Nat","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_42","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":108,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":120,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.dropLast","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_43","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":145,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":622,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.dropLast","List.getElem_append._proof_1","List.getLast","List.instAppend","List.length","List.nil","List.reverseRec._proof_3","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_44","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":264,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.instAppend","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_24","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_45","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":254,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropLast","List.length","List.length_dropLast","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_28","eagerReduce","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_46","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":523,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.dropLast","List.dropLast_concat","List.instAppend","List.length","List.length_dropLast","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_15","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_43","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_47","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.length","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":454,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.dropLast","List.dropLast_concat","List.instAppend","List.length","List.length_dropLast","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_40","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_48","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.cons","List.instAppend","List.length","List.nil","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":432,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.dropLast","List.dropLast_concat","List.instAppend","List.length","List.length_dropLast","List.nil","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_37","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_49","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":29,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":46,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_append._proof_1","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_5","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":40,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne"],"value_dag_size":316,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","cast","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_50","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":56,"type_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":82,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_31","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_51","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":351,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_concat","List.getLast","List.instAppend","List.nil","List.reverseRec._proof_3","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_52","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":103,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":413,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_concat","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.reverseRec._proof_3","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","cast","congrArg","eq_false","eq_true","instHAppendOfAppend","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_53","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":130,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":130,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_54","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":435,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","List.reverseRec._proof_3","Not","True","cast","congrArg","eq_false","eq_true","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_55","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":88,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":479,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","List.reverseRec._proof_3","Not","True","cast","congrArg","eq_false","eq_true","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_56","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":102,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":102,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_57","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.dropLast","List.getLast","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":187,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_concat","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_56","congrArg","eq_false'","implies_congr","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_58","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":398,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.getLast","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_false'","eq_true","implies_congr","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_59","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":100,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":443,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.getLast","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","cast","congrArg","eq_false","eq_false'","eq_true","implies_congr","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_6","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":34,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":32,"value_refs":["Bool","Bool.true","Eq","List.cons","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_60","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":104,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.instAppend","List.isEmpty","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":104,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.dropLast","List.getLast","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_61","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.dropLast","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":276,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","True","cast","eq_false","eq_false'","eq_true","implies_congr","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_62","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":50,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.dropLast","List.isEmpty","List.nil","Ne"],"value_dag_size":294,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_append","List.dropLast_concat","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","Not","True","cast","eq_false","eq_false'","eq_true","implies_congr","instDecidableEqBool","instHAppendOfAppend","ite","ite_cond_eq_false","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_63","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":39,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.dropLast","List.isEmpty","List.nil","Ne","Not"],"value_dag_size":37,"value_refs":["Bool","Bool.true","Eq","List.cons","List.dropLast","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_65","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.cons","List.cons_ne_nil","List.getLast","List.instAppend","List.nil","Ne","Not","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","instHAppendOfAppend"],"value_dag_size":699,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","HEq.trans","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_singleton","List.head_append._proof_2","List.instAppend","List.isEmpty","List.nil","List.nil_of_isEmpty","List.reverseRec._proof_3","Not","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_16","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_17","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_53","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_6","cast","congrArg","dite","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","implies_congr","instDecidableEqBool","instHAppendOfAppend","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_66","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reverseRec","instHAppendOfAppend"],"value_dag_size":1600,"value_refs":["Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","HEq","HEq.refl","HEq.trans","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.eqRec_heq","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.casesOn","List.cons","List.cons_append","List.cons_ne_nil","List.ctorIdx","List.dropLast","List.dropLast_concat","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_singleton","List.head_append._proof_2","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","List.reverseRec","List.reverseRec._proof_3","List.reverseRec.eq_2","List.reverseRec.hcongr_5","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_11","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_16","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_17","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_6","cast","congrArg","dite","eagerReduce","eq_false","eq_false'","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_7","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","Not","instHAppendOfAppend"],"value_dag_size":338,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.ctorIdx","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","cast","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_8","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":354,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.ctorIdx","List.getLast_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","Nat","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_3","cast","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Induction","name":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_nil._proof_1_3","namespace":"_private.Mathlib.Data.List.Induction.0.List.reverseRec_nil","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reverseRec","instHAppendOfAppend"],"value_dag_size":123,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reverseRec","List.reverseRec.eq_1","Not","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.IsPrefix.take._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.IsPrefix.take","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","LE.le","List","List.IsPrefix","List.length","List.take","Nat","instLENat"],"value_dag_size":43,"value_refs":["And","LE.le","List","List.IsPrefix","List.length","List.prefix_take_iff","List.take","Nat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.IsPrefix.take._simp_1_2","namespace":"_private.Mathlib.Data.List.Infix.0.List.IsPrefix.take","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","LE.le","Min.min","Nat","True","instLENat","instMinNat"],"value_dag_size":23,"value_refs":["LE.le","Min.min","Nat","Nat.min_le_left","eq_true","instLENat","instMinNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.infix_singleton_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.infix_singleton_iff","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":74,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.inits_append.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.inits_append","reducibility":"abbrev","statement_dag_size":52,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":78,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails._simp_1_3","namespace":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":56,"value_refs":["Eq","List","List.instMembership","List.map","List.map_inj_left","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails._simp_1_4","namespace":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.inits_eq_tails","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.inits_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.inits_reverse","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.insert_eq_ite._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.insert_eq_ite","reducibility":null,"statement_dag_size":42,"type_refs":["BEq","Bool","Bool.true","Eq","LawfulBEq","List","List.elem","List.instMembership","Membership.mem"],"value_dag_size":54,"value_refs":["BEq","Bool","Bool.true","Eq","Eq.symm","LawfulBEq","List","List.elem","List.elem_iff","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.map_reverse_inits._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.map_reverse_inits","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.map_reverse_tails._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.map_reverse_tails","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_inits._simp_1_7","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_inits","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_inits.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_inits","reducibility":"abbrev","statement_dag_size":209,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","List","List.cons","List.inits","List.instMembership","List.nil","Membership.mem","Or","Or.inl","Or.inr","Unit"],"value_dag_size":475,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.cons","List.inits","List.instMembership","List.nil","Membership.mem","Or","Or.casesOn","Or.inl","Or.inr","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_inits.match_1_3","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_inits","reducibility":"abbrev","statement_dag_size":146,"type_refs":["Eq","Eq.refl","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.cons","List.instAppend","List.nil","Unit","instHAppendOfAppend"],"value_dag_size":401,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.IsPrefix","List.casesOn","List.cons","List.instAppend","List.nil","Unit","Unit.unit","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_inits.match_1_5","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_inits","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":55,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_inits.match_1_8","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_inits","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Eq","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.instAppend","instHAppendOfAppend"],"value_dag_size":96,"value_refs":["Eq","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails._simp_1_3","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails._simp_1_4","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","List","List.IsSuffix","List.nil"],"value_dag_size":25,"value_refs":["Eq","List","List.IsSuffix","List.nil","List.suffix_nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails._simp_1_5","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":55,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails.match_1_6","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":"abbrev","statement_dag_size":137,"type_refs":["Eq","Eq.refl","Exists.intro","HAppend.hAppend","List","List.IsSuffix","List.cons","List.instAppend","Or","Or.inl","Or.inr","instHAppendOfAppend"],"value_dag_size":520,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.IsSuffix","List.cons","List.instAppend","Or","Or.casesOn","Or.inl","Or.inr","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.mem_tails.match_1_8","namespace":"_private.Mathlib.Data.List.Infix.0.List.mem_tails","reducibility":"abbrev","statement_dag_size":150,"type_refs":["Eq","Eq.refl","Exists.intro","HAppend.hAppend","List","List.IsSuffix","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":418,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.IsSuffix","List.casesOn","List.cons","List.instAppend","List.nil","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.singleton_infix_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.singleton_infix_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.suffix_insert._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.suffix_insert","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","List","List.IsSuffix","True"],"value_dag_size":17,"value_refs":["List","List.IsSuffix","List.suffix_refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.suffix_insert._simp_1_2","namespace":"_private.Mathlib.Data.List.Infix.0.List.suffix_insert","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","List","List.IsSuffix","List.cons","True"],"value_dag_size":24,"value_refs":["List","List.IsSuffix","List.cons","List.suffix_cons","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.tails_append.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.tails_append","reducibility":"abbrev","statement_dag_size":52,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":78,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.tails_eq_inits.match_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.tails_eq_inits","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.tails_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.tails_reverse","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.take_inits._proof_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.take_inits","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","LT.lt","List","List.length","Min.min","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instMinNat","instOfNatNat"],"value_dag_size":408,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_simp_lhs_ac","Lean.Grind.AC.diseq_simp_lhs_exact","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ac","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_lhs_ac","Lean.Grind.AC.eq_simp_lhs_exact","Lean.Grind.AC.superpose_ac_idempotent","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toDecidableLE","LinearOrder.toMin","LinearOrder.toPartialOrder","List","List.length","Min.min","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","Nat.instAssociativeMin","Nat.instCommutativeMin","Nat.instIdempotentOpMin","Nat.instLinearOrder","Not","OfNat.ofNat","PLift","PLift.up","PartialOrder.toPreorder","Preorder.toLE","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instMinNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","min_def","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take._proof_1_3","namespace":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take","reducibility":null,"statement_dag_size":41,"type_refs":["False","Iff","LE.le","List","List.length","Min.min","Nat","Not","Or","instLENat","instMinNat"],"value_dag_size":1365,"value_refs":["And","And.left","And.right","Bool","Bool.true","Classical.propDecidable","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMin","Int.instNegInt","Int.instSub","Int.min_def","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Decidable.and_not_or_not_and_of_not_iff","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_min","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.and_not_not_of_not_or","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Min.min","Nat","Nat.cast","Nat.lt_of_not_le","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or","Or.elim","id","instDecidableEqBool","instHAdd","instHSub","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take._simp_1_1","namespace":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","LE.le","List","List.IsPrefix","List.length","List.take","Nat","instLENat"],"value_dag_size":43,"value_refs":["And","LE.le","List","List.IsPrefix","List.length","List.prefix_take_iff","List.take","Nat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Infix","name":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take._simp_1_2","namespace":"_private.Mathlib.Data.List.Infix.0.List.take_isPrefix_take","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","List","List.IsPrefix","List.take","Nat","True"],"value_dag_size":25,"value_refs":["List","List.IsPrefix","List.take","List.take_prefix","Nat","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.eraseIdx_pmap.match_1_1","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.eraseIdx_pmap","reducibility":"abbrev","statement_dag_size":128,"type_refs":["List","List.cons","List.instMembership","List.nil","Membership.mem","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":185,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ._proof_1","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ","reducibility":null,"statement_dag_size":42,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instLENat","instLTNat"],"value_dag_size":298,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ._proof_1_1","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LT.lt","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":220,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.rec","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_insertIdx._proof_4","List.insertIdx","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_le","Nat.decLe","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ._proof_1_2","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ","reducibility":null,"statement_dag_size":92,"type_refs":["Eq","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.insertIdx","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":577,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_insertIdx","List.getElem_insertIdx._proof_1","List.getElem_insertIdx._proof_4","List.insertIdx","List.instGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_le","Nat.decLe","Nat.decLt","Not","OfNat.ofNat","True","True.intro","_private.Mathlib.Data.List.InsertIdx.0.List.getElem_insertIdx_add_succ._proof_1_1","congrArg","dite","dite_cond_eq_false","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_1","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","LE.le","List","List.eraseIdx","List.length","List.take","Nat","instLENat"],"value_dag_size":1790,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.eraseIdx","List.length","List.length_eraseIdx","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_2","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.eraseIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.eraseIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_3","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_4","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":76,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_3","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_5","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.eraseIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.eraseIdx","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_2","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_6","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.eraseIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":78,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.eraseIdx","List.getElem_eraseIdx._proof_2","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_7","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.eraseIdx","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":100,"value_refs":["Eq.mpr_not","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.eraseIdx","List.getElem_eraseIdx._proof_5","List.length","List.take","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_8","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","GetElem.getElem","LE.le","LT.lt","List","List.eraseIdx","List.instGetElemNatLtLength","List.length","List.take","Nat","instLENat","instLTNat"],"value_dag_size":1377,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_not","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HEq.trans","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.eraseIdx","List.getElem_eraseIdx","List.getElem_eraseIdx._proof_2","List.getElem_eraseIdx._proof_5","List.getElem_take","List.instGetElemNatLtLength","List.length","List.length_eraseIdx","List.length_take","List.length_take_le'","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.lt_of_lt_of_le","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_2","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_3","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_4","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_5","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_6","_private.Mathlib.Data.List.InsertIdx.0.List.take_eraseIdx_eq_take_of_le._proof_1_7","congrArg","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_1","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","List","List.insertIdx","List.length","List.take","Nat","instLENat"],"value_dag_size":1083,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.insertIdx","List.length","List.length_insertIdx","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_10","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","GetElem.getElem","LE.le","LT.lt","List","List.insertIdx","List.instGetElemNatLtLength","List.length","List.take","Nat","instLENat","instLTNat"],"value_dag_size":1447,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_not","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HEq.trans","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_insertIdx","List.getElem_insertIdx._proof_1","List.getElem_insertIdx._proof_4","List.getElem_take","List.insertIdx","List.instGetElemNatLtLength","List.length","List.length_insertIdx","List.length_take","List.length_take_le'","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.lt_of_lt_of_le","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_2","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_3","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_4","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_5","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_6","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_7","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_8","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_9","congrArg","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_2","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":81,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_3","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_4","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":76,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_3","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_5","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":66,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":91,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.insertIdx","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_2","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_6","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":68,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":104,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_1","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_7","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":114,"value_refs":["Eq","Eq.mpr_not","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_4","List.insertIdx","List.length","List.take","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_8","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":83,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":462,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.insertIdx","List.length","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_6","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.InsertIdx","name":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_9","namespace":"_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":679,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.insertIdx","List.length","List.length_insertIdx","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.InsertIdx.0.List.take_insertIdx_eq_take_of_le._proof_1_6","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.append_consecutive._proof_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.append_consecutive","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":1370,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.filter_lt_of_le_bot._simp_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.filter_lt_of_le_bot","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive._simp_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive._simp_1_2","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive._simp_1_3","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive._simp_1_4","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.inter_consecutive","reducibility":null,"statement_dag_size":50,"type_refs":["And","BEq","Eq","Inter.inter","LawfulBEq","List","List.instInterOfBEq_batteries","List.instMembership","Membership.mem"],"value_dag_size":56,"value_refs":["And","BEq","Inter.inter","LawfulBEq","List","List.instInterOfBEq_batteries","List.instMembership","List.mem_inter_iff","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.mem._proof_1_2","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.mem","reducibility":null,"statement_dag_size":49,"type_refs":["And","HAdd.hAdd","HSub.hSub","Iff","LE.le","LT.lt","Nat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instSubNat"],"value_dag_size":1407,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.nodup._simp_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.nodup","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","LT.lt","List.Nodup","List.nodup_range'._auto_1","List.range'","Nat","OfNat.ofNat","True","autoParam","instLTNat","instOfNatNat","optParam"],"value_dag_size":49,"value_refs":["LT.lt","List.Nodup","List.nodup_range'","List.nodup_range'._auto_1","List.range'","Nat","OfNat.ofNat","autoParam","eq_true","instLTNat","instOfNatNat","optParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.pairwise_lt._simp_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.pairwise_lt","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","LT.lt","List.Pairwise","List.pairwise_lt_range'._auto_1","List.range'","Nat","OfNat.ofNat","True","autoParam","instLTNat","instOfNatNat","optParam"],"value_dag_size":56,"value_refs":["LT.lt","List.Pairwise","List.pairwise_lt_range'","List.pairwise_lt_range'._auto_1","List.range'","Nat","OfNat.ofNat","autoParam","eq_true","instLTNat","instOfNatNat","optParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Intervals","name":"_private.Mathlib.Data.List.Intervals.0.List.Ico.trichotomy._proof_1_1","namespace":"_private.Mathlib.Data.List.Intervals.0.List.Ico.trichotomy","reducibility":null,"statement_dag_size":37,"type_refs":["LE.le","LT.lt","List","List.Ico","List.instMembership","Membership.mem","Nat","Or","instLENat","instLTNat"],"value_dag_size":369,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray.branch","Lean.RArray.leaf","List","List.Ico","List.Ico.mem","List.instMembership","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","Or","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.List.getElem?_iterate.match_1_1","namespace":"_private.Mathlib.Data.List.Iterate.0.List.getElem?_iterate","reducibility":"abbrev","statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":196,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LT.lt","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.List.mem_iterate._simp_1_1","namespace":"_private.Mathlib.Data.List.Iterate.0.List.mem_iterate","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Exists","Fin","List","List.get","List.instMembership","List.length","Membership.mem"],"value_dag_size":44,"value_refs":["Eq","Exists","Fin","List","List.get","List.instMembership","List.length","List.mem_iff_get","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.List.mem_iterate._simp_1_2","namespace":"_private.Mathlib.Data.List.Iterate.0.List.mem_iterate","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Exists","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":42,"value_refs":["Exists","Fin","Fin.exists_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":43,"value_refs":["Eq.refl","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.iterate.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Iterate","name":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1.splitter","namespace":"_private.Mathlib.Data.List.Iterate.0.Nat.iterate.match_1","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.iterate.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_left._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_left","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","LE.le","List","List.Nodup","List.bagInter","List.count","Nat","OfNat.ofNat","instBEqOfDecidableEq","instLENat","instOfNatNat"],"value_dag_size":582,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.bagInter","List.count","List.count_bagInter","List.nodup_iff_count","Min.min","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instHAdd","instIntCastInt","instLENat","instLawfulBEq","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_right","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","LE.le","List","List.Nodup","List.bagInter","List.count","Nat","OfNat.ofNat","instBEqOfDecidableEq","instLENat","instOfNatNat"],"value_dag_size":606,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.bagInter","List.count","List.count_bagInter","List.nodup_iff_count","Min.min","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instHAdd","instIntCastInt","instLENat","instLawfulBEq","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.bagInter_inter._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.bagInter_inter","reducibility":null,"statement_dag_size":25,"type_refs":["DecidableEq","List","List.Sublist","List.erase","instBEqOfDecidableEq"],"value_dag_size":83,"value_refs":["Classical.byContradiction","DecidableEq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Sublist","List.erase","List.erase_sublist","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.inter_left._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.inter_left","reducibility":null,"statement_dag_size":39,"type_refs":["DecidableEq","Inter.inter","List","List.Sublist","List.instInterOfBEq_batteries","instBEqOfDecidableEq"],"value_dag_size":840,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HasSubset.Subset","Iff","Inter.inter","Lean.Grind.alreadyNorm","Lean.Grind.bool_eq_to_prop","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_and","Lean.Grind.or_eq_of_eq_false_right","List","List.Sublist","List.Sublist.refl","List.Sublist.subset","List.contains","List.contains_eq_mem","List.elem","List.filter","List.instDecidableMemOfLawfulBEq","List.instHasSubset","List.instInterOfBEq_batteries","List.instMembership","List.inter_def","List.monotone_filter_right","List.sublist_filter_iff","List.subset_def","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","decide_eq_true_eq","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instBEqOfDecidableEq","instLawfulBEq","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.inter_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.Sublist.inter_right","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","Inter.inter","List","List.Sublist","List.instInterOfBEq_batteries","instBEqOfDecidableEq"],"value_dag_size":201,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Inter.inter","Lean.Grind.imp_eq_of_eq_true_left","List","List.Sublist","List.Sublist.filter","List.elem","List.filter","List.instInterOfBEq_batteries","List.inter_def","Not","True","True.intro","congr","congrArg","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.congr_eq_1._sparseCasesOn_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.congr_eq_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","List","List.bagInter.match_1","List.cons","List.nil"],"value_dag_size":57,"value_refs":["Eq.refl","List","List.bagInter.match_1","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","False","List","List.bagInter.match_1","List.cons","List.nil"],"value_dag_size":339,"value_refs":["Eq","Eq.refl","False","List","List.bagInter._sparseCasesOn_1","List.bagInter.match_1","List.casesOn","List.cons","List.ctorIdx","List.nil","List.rec","Nat.hasNotBit","absurd","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","False","List","List.bagInter.match_1","List.cons","List.nil"],"value_dag_size":357,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","List","List.bagInter._sparseCasesOn_1","List.bagInter._sparseCasesOn_1.else_eq","List.bagInter.match_1","List.casesOn","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.splitter._sparseCasesOn_3","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1","reducibility":"abbrev","statement_dag_size":65,"type_refs":["Eq","False","List","List.cons","List.nil"],"value_dag_size":184,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","List","List.casesOn","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter.match_1.splitter","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_cons_of_not_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_cons_of_not_mem","reducibility":null,"statement_dag_size":33,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.nil","instBEqOfDecidableEq"],"value_dag_size":117,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.bagInter","List.cons","List.nil","List.nil_bagInter","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_cons_of_not_mem._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_cons_of_not_mem","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.instMembership","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":650,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.bagInter","List.cons","List.cons_bagInter","List.erase","List.erase_cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_erase_of_not_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_erase_of_not_mem","reducibility":null,"statement_dag_size":34,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.erase","List.nil","instBEqOfDecidableEq"],"value_dag_size":119,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.bagInter","List.erase","List.nil","List.nil_bagInter","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_erase_of_not_mem._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_erase_of_not_mem","reducibility":null,"statement_dag_size":83,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.erase","List.instMembership","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":588,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.bagInter","List.cons","List.cons_bagInter","List.erase","List.erase_comm","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_cons","List.mem_erase_of_ne","Membership.mem","Ne","Not","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","id","implies_congr","instBEqOfDecidableEq","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_nil_iff_inter_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_nil_iff_inter_nil","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":54,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_singleton._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_singleton","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","Membership.mem","instBEqOfDecidableEq","instLawfulBEq","ite"],"value_dag_size":172,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.nestedDecidable","List","List.bagInter","List.cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","List.nil_bagInter","List.not_mem_nil","Membership.mem","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq","instLawfulBEq","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_singleton._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_singleton","reducibility":null,"statement_dag_size":93,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","Membership.mem","instBEqOfDecidableEq","instLawfulBEq","ite"],"value_dag_size":1203,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","List","List.bagInter","List.bagInter_nil","List.cons","List.cons_bagInter","List.erase","List.erase_cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left","reducibility":null,"statement_dag_size":9,"type_refs":["List.Sublist","List.nil"],"value_dag_size":60,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.Sublist","List.Sublist.refl","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left","reducibility":null,"statement_dag_size":13,"type_refs":["List","List.Sublist","List.nil"],"value_dag_size":64,"value_refs":["Classical.byContradiction","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Sublist","List.nil","List.nil_sublist","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_4","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","List","List.Sublist","List.bagInter","List.cons","List.erase","instBEqOfDecidableEq"],"value_dag_size":135,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","List","List.Sublist","List.bagInter","List.cons","List.cons_sublist_cons","List.erase","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_5","namespace":"_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","List","List.Sublist","List.bagInter","List.cons","instBEqOfDecidableEq"],"value_dag_size":128,"value_refs":["Classical.byContradiction","DecidableEq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","List","List.Sublist","List.Sublist.cons","List.bagInter","List.cons","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_mem._proof_1_5","namespace":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_mem","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.erase","List.instMembership","List.nil","Membership.mem","instBEqOfDecidableEq"],"value_dag_size":108,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.bagInter","List.cons","List.erase","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_mem._proof_1_6","namespace":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_mem","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.erase","List.instMembership","Membership.mem","instBEqOfDecidableEq"],"value_dag_size":336,"value_refs":["Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.MatchCond","Lean.Grind.PreMatchCond","Lean.Grind.bool_eq_to_prop","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","List","List.bagInter","List.bagInter.eq_3","List.cons","List.contains","List.contains_eq_mem","List.ctorIdx","List.elem","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","Membership.mem","Not","True","True.intro","congrArg","decide_eq_true_eq","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_true","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_not_mem._proof_1_5","namespace":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_not_mem","reducibility":null,"statement_dag_size":34,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.nil","instBEqOfDecidableEq"],"value_dag_size":191,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.MatchCond","Lean.Grind.PreMatchCond","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","List","List.bagInter","List.bagInter.eq_2","List.bagInter_nil","List.cons","List.ctorIdx","List.nil","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_not_mem._proof_1_6","namespace":"_private.Mathlib.Data.List.Lattice.0.List.cons_bagInter_of_not_mem","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.instMembership","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":332,"value_refs":["Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.MatchCond","Lean.Grind.PreMatchCond","Lean.Grind.bool_eq_to_prop","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","List","List.bagInter","List.bagInter.eq_3","List.cons","List.contains","List.contains_eq_mem","List.ctorIdx","List.elem","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","Membership.mem","Not","True","True.intro","congrArg","decide_eq_true_eq","eq_false","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_false","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","List","List.count","List.nil","Min.min","Nat","instBEqOfDecidableEq","instMinNat"],"value_dag_size":443,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","List.count_nil","List.nil","Min.min","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","List","List.count","List.nil","Min.min","Nat","instBEqOfDecidableEq","instMinNat"],"value_dag_size":428,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","List.count_nil","List.nil","Min.min","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_4","namespace":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter","reducibility":null,"statement_dag_size":90,"type_refs":["Bool","Bool.true","DecidableEq","Eq","List","List.bagInter","List.cons","List.count","List.elem","List.erase","Min.min","Nat","instBEqOfDecidableEq","instMinNat"],"value_dag_size":3622,"value_refs":["And","And.casesOn","BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.bagInter","List.cons","List.contains","List.contains_iff_exists_mem_beq","List.count","List.count_cons","List.count_eq_zero","List.count_erase","List.elem","List.erase","List.instMembership","Membership.mem","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","funext","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instHMul","instHSub","instLENat","instLawfulBEq","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_5","namespace":"_private.Mathlib.Data.List.Lattice.0.List.count_bagInter","reducibility":null,"statement_dag_size":82,"type_refs":["Bool","Bool.true","DecidableEq","Eq","List","List.bagInter","List.cons","List.count","List.elem","Min.min","Nat","Not","instBEqOfDecidableEq","instMinNat"],"value_dag_size":2934,"value_refs":["BEq.beq","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.bool_eq_to_prop","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.bagInter","List.cons","List.contains","List.contains_eq_mem","List.count","List.count_cons","List.count_eq_zero","List.elem","List.instDecidableMemOfLawfulBEq","List.instMembership","Membership.mem","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLENat","instLawfulBEq","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.erase_bagInter_of_not_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.erase_bagInter_of_not_mem","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.erase","List.nil","instBEqOfDecidableEq"],"value_dag_size":117,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.bagInter","List.erase","List.erase_nil","List.nil","Not","True","True.intro","congrArg","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.erase_bagInter_of_not_mem._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.erase_bagInter_of_not_mem","reducibility":null,"statement_dag_size":82,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.erase","List.instMembership","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":869,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","List","List.bagInter","List.cons","List.cons_bagInter","List.erase","List.erase_cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_erase_of_ne","Membership.mem","Ne","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_true","id","implies_congr","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union._simp_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union","reducibility":null,"statement_dag_size":50,"type_refs":["BEq","Eq","LawfulBEq","List","List.instMembership","List.instUnionOfBEq_batteries","Membership.mem","Or","Union.union"],"value_dag_size":56,"value_refs":["BEq","LawfulBEq","List","List.instMembership","List.instUnionOfBEq_batteries","List.mem_union_iff","Membership.mem","Or","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union._simp_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union._simp_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.forall_mem_union","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.instMembership","List.nil","Membership.mem","Not"],"value_dag_size":34,"value_refs":["Eq","List","List.eq_nil_iff_forall_not_mem","List.instMembership","List.nil","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint._simp_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint","reducibility":null,"statement_dag_size":50,"type_refs":["And","BEq","Eq","Inter.inter","LawfulBEq","List","List.instInterOfBEq_batteries","List.instMembership","Membership.mem"],"value_dag_size":56,"value_refs":["And","BEq","Inter.inter","LawfulBEq","List","List.instInterOfBEq_batteries","List.instMembership","List.mem_inter_iff","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint._simp_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_eq_nil_iff_disjoint","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_nil'._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_nil'","reducibility":null,"statement_dag_size":26,"type_refs":["DecidableEq","Eq","Inter.inter","List","List.instInterOfBEq_batteries","List.nil","instBEqOfDecidableEq"],"value_dag_size":87,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Inter.inter","List","List.instInterOfBEq_batteries","List.inter_nil","List.nil","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_nil'._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_nil'","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Eq","Inter.inter","List","List.cons","List.instInterOfBEq_batteries","List.nil","instBEqOfDecidableEq"],"value_dag_size":179,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Inter.inter","Lean.Grind.nestedDecidable","List","List.cons","List.instDecidableMemOfLawfulBEq","List.instInterOfBEq_batteries","List.instMembership","List.inter_cons","List.nil","List.not_mem_nil","Membership.mem","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq","instLawfulBEq","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.inter_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.inter_reverse","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","List","List.instMembership","List.reverse","Membership.mem"],"value_dag_size":31,"value_refs":["List","List.instMembership","List.mem_reverse","List.reverse","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter._proof_1_2","namespace":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter","reducibility":null,"statement_dag_size":28,"type_refs":["And","Iff","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":165,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_right","List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Not","Or","True","True.intro","congrArg","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter._proof_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter","reducibility":null,"statement_dag_size":28,"type_refs":["And","Iff","List","List.instMembership","List.nil","Membership.mem"],"value_dag_size":149,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Not","Or","True","True.intro","congrArg","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter._proof_1_4","namespace":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter","reducibility":null,"statement_dag_size":97,"type_refs":["And","Bool","Bool.true","DecidableEq","Eq","Iff","List","List.bagInter","List.cons","List.elem","List.erase","List.instMembership","Membership.mem","instBEqOfDecidableEq"],"value_dag_size":1048,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.bool_eq_to_prop","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.bagInter","List.cons","List.contains","List.contains_eq_mem","List.elem","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_cons","List.mem_erase_of_ne","List.mem_of_mem_erase","Membership.mem","Ne","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","decide_eq_true_eq","eq_false","eq_true","id","implies_congr","instBEqOfDecidableEq","instLawfulBEq","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter._proof_1_5","namespace":"_private.Mathlib.Data.List.Lattice.0.List.mem_bagInter","reducibility":null,"statement_dag_size":89,"type_refs":["And","Bool","Bool.true","DecidableEq","Eq","Iff","List","List.bagInter","List.cons","List.elem","List.instMembership","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":631,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.Bool.ne_of_eq_false_of_eq_true","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.bool_eq_to_prop","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","List","List.bagInter","List.cons","List.contains","List.contains_eq_mem","List.elem","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","decide_eq_true_eq","eq_false","eq_true","id","instBEqOfDecidableEq","instLawfulBEq","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.singleton_bagInter._proof_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.singleton_bagInter","reducibility":null,"statement_dag_size":55,"type_refs":["DecidableEq","Eq","List","List.bagInter","List.cons","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","Membership.mem","instBEqOfDecidableEq","instLawfulBEq","ite"],"value_dag_size":280,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","List","List.bagInter","List.cons","List.cons_bagInter","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nil","List.nil_bagInter","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","id","instBEqOfDecidableEq","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.sublist_suffix_of_union.match_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.sublist_suffix_of_union","reducibility":"abbrev","statement_dag_size":184,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","HAppend.hAppend","List","List.Sublist","List.instAppend","List.instUnionOfBEq_batteries","Union.union","instBEqOfDecidableEq","instHAppendOfAppend"],"value_dag_size":263,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.Sublist","List.instAppend","List.instUnionOfBEq_batteries","Union.union","instBEqOfDecidableEq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.sublist_suffix_of_union.match_1_3","namespace":"_private.Mathlib.Data.List.Lattice.0.List.sublist_suffix_of_union","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":54,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lattice","name":"_private.Mathlib.Data.List.Lattice.0.List.union_sublist_append.match_1_1","namespace":"_private.Mathlib.Data.List.Lattice.0.List.union_sublist_append","reducibility":"abbrev","statement_dag_size":185,"type_refs":["And","And.intro","DecidableEq","Eq","Exists","Exists.intro","HAppend.hAppend","List","List.Sublist","List.instAppend","List.instUnionOfBEq_batteries","Union.union","instBEqOfDecidableEq","instHAppendOfAppend"],"value_dag_size":264,"value_refs":["And","And.casesOn","And.intro","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.Sublist","List.instAppend","List.instUnionOfBEq_batteries","Union.union","instBEqOfDecidableEq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem._simp_1_1","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Set","Set.instMembership","Set.instSingletonSet","Set.mem_singleton_iff","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem._simp_1_2","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem._simp_1_3","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem._simp_1_4","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.injOn_insertIdx_index_of_notMem","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.cons","List.mapAccumr.match_1","List.nil"],"value_dag_size":49,"value_refs":["Eq.refl","List","List.cons","List.mapAccumr.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","List","List.cons","List.mapAccumr.match_1","List.nil"],"value_dag_size":56,"value_refs":["Eq.refl","List","List.cons","List.mapAccumr.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1.splitter","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr.match_1","reducibility":"abbrev","statement_dag_size":40,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.mapAccumr.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr_eq_foldr.match_1_1","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr_eq_foldr","reducibility":"abbrev","statement_dag_size":40,"type_refs":["List","List.cons","List.nil"],"value_dag_size":55,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","List","List.cons","List.mapAccumr₂.match_1","List.nil"],"value_dag_size":84,"value_refs":["Eq.refl","List","List.cons","List.mapAccumr₂.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","False","List","List.cons","List.mapAccumr₂.match_1","List.nil"],"value_dag_size":376,"value_refs":["Eq","Eq.refl","False","List","List.casesOn","List.cons","List.mapAccumr₂.match_1","List.nil","List.rec","absurd","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1","reducibility":null,"statement_dag_size":103,"type_refs":["Eq","List","List.cons","List.mapAccumr₂.match_1","List.nil"],"value_dag_size":97,"value_refs":["Eq.refl","List","List.cons","List.mapAccumr₂.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1.splitter","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂.match_1","reducibility":"abbrev","statement_dag_size":81,"type_refs":["Eq","False","List","List.cons","List.nil"],"value_dag_size":140,"value_refs":["Eq","False","False.elim","List","List.casesOn","List.cons","List.ctorIdx","List.nil","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lemmas","name":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂_eq_foldr.match_1_1","namespace":"_private.Mathlib.Data.List.Lemmas.0.List.mapAccumr₂_eq_foldr","reducibility":"abbrev","statement_dag_size":89,"type_refs":["List","List.cons","List.nil"],"value_dag_size":140,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.append_left.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.append_left","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.append_right.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.append_right","reducibility":"abbrev","statement_dag_size":130,"type_refs":["List","List.Lex","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil"],"value_dag_size":586,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm.aux","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm","reducibility":null,"statement_dag_size":33,"type_refs":["False","List","List.Lex","Std.Asymm"],"value_dag_size":270,"value_refs":["False","List","List.Lex","List.Lex.below","List.Lex.brecOn","Std.Asymm","_private.Mathlib.Data.List.Lex.0.List.Lex.asymm.aux.match_1","asymm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm.aux.match_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm.aux","reducibility":"abbrev","statement_dag_size":409,"type_refs":["List","List.Lex","List.Lex.below","List.Lex.below.cons","List.Lex.below.rel","List.Lex.cons","List.Lex.rel","List.cons"],"value_dag_size":3632,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.below","List.Lex.below.casesOn","List.Lex.below.cons","List.Lex.below.nil","List.Lex.below.rel","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm.match_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.asymm","reducibility":"abbrev","statement_dag_size":196,"type_refs":["List","List.Lex","List.Lex.cons","List.Lex.rel","List.cons"],"value_dag_size":2519,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.imp.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.imp","reducibility":"abbrev","statement_dag_size":116,"type_refs":["List","List.Lex","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil"],"value_dag_size":570,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.imp.match_1_7","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.imp","reducibility":"abbrev","statement_dag_size":238,"type_refs":["List","List.Lex","List.Lex.below","List.Lex.below.cons","List.Lex.below.nil","List.Lex.below.rel","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil"],"value_dag_size":1276,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Lex","List.Lex.below","List.Lex.below.casesOn","List.Lex.below.cons","List.Lex.below.nil","List.Lex.below.rel","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.aux","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected","reducibility":null,"statement_dag_size":44,"type_refs":["IsOrderConnected","List","List.Lex","Or","Std.Trichotomous"],"value_dag_size":72,"value_refs":["IsOrderConnected","List","List.Lex","List.brecOn","Or","Std.Trichotomous","_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.aux._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.aux._f","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.aux","reducibility":"abbrev","statement_dag_size":60,"type_refs":["IsOrderConnected","List","List.Lex","List.below","Or","Std.Trichotomous"],"value_dag_size":467,"value_refs":["Eq","Eq.ndrec","IsOrderConnected","IsOrderConnected.conn","List","List.Lex","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.below","List.cons","List.nil","Or","Or.casesOn","Or.imp","Or.inl","Or.inr","Std.Trichotomous","_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.match_1","trichotomous_of"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected.match_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.isOrderConnected","reducibility":"abbrev","statement_dag_size":212,"type_refs":["List","List.Lex","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.nil"],"value_dag_size":2056,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.to_ne.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.to_ne","reducibility":"abbrev","statement_dag_size":154,"type_refs":["Eq","List","List.Lex","List.Lex.cons","List.Lex.rel","List.cons","Ne"],"value_dag_size":805,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.ctorIdx","List.nil","Ne","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.to_ne.match_1_7","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.to_ne","reducibility":"abbrev","statement_dag_size":315,"type_refs":["Eq","List","List.Lex","List.Lex.below","List.Lex.below.cons","List.Lex.below.rel","List.Lex.cons","List.Lex.rel","List.cons","Ne"],"value_dag_size":1644,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.below","List.Lex.below.casesOn","List.Lex.below.cons","List.Lex.below.nil","List.Lex.below.rel","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.ctorIdx","List.nil","Ne","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.aux","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.Lex","Not","Std.Trichotomous"],"value_dag_size":73,"value_refs":["Eq","List","List.Lex","List.brecOn","Not","Std.Trichotomous","_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.aux._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.aux._f","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.aux","reducibility":"abbrev","statement_dag_size":59,"type_refs":["Eq","List","List.Lex","List.below","Not","Std.Trichotomous"],"value_dag_size":410,"value_refs":["Eq","Eq.mpr","Eq.ndrec","Eq.refl","False.elim","List","List.Lex","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.below","List.cons","List.nil","Not","Std.Trichotomous","Std.Trichotomous.trichotomous","_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.match_1","congrArg","id","mt","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous.match_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.Lex.trichotomous","reducibility":"abbrev","statement_dag_size":176,"type_refs":["List","List.Lex","List.cons","List.nil","Not"],"value_dag_size":341,"value_refs":["List","List.Lex","List.casesOn","List.cons","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.head_le_of_lt.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.head_le_of_lt","reducibility":"abbrev","statement_dag_size":125,"type_refs":["LT.lt","List","List.Lex","List.Lex.cons","List.Lex.rel","List.cons","List.instLT","Preorder","Preorder.toLT"],"value_dag_size":1028,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False.elim","HEq","HEq.refl","LT.lt","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.cons.noConfusion","List.ctorIdx","List.instLT","List.nil","Preorder","Preorder.toLT","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.lex_nil_or_eq_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.lex_nil_or_eq_nil","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lex","name":"_private.Mathlib.Data.List.Lex.0.List.lex_singleton_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Lex.0.List.lex_singleton_iff","reducibility":"abbrev","statement_dag_size":58,"type_refs":["List.Lex","List.Lex.rel","List.cons","List.nil"],"value_dag_size":1048,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","eq_of_heq","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","List.lookmap.go.match_1","Option","Option.none","Option.some","Unit"],"value_dag_size":37,"value_refs":["Eq.refl","List.lookmap.go.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","List.lookmap.go.match_1","Option","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":32,"value_refs":["Eq.refl","List.lookmap.go.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1.splitter","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["List.lookmap.go.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go_append","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap","reducibility":null,"statement_dag_size":34,"type_refs":["Array","Array.toListAppend","Eq","List","List.lookmap","List.lookmap.go","Option"],"value_dag_size":49,"value_refs":["Array","Array.toListAppend","Eq","List","List.brecOn","List.lookmap","List.lookmap.go","Option","_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go_append._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go_append._f","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap.go_append","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Array","Array.toListAppend","Eq","List","List.below","List.lookmap","List.lookmap.go","Option"],"value_dag_size":779,"value_refs":["Array","Array.push","Array.toList","Array.toListAppend","Array.toListAppend_eq","Array.toList_push","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","HAppend.hAppend","List","List.append_assoc","List.append_nil","List.below","List.casesOn","List.cons","List.instAppend","List.lookmap","List.lookmap.eq_1","List.lookmap.go","List.lookmap.go.eq_2","List.lookmap.go.match_1","List.nil","List.toArray","Option","Option.casesOn","Option.none","Option.some","True","Unit","congr","congrArg","congrFun'","eq_self","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_congr.match_1_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_congr","reducibility":"abbrev","statement_dag_size":109,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem","Option"],"value_dag_size":162,"value_refs":["Eq","List","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Option"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_map_eq.match_1_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_map_eq","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_none.match_1_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_none","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_some.match_1_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.lookmap_some","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.perm_lookmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.perm_lookmap","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","Membership.mem","Option","Option.instMembership"],"value_dag_size":458,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_and","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.or_eq_of_eq_false_left","Membership.mem","Not","Option","Option.instMembership","Or","True","True.intro","eq_true","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1","reducibility":null,"statement_dag_size":52,"type_refs":["Array","Eq","List","List.cons","List.nil","List.replaceFTR.go.match_1"],"value_dag_size":50,"value_refs":["Array","Eq.refl","List","List.cons","List.nil","List.replaceFTR.go.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1","reducibility":null,"statement_dag_size":62,"type_refs":["Array","Eq","List","List.cons","List.nil","List.replaceFTR.go.match_1"],"value_dag_size":58,"value_refs":["Array","Eq.refl","List","List.cons","List.nil","List.replaceFTR.go.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Lookmap","name":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1.splitter","namespace":"_private.Mathlib.Data.List.Lookmap.0.List.replaceFTR.go.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Array","List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.replaceFTR.go.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Map2","name":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_map₂Left'.match_1_1","namespace":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_map₂Left'","reducibility":"abbrev","statement_dag_size":64,"type_refs":["List","List.cons","List.nil"],"value_dag_size":95,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Map2","name":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_zipWith._simp_1_3","namespace":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_zipWith","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Map2","name":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_zipWith.match_1_1","namespace":"_private.Mathlib.Data.List.Map2.0.List.map₂Left_eq_zipWith","reducibility":"abbrev","statement_dag_size":146,"type_refs":["LE.le","List","List.cons","List.length","List.nil","Nat","instLENat"],"value_dag_size":267,"value_refs":["LE.le","List","List.casesOn","List.cons","List.length","List.nil","Nat","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Map2","name":"_private.Mathlib.Data.List.Map2.0.List.zipWith_flip.match_1_1","namespace":"_private.Mathlib.Data.List.Map2.0.List.zipWith_flip","reducibility":"abbrev","statement_dag_size":76,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":123,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq","reducibility":null,"statement_dag_size":38,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List.maximum","List.nil","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","WithBot","instDistribLatticeOfLinearOrder"],"value_dag_size":76,"value_refs":["Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.trans","False","False.casesOn","Lattice.toSemilatticeInf","Lean.Grind.intro_with_eq","Lean.Grind.not_true","LinearOrder","LinearOrder.toDecidableLT","List.maximum","List.nil","Not","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","WithBot","congrArg","eq_self","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq","reducibility":null,"statement_dag_size":74,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.maximum","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","WithBot","instDistribLatticeOfLinearOrder"],"value_dag_size":345,"value_refs":["Bool","Bool.true","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","False","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_simp_lhs_ac","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ac","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.maximum","List.maximum_cons","Max.max","Nat","Not","OfNat.ofNat","PLift","PLift.up","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","WithBot","WithBot.linearOrder","WithBot.semilatticeSup","WithBot.some","eagerReduce","id","instAssociativeMax","instCommutativeMax","instDistribLatticeOfLinearOrder","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq","reducibility":null,"statement_dag_size":53,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.maximum","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","WithBot","instDistribLatticeOfLinearOrder"],"value_dag_size":426,"value_refs":["Bool","Bool.true","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","False","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ac","Lean.Grind.AC.eq_orient","Lean.Grind.AC.superpose_ac","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.maximum","List.maximum_cons","Max.max","Nat","Not","OfNat.ofNat","PLift","PLift.up","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SemilatticeSup.toMax","WithBot","WithBot.linearOrder","WithBot.semilatticeSup","WithBot.some","eagerReduce","id","instAssociativeMax","instCommutativeMax","instDistribLatticeOfLinearOrder","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq._proof_1_4","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.maximum_eq","reducibility":null,"statement_dag_size":93,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.maximum","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","WithBot","instDistribLatticeOfLinearOrder"],"value_dag_size":159,"value_refs":["Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.maximum","Not","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","WithBot","eq_false","eq_true","id","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq","reducibility":null,"statement_dag_size":38,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List.minimum","List.nil","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","WithTop","instDistribLatticeOfLinearOrder"],"value_dag_size":76,"value_refs":["Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.trans","False","False.casesOn","Lattice.toSemilatticeSup","Lean.Grind.intro_with_eq","Lean.Grind.not_true","LinearOrder","LinearOrder.toDecidableLT","List.minimum","List.nil","Not","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","True","WithTop","congrArg","eq_self","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq","reducibility":null,"statement_dag_size":74,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.minimum","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","WithTop","instDistribLatticeOfLinearOrder"],"value_dag_size":345,"value_refs":["Bool","Bool.true","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","False","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_simp_lhs_ac","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ac","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.minimum","List.minimum_cons","Min.min","Nat","Not","OfNat.ofNat","PLift","PLift.up","PartialOrder.toPreorder","SemilatticeInf.toMin","SemilatticeSup.toPartialOrder","WithTop","WithTop.linearOrder","WithTop.semilatticeInf","WithTop.some","eagerReduce","id","instAssociativeMin","instCommutativeMin","instDistribLatticeOfLinearOrder","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq","reducibility":null,"statement_dag_size":53,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.minimum","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","WithTop","instDistribLatticeOfLinearOrder"],"value_dag_size":426,"value_refs":["Bool","Bool.true","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","False","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ac","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ac","Lean.Grind.AC.eq_orient","Lean.Grind.AC.superpose_ac","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder","LinearOrder.toDecidableLT","List","List.cons","List.minimum","List.minimum_cons","Min.min","Nat","Not","OfNat.ofNat","PLift","PLift.up","PartialOrder.toPreorder","SemilatticeInf.toMin","SemilatticeSup.toPartialOrder","WithTop","WithTop.linearOrder","WithTop.semilatticeInf","WithTop.some","eagerReduce","id","instAssociativeMin","instCommutativeMin","instDistribLatticeOfLinearOrder","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq._proof_1_4","namespace":"_private.Mathlib.Data.List.MinMax.0.List.Perm.minimum_eq","reducibility":null,"statement_dag_size":93,"type_refs":["DistribLattice.toLattice","Eq","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.minimum","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","WithTop","instDistribLatticeOfLinearOrder"],"value_dag_size":159,"value_refs":["Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.minimum","Not","PartialOrder.toPreorder","SemilatticeSup.toPartialOrder","True","True.intro","WithTop","eq_false","eq_true","id","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.argmax_mem.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.argmax_mem","reducibility":"abbrev","statement_dag_size":38,"type_refs":["List","List.cons","List.nil"],"value_dag_size":52,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.argmin_mem.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.argmin_mem","reducibility":"abbrev","statement_dag_size":38,"type_refs":["List","List.cons","List.nil"],"value_dag_size":52,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_eq_none._simp_1_3","namespace":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_eq_none","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","HAppend.hAppend","List","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":44,"value_refs":["And","Eq","HAppend.hAppend","List","List.append_eq_nil_iff","List.instAppend","List.nil","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem","namespace":"_private.Mathlib.Data.List.MinMax.0.List","reducibility":null,"statement_dag_size":59,"type_refs":["DecidableRel","List","List.argAux","List.cons","List.foldl","List.instMembership","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":659,"value_refs":["DecidableRel","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.argAux","List.cons","List.foldl","List.foldl_append","List.instAppend","List.instMembership","List.mem_cons._simp_1","List.nil","List.not_mem_nil._simp_1","List.reverseRecOn","Membership.mem","Option","Option.casesOn","Option.instMembership","Option.mem_def._simp_1","Option.none","Option.rec","Option.some","Option.some.injEq","Or","True","_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._proof_1_4","_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._proof_1_5","_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._simp_1_1","congr","congrArg","congrFun'","forall_congr","id","imp_self._simp_1","implies_congr","implies_true","instHAppendOfAppend","ite","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._proof_1_4","namespace":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem","reducibility":null,"statement_dag_size":56,"type_refs":["HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","Option.some","instHAppendOfAppend"],"value_dag_size":273,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.nil","Membership.mem","Not","Option","Option.instMembership","Option.mem_some","Option.some","Or","True","True.intro","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._proof_1_5","namespace":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem","reducibility":null,"statement_dag_size":135,"type_refs":["DecidableRel","Eq","HAppend.hAppend","Lean.Grind.nestedDecidable","List","List.argAux","List.cons","List.foldl","List.instAppend","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","Option.some","instHAppendOfAppend","ite"],"value_dag_size":555,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_right","List","List.argAux","List.cons","List.cons_append","List.foldl","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.nil","Membership.mem","Not","Option","Option.instMembership","Option.mem_some","Option.some","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem._simp_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.foldl_argAux_mem","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax._simp_1_3","namespace":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":33,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax._simp_1_4","namespace":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmax","reducibility":"abbrev","statement_dag_size":294,"type_refs":["DistribLattice.toLattice","LE.le","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.argmax","List.cons","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":395,"value_refs":["DistribLattice.toLattice","LE.le","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableLT","List","List.argmax","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmin.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.index_of_argmin","reducibility":"abbrev","statement_dag_size":294,"type_refs":["DistribLattice.toLattice","LE.le","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.argmin","List.cons","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":395,"value_refs":["DistribLattice.toLattice","LE.le","Lattice.toSemilatticeSup","LinearOrder","LinearOrder.toDecidableLT","List","List.argmin","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_concat._simp_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_concat","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","LT","LT.lt","WithBot","WithBot.instLT","WithBot.some"],"value_dag_size":38,"value_refs":["LT","LT.lt","WithBot","WithBot.coe_lt_coe","WithBot.instLT","WithBot.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_eq_coe_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_eq_coe_iff","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_eq_coe_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_eq_coe_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_le_of_forall_le._simp_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_le_of_forall_le","reducibility":null,"statement_dag_size":56,"type_refs":["And","DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeSup","LinearOrder","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":61,"value_refs":["And","DistribLattice.toLattice","LE.le","Lattice.toSemilatticeSup","LinearOrder","Max.max","PartialOrder.toPreorder","Preorder.toLE","SemilatticeSup.toMax","SemilatticeSup.toPartialOrder","instDistribLatticeOfLinearOrder","max_le_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_ne_bot_of_length_pos.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_ne_bot_of_length_pos","reducibility":"abbrev","statement_dag_size":57,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":180,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","LT.lt","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","OfNat.ofNat","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.maximum_ne_bot_of_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.maximum_ne_bot_of_ne_nil","reducibility":"abbrev","statement_dag_size":50,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":99,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.casesOn","List.cons","List.nil","Ne","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.minimum_ne_top_of_length_pos.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.minimum_ne_top_of_length_pos","reducibility":"abbrev","statement_dag_size":57,"type_refs":["LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":180,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","LT.lt","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","OfNat.ofNat","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.minimum_ne_top_of_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.MinMax.0.List.minimum_ne_top_of_ne_nil","reducibility":"abbrev","statement_dag_size":50,"type_refs":["List","List.cons","List.nil","Ne"],"value_dag_size":99,"value_refs":["Eq","Eq.refl","False","False.elim","List","List.casesOn","List.cons","List.nil","Ne","absurd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.MinMax","name":"_private.Mathlib.Data.List.MinMax.0.List.not_of_mem_foldl_argAux._proof_1_3","namespace":"_private.Mathlib.Data.List.MinMax.0.List.not_of_mem_foldl_argAux","reducibility":null,"statement_dag_size":155,"type_refs":["DecidableRel","Eq","HAppend.hAppend","IsTrans","List","List.argAux","List.cons","List.foldl","List.instAppend","List.instMembership","List.nil","Membership.mem","Not","Option","Option.casesOn","Option.instMembership","Option.some","Std.Irrefl","instHAppendOfAppend","ite"],"value_dag_size":868,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","HEq","HEq.refl","Iff","IsTrans","IsTrans.casesOn","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","List","List.argAux","List.cons","List.foldl","List.instAppend","List.instMembership","List.mem_append","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Not","Option","Option.casesOn","Option.instMembership","Option.mem_some","Option.some","Option.some.inj","Or","Or.casesOn","Std.Irrefl","Std.Irrefl.casesOn","True","True.intro","congrArg","eq_false","eq_of_heq","eq_self","eq_true","id","instHAppendOfAppend","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.eq_1","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1","reducibility":null,"statement_dag_size":63,"type_refs":["Array","Eq","List","List.cons","List.modifyLast.go.match_1","List.nil"],"value_dag_size":61,"value_refs":["Array","Eq.refl","List","List.cons","List.modifyLast.go.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.eq_2","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1","reducibility":null,"statement_dag_size":69,"type_refs":["Array","Eq","List","List.cons","List.modifyLast.go.match_1","List.nil"],"value_dag_size":66,"value_refs":["Array","Eq.refl","List","List.cons","List.modifyLast.go.match_1","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.eq_3","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1","reducibility":null,"statement_dag_size":81,"type_refs":["Array","Eq","False","List","List.cons","List.modifyLast.go.match_1","List.nil"],"value_dag_size":372,"value_refs":["Array","Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","List","List.bagInter._sparseCasesOn_1","List.bagInter._sparseCasesOn_1.else_eq","List.casesOn","List.cons","List.ctorIdx","List.modifyLast.go.match_1","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.splitter._sparseCasesOn_3","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.splitter","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1","reducibility":"abbrev","statement_dag_size":64,"type_refs":["Array","Eq","False","List","List.cons","List.nil"],"value_dag_size":168,"value_refs":["Array","Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","List","List.casesOn","List.cons","List.ctorIdx","List.nil","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go.match_1.splitter","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.ctorIdx","List.nil","Nat.hasNotBit"],"value_dag_size":97,"value_refs":["Bool","Bool.false","Eq.refl","List","List.cons","List.ctorIdx","List.nil","List.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go_concat","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast","reducibility":null,"statement_dag_size":52,"type_refs":["Array","Array.toListAppend","Eq","HAppend.hAppend","List","List.cons","List.instAppend","List.modifyLast.go","List.nil","List.toArray","instHAppendOfAppend"],"value_dag_size":68,"value_refs":["Array","Array.toListAppend","Eq","HAppend.hAppend","List","List.brecOn","List.cons","List.instAppend","List.modifyLast.go","List.nil","List.toArray","_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go_concat._f","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ModifyLast","name":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go_concat._f","namespace":"_private.Mathlib.Data.List.ModifyLast.0.List.modifyLast.go_concat","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Array","Array.toListAppend","Eq","HAppend.hAppend","List","List.below","List.cons","List.instAppend","List.modifyLast.go","List.nil","List.toArray","instHAppendOfAppend"],"value_dag_size":631,"value_refs":["Array","Array.push","Array.toList","Array.toListAppend","Array.toListAppend_eq","Array.toList_push","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","HAppend.hAppend","List","List.append_assoc","List.append_ne_nil_of_right_ne_nil","List.below","List.casesOn","List.cons","List.cons_ne_nil","List.instAppend","List.modifyLast.go","List.modifyLast.go.eq_2","List.modifyLast.go.eq_3","List.nil","List.toArray","True","congr","congrArg","congrFun'","eq_self","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NatAntidiagonal","name":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.antidiagonal_succ'._simp_1_2","namespace":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.antidiagonal_succ'","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LE.le","LT.lt","Nat","True","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.le_of_lt","eq_true","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NatAntidiagonal","name":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.map_swap_antidiagonal._simp_1_2","namespace":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.map_swap_antidiagonal","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NatAntidiagonal","name":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.mem_antidiagonal._proof_1_2","namespace":"_private.Mathlib.Data.List.NatAntidiagonal.0.List.Nat.mem_antidiagonal","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","HAdd.hAdd","HSub.hSub","Iff","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1420,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsPrefix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":863,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsPrefix","List.IsPrefix.mem","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsPrefix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":969,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsPrefix","List.IsPrefix.mem","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":114,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":57,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":130,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":48,"type_refs":["Bool","Bool.true","Eq","HSub.hSub","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":39,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_8","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.IsPrefix","List.Nodup","List.getLast","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":984,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAppend.hAppend","HSub.hSub","Iff","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_suffix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsPrefix","List.IsPrefix.eq_1","List.Nodup","List.Pairwise","List.getElem_mem","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.head_append._proof_2","List.instAppend","List.instAssociativeHAppend","List.instGetElemNatLtLength","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.nil","List.nil_of_isEmpty","List.nodup_iff_pairwise_ne","List.pairwise_append","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_5","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_6","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_getLast_mem_of_prefix._proof_1_7","cast","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_10","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":137,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_11","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":72,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":147,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":50,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.head_append._proof_2","List.instAppend","List.isEmpty","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_13","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":897,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_14","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_15","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1012,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_16","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":560,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_17","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_18","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":631,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_19","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":156,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.instAppend","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_9","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_20","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":72,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":182,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_9","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_21","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":50,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.head_append._proof_2","List.instAppend","List.isEmpty","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_22","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":172,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_9","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_23","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":67,"type_refs":["HAppend.hAppend","LT.lt","List","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":228,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_true_right","List","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_7","eq_true","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_24","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":70,"type_refs":["LE.le","LT.lt","List","List.getLast","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":155,"value_refs":["Eq","Eq.mpr_not","Eq.rec","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.zero_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_23","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_25","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":63,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.instAppend","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.instAppend","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_26","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":49,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_27","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":117,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1074,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_4","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_28","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":136,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":305,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Ne","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_27","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_29","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":104,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","HAppend.hAppend","Lean.Grind.nestedProof","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":870,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_30","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":59,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":116,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","HAppend.hAppend","Lean.Grind.nestedProof","List","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_31","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":59,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":116,"value_refs":["Bool","Bool.true","Eq","Eq.symm","Eq.trans","HAppend.hAppend","Lean.Grind.nestedProof","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_12","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_32","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":121,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1131,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_33","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":158,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1257,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.head","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_34","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":109,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":794,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_35","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":131,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":876,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.head","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_36","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":77,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":427,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_19","cast","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_37","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":87,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":448,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.getLast_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_19","cast","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_38","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":49,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":47,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.head_append._proof_2","List.instAppend","List.isEmpty","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_39","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":87,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":448,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.head_append._proof_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_19","cast","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":89,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":101,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_40","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":68,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":379,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.head_append._proof_2","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.isEmpty","List.nil","List.nil_of_isEmpty","Nat","Ne","Not","OfNat.ofNat","PLift","PLift.up","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_22","congrArg","eagerReduce","eq_true","id","instHAppendOfAppend","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_41","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":74,"type_refs":["Bool","Bool.true","Eq","LT.lt","List","List.getLast","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":374,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List","List.getLast","List.instMembership","List.isEmpty","List.length","List.length_nil","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_24","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_42","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":111,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":403,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.length_nil","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_18","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_43","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":125,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":979,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.length_nil","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_28","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_44","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":135,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":978,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.length_nil","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_15","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_45","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":37,"type_refs":["Bool","Bool.true","Eq","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["Bool","Bool.true","Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.head_append._proof_2","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_46","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":48,"type_refs":["Bool","Bool.true","Eq","HSub.hSub","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":39,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_47","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","List","List.IsInfix","List.Nodup","List.getLast","List.head","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":1886,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAppend.hAppend","HSub.hSub","Iff","Iff.mpr","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_simp_rhs_suffix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_erase0","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_lhs_prefix","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_true","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.eq_1","List.Nodup","List.Pairwise","List.append_assoc","List.getElem_mem","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.head","List.head.hcongr_3","List.head_append","List.head_append._proof_1","List.head_append._proof_2","List.head_eq_getElem","List.instAppend","List.instAssociativeHAppend","List.instGetElemNatLtLength","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_iff","List.mem_append","List.nil","List.nil_of_isEmpty","List.nodup_iff_pairwise_ne","List.pairwise_append","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_10","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_19","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_22","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_45","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_46","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_9","cast","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":145,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":995,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_2","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":533,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["HAppend.hAppend","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":73,"value_refs":["Eq.mpr_prop","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_8","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":614,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix._proof_1_9","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":121,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.IsSuffix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":526,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsSuffix","List.IsSuffix.mem","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":95,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsSuffix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":588,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsSuffix","List.IsSuffix.mem","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":114,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":57,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":130,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":37,"type_refs":["Bool","Bool.true","Eq","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["Bool","Bool.true","Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.head_append._proof_2","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_8","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.IsSuffix","List.Nodup","List.head","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":974,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAppend.hAppend","Iff","Iff.mpr","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsSuffix","List.IsSuffix.eq_1","List.Nodup","List.Pairwise","List.getElem_mem","List.head","List.head.hcongr_3","List.head_append","List.head_append._proof_1","List.head_append._proof_2","List.head_eq_getElem","List.instAppend","List.instAssociativeHAppend","List.instGetElemNatLtLength","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_iff","List.nil","List.nil_of_isEmpty","List.nodup_iff_pairwise_ne","List.pairwise_append","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_5","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_6","_private.Mathlib.Data.List.Nodup.0.List.Nodup.eq_of_head_mem_of_suffix._proof_1_7","cast","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":196,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":35,"value_refs":["LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_1","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem","reducibility":null,"statement_dag_size":135,"type_refs":["BEq","Eq","GetElem.getElem","HAdd.hAdd","LT.lt","LawfulBEq","List","List.Nodup","List.cons","List.erase","List.eraseIdx","List.instGetElemNatLtLength","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":1355,"value_refs":["And","BEq","BEq.beq","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HSub.hSub","Iff","Iff.mp","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LawfulBEq","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_of_beq_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.cons","List.erase","List.eraseIdx","List.eraseIdx_cons_succ","List.erase_cons","List.getElem_cons","List.getElem_cons.match_1","List.getElem_mem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.nodup_cons","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.decLt","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_1","_private.Mathlib.Data.List.Nodup.0.List.Nodup.erase_getElem._proof_1_2","congrArg","dite","dite_cond_eq_false","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Exists","Iff","List","List.cons","List.getLast","List.head","List.nil","Ne"],"value_dag_size":95,"value_refs":["Eq","Eq.mp","Eq.symm","Eq.trans","Exists","False","False.elim","Iff","Lean.Grind.not_true","List","List.cons","List.getLast","List.head","List.nil","Ne","Not","True","True.intro","congrArg","eq_self","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":42,"type_refs":["LT.lt","List","List.cons","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":61,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":53,"type_refs":["HSub.hSub","LT.lt","List","List.cons","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":40,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.cons","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","HSub.hSub","LT.lt","List","List.cons","List.length","List.nil","Nat","Ne","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":205,"value_refs":["Eq","Eq.mpr_not","Eq.rec","Eq.refl","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","List.nil","Nat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_3","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.cons","List.nil","Ne","Not"],"value_dag_size":93,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.nil","Ne","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","Exists","Iff","List","List.Nodup","List.cons","List.getLast","List.head","List.nil","Ne"],"value_dag_size":1882,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_not","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","GetElem.getElem","GetElem.getElem.congr_simp","HAdd.hAdd","HEq","HMul.hMul","HSub.hSub","Iff","Iff.mp","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.leaf","List","List.Nodup","List.cons","List.cons.noConfusion","List.ctorIdx","List.eq_nil_of_length_eq_zero","List.getElem_cons","List.getElem_cons.match_1","List.getElem_mem","List.getLast","List.getLast.hcongr_3","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.getLast_singleton","List.head","List.head_cons","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_cons","List.nil","List.nodup_cons","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_2","_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_3","_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_4","_private.Mathlib.Data.List.Nodup.0.List.Nodup.head_eq_getLast_iff._proof_1_5","cast","congrArg","congrFun'","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","funext","heq_eq_eq","heq_of_eq","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.map_on.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.map_on","reducibility":"abbrev","statement_dag_size":99,"type_refs":["And","And.intro","List","List.instMembership","Membership.mem","Ne"],"value_dag_size":155,"value_refs":["And","And.casesOn","And.intro","List","List.instMembership","Membership.mem","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.map_update._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.map_update","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.ne_singleton_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.ne_singleton_iff","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.ne_singleton_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.ne_singleton_iff","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Or"],"value_dag_size":25,"value_refs":["And","Or","and_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.pairwise_of_forall_ne._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.pairwise_of_forall_ne","reducibility":null,"statement_dag_size":53,"type_refs":["List","List.Nodup","List.Pairwise","List.instMembership","Membership.mem","Ne"],"value_dag_size":1022,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HasSubset.Subset","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_true","Lean.Grind.of_forall_eq_false","List","List.Nodup","List.Nodup.sublist","List.Pairwise","List.Pairwise.sublist","List.Sublist","List.Sublist.subset","List.cons","List.instHasSubset","List.instMembership","List.mem_cons","List.nil","List.nodup_cons","List.nodup_iff_pairwise_ne","List.pairwise_cons_cons","List.pairwise_iff_forall_sublist","List.subset_def","Membership.mem","Ne","Not","Or","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","false_and","id","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.pmap._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.pmap","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","List","List.Nodup","List.instMembership","List.pmap","Membership.mem"],"value_dag_size":732,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.Nodup","List.Pairwise","List.Pairwise.pmap","List.instMembership","List.nodup_iff_pairwise_ne","List.pmap","Membership.mem","Ne","Not","Or","True","True.intro","eq_false","eq_true","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":33,"type_refs":["LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_10","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":631,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_11","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":156,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.instAppend","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_5","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_12","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":172,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_5","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_13","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":67,"type_refs":["HAppend.hAppend","LT.lt","List","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":228,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_true_right","List","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_3","eq_true","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_14","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":70,"type_refs":["LE.le","LT.lt","List","List.head","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":155,"value_refs":["Eq","Eq.mpr_not","Eq.rec","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Nat.zero_sub","Ne","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_13","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_15","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":63,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.instAppend","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.instAppend","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_7","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_16","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":49,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Lean.Grind.nestedProof","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Not","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_7","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_17","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":59,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.instAppend","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":84,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.instAppend","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_16","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_18","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":54,"type_refs":["LT.lt","List","List.head","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":525,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray.leaf","List","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_13","cast","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_19","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":65,"type_refs":["Bool","Bool.true","Eq","LT.lt","List","List.head","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":311,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List","List.head","List.instMembership","List.isEmpty","List.length","List.length_nil","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_14","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":533,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_20","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":105,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":343,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.leaf","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.isEmpty","List.length","List.length_nil","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_10","congrArg","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_21","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":93,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.Nodup","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":717,"value_refs":["And","Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray.leaf","List","List.Nodup","List.Pairwise","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","List.nodup_iff_pairwise_ne","List.pairwise_append","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_self","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_22","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.Nodup","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":776,"value_refs":["And","Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_true","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray.leaf","List","List.Nodup","List.Pairwise","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.mem_append","List.nil","List.nodup_iff_pairwise_ne","List.pairwise_append","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_self","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_23","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":51,"type_refs":["LT.lt","List","List.head","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":168,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","List","List.head","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_9","eq_true","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_24","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":37,"type_refs":["Bool","Bool.true","Eq","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["Bool","Bool.true","Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.head_append._proof_2","List.isEmpty","List.length","List.length_pos_iff","List.nil","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_25","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":49,"type_refs":["List","List.IsInfix","List.IsPrefix","List.Nodup","List.head","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":1213,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAppend.hAppend","Iff","Iff.mpr","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_prefix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.eq_1","List.IsPrefix","List.Nodup","List.Pairwise","List.append_assoc","List.getElem_mem","List.head","List.head.hcongr_3","List.head_append","List.head_append._proof_1","List.head_append._proof_2","List.head_eq_getElem","List.instAppend","List.instAssociativeHAppend","List.instGetElemNatLtLength","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_iff","List.nil","List.nil_of_isEmpty","List.nodup_iff_pairwise_ne","List.pairwise_append","List.prefix_append","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_11","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_12","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_24","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_5","cast","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["HAppend.hAppend","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":73,"value_refs":["Eq.mpr_prop","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Eq","HAppend.hAppend","LE.le","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":614,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.getElem_append._proof_1","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.zero_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":121,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":72,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":147,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":50,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.head_append._proof_2","List.instAppend","List.isEmpty","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_8","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","HAppend.hAppend","LT.lt","List","List.IsInfix","List.head","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":560,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.head","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix._proof_1_9","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.prefix_of_head_mem_of_infix","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.sdiff_eq_filter.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.sdiff_eq_filter","reducibility":"abbrev","statement_dag_size":59,"type_refs":["List","List.Nodup","List.cons","List.nil"],"value_dag_size":75,"value_refs":["List","List.Nodup","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.set.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.set","reducibility":"abbrev","statement_dag_size":157,"type_refs":["List","List.Nodup","List.cons","List.instMembership","List.nil","Membership.mem","Nat","Nat.succ","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":231,"value_refs":["List","List.Nodup","List.casesOn","List.cons","List.instMembership","List.nil","Membership.mem","Nat","Nat.casesOn","Nat.succ","Not","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":31,"value_refs":["Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.nil","Ne","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_10","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":156,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.instAppend","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_5","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_11","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":72,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":182,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.append_assoc","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_5","cast","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_12","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":50,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.head_append._proof_2","List.instAppend","List.isEmpty","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_13","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":117,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1074,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getLast","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.length_pos_of_mem","List.nil","List.nil_of_isEmpty","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PLift","PLift.up","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_3","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_14","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":136,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":305,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.IsInfix","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.isEmpty","List.length","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Ne","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_13","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_15","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":48,"type_refs":["Bool","Bool.true","Eq","HSub.hSub","LT.lt","List","List.isEmpty","List.length","Nat","Not","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":39,"value_refs":["Bool","Bool.true","Eq","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.head_append._proof_2","List.isEmpty","List.nil","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_16","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":49,"type_refs":["List","List.IsInfix","List.IsSuffix","List.Nodup","List.getLast","List.instMembership","List.nil","Membership.mem","Ne"],"value_dag_size":1143,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","HAppend.hAppend","HSub.hSub","Iff","LT.lt","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_erase0_rhs","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_simp_rhs_suffix","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.imp_false_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_true","Lean.Grind.or_eq_of_eq_true_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.eq_1","List.IsSuffix","List.Nodup","List.Pairwise","List.append_assoc","List.getElem_mem","List.getLast","List.getLast.hcongr_3","List.getLast_append","List.getLast_append._proof_1","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.head_append._proof_2","List.instAppend","List.instAssociativeHAppend","List.instGetElemNatLtLength","List.instLawfulIdentityHAppendNil","List.instMembership","List.isEmpty","List.length","List.mem_append","List.nil","List.nil_of_isEmpty","List.nodup_iff_pairwise_ne","List.pairwise_append","List.suffix_append","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_15","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_5","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_6","cast","congrArg","dite","eagerReduce","eq_false","eq_of_heq","eq_self","eq_true","heq_of_eq","id","implies_congr","instDecidableEqBool","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":870,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":89,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":101,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":145,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":995,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","Ne","Not","instHAppendOfAppend"],"value_dag_size":121,"value_refs":["Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.instAppend","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":71,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.instAppend","List.isEmpty","List.nil","Ne","instHAppendOfAppend"],"value_dag_size":137,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.eq_congr","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","Ne","Not","True","cast","eq_false","eq_true","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":108,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":897,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_8","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_9","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.getLast","List.instAppend","List.instMembership","List.length","List.nil","Membership.mem","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1012,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.mem","List.append_assoc","List.getElem_append._proof_1","List.getLast","List.instAppend","List.instMembership","List.length","List.length_pos_of_mem","List.nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Nodup.0.List.Nodup.suffix_of_getLast_mem_of_infix._proof_1_1","cast","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.take_eq_filter_mem._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.take_eq_filter_mem","reducibility":null,"statement_dag_size":41,"type_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["And","Bool","Bool.true","Eq","List","List.filter","List.instMembership","List.mem_filter","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.take_eq_filter_mem.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.Nodup.take_eq_filter_mem","reducibility":"abbrev","statement_dag_size":87,"type_refs":["List","List.Nodup","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":131,"value_refs":["List","List.Nodup","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.get_bijective_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.get_bijective_iff","reducibility":null,"statement_dag_size":43,"type_refs":["BEq","Eq","LE.le","List","List.count","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":262,"value_refs":["BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","List","List.count","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastNat","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":27,"value_refs":["Eq","Eq.symm","Ne","Ne.eq_def","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map._simp_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.inj_on_of_nodup_map","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append'._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append'","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","Membership.mem","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["And","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","List.pairwise_append","Membership.mem","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append'._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append'","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","List","List.Disjoint","List.instMembership","Membership.mem","Ne"],"value_dag_size":50,"value_refs":["List","List.Disjoint","List.disjoint_iff_ne","List.instMembership","Membership.mem","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","instHAppendOfAppend"],"value_dag_size":45,"value_refs":["And","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","List.nodup_append'","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_append_comm","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","List","List.Disjoint"],"value_dag_size":24,"value_refs":["List","List.Disjoint","List.disjoint_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatten","List.instMembership","Membership.mem"],"value_dag_size":47,"value_refs":["And","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatten","List.instMembership","List.nodup_flatten","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap._simp_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatMap","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatten._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatten","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","List","List.Pairwise","List.flatten","List.instMembership","Membership.mem"],"value_dag_size":77,"value_refs":["And","List","List.Pairwise","List.flatten","List.instMembership","List.pairwise_flatten","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatten._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_flatten","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["Eq","List","List.forall_mem_ne","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_count_eq_one._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_count_eq_one","reducibility":null,"statement_dag_size":55,"type_refs":["BEq","Eq","Iff","LE.le","LT.lt","List","List.count","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":729,"value_refs":["And","And.casesOn","BEq","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","List","List.count","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congr","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":402,"value_refs":["Bool","Bool.true","Eq","Eq.refl","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_1","eagerReduce","eq_false","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":147,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","List","List.instGetElem?NatLtLength","List.length","Nat","Not","OfNat.ofNat","Option","_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_1","eq_false","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","GetElem?.getElem?","Iff","LT.lt","List","List.Nodup","List.instGetElem?NatLtLength","List.length","Nat","Not","Option","instLTNat"],"value_dag_size":2196,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.Pairwise","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.nodup_iff_pairwise_ne","List.pairwise_iff_getElem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Option.some.inj","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_1","_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_2","_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_getElem?_ne_getElem?._proof_1_3","congrArg","eagerReduce","eq_false","eq_true","forall_congr","forall_prop_domain_congr","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_injective_getElem._proof_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_injective_getElem","reducibility":null,"statement_dag_size":30,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","instHAppendOfAppend"],"value_dag_size":45,"value_refs":["And","HAppend.hAppend","List","List.Disjoint","List.Nodup","List.instAppend","List.nodup_append'","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_5","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_6","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle._simp_1_7","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_middle","reducibility":null,"statement_dag_size":40,"type_refs":["And","Eq","List","List.Disjoint","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":44,"value_refs":["And","List","List.Disjoint","List.cons","List.disjoint_cons_right","List.instMembership","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_reverse","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_tail_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_tail_reverse","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LT.lt","Nat","Nat.succ","OfNat.ofNat","True","instLTNat","instOfNatNat"],"value_dag_size":23,"value_refs":["LT.lt","Nat","Nat.succ","Nat.zero_lt_succ","OfNat.ofNat","eq_true","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.nodup_tail_reverse._simp_1_2","namespace":"_private.Mathlib.Data.List.Nodup.0.List.nodup_tail_reverse","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","True","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":32,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.lt_add_one","OfNat.ofNat","eq_true","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup._simp_1_3","namespace":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","List.Nodup","List.nil","True"],"value_dag_size":13,"value_refs":["List.Nodup","List.nil","List.nodup_nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup._simp_1_4","namespace":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup","reducibility":"abbrev","statement_dag_size":103,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":473,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup.match_1_9","namespace":"_private.Mathlib.Data.List.Nodup.0.List.rel_nodup","reducibility":"abbrev","statement_dag_size":238,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1126,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Nodup","name":"_private.Mathlib.Data.List.Nodup.0.Option.toList_nodup.match_1_1","namespace":"_private.Mathlib.Data.List.Nodup.0.Option.toList_nodup","reducibility":"abbrev","statement_dag_size":27,"type_refs":["Option","Option.none","Option.some","Unit"],"value_dag_size":39,"value_refs":["Option","Option.casesOn","Option.none","Option.some","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get._simp_1_1","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get._simp_1_2","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get._simp_1_3","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.duplicate_iff_exists_distinct_get","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":26,"value_refs":["Eq","LE.le","Nat","Nat.le_zero","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_10","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":734,"type_refs":["DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mpr","Fin","Fin.instPartialOrder","Fin.mk","Fin.val","Fin.val_fin_lt","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","LT.lt.trans","Lattice.toSemilatticeInf","List","List.get","List.instGetElem?NatLtLength","List.length","Nat","Nat.add_lt_add_iff_right._simp_1","Nat.decLt","Nat.instLinearOrder","Nat.instPreorder","Not","Option","OrderEmbedding","OrderEmbedding.lt_iff_lt","OrderEmbedding.ofStrictMono","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","RelEmbedding","SemilatticeInf.toPartialOrder","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_2","absurd","congrArg","congrFun'","dif_neg","dif_pos","dite","id","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTFin","instLTNat","propext"],"value_dag_size":2693,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mp","Eq.mpr","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","Fin","Fin.instPartialOrder","Fin.isLt","Fin.mk","Fin.val","Fin.val_fin_lt","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.refl","HEq.trans","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","LT.lt.trans","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.get","List.get_eq_getElem","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.add_lt_add_iff_right._simp_1","Nat.decLe","Nat.decLt","Nat.instLinearOrder","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.none","Option.some","Or","Or.casesOn","OrderEmbedding","OrderEmbedding.coe_ofStrictMono","OrderEmbedding.lt_iff_lt","OrderEmbedding.ofStrictMono","OrderEmbedding.ofStrictMono.congr_simp","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","RelEmbedding","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","StrictMono","True","True.intro","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_2","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_5","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_6","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_7","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_8","absurd","congrArg","congrFun","congrFun'","dif_neg","dif_pos","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","funext","getElem?_neg","getElem?_pos","heq_of_eq","id","implies_congr","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLEFin","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":141,"type_refs":["DFunLike.coe","DistribLattice.toLattice","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lattice.toSemilatticeInf","List","List.length","Nat","Nat.instLinearOrder","Nat.instPreorder","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLT","RelEmbedding","SemilatticeInf.toPartialOrder","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLTNat"],"value_dag_size":663,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.mk","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.instLinearOrder","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","OrderEmbedding","PartialOrder.toPreorder","Preorder.toLT","RelEmbedding","SemilatticeInf.toPartialOrder","congrArg","eagerReduce","id","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instHMul","instLEFin","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":59,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":158,"type_refs":["DFunLike.coe","DistribLattice.toLattice","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","Lattice.toSemilatticeInf","List","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","PartialOrder.toPreorder","RelEmbedding","SemilatticeInf.toPartialOrder","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","dite","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instOfNatNat"],"value_dag_size":775,"value_refs":["DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mpr","Eq.mpr_prop","Eq.rec","Eq.refl","Fin","Fin.instPartialOrder","Fin.mk","Fin.val","Fin.val_fin_lt","HAdd.hAdd","LE.le","LT.lt","LT.lt.trans","Lattice.toSemilatticeInf","Lean.Grind.Nat.lt_eq","List","List.length","Nat","Nat.add_lt_add_iff_right._simp_1","Nat.decLe","Nat.decLt","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","OrderEmbedding.lt_iff_lt","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","RelEmbedding","SemilatticeInf.toPartialOrder","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_2","absurd","congrArg","congrFun'","dif_neg","dif_pos","dite","dite_congr","funext","id","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTFin","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_5","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":229,"type_refs":["DFunLike.coe","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","OrderEmbedding.ofStrictMono","RelEmbedding","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","dite","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"],"value_dag_size":245,"value_refs":["DFunLike.coe","Eq.substr","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","OrderEmbedding.ofStrictMono","RelEmbedding","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","dite","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_6","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":170,"type_refs":["DFunLike.coe","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","OrderEmbedding.ofStrictMono","RelEmbedding","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","dite","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"],"value_dag_size":404,"value_refs":["DFunLike.coe","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.trans","Fin","Fin.isLt","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.Nat.lt_eq","Lean.Grind.dite_cond_eq_true'","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","OrderEmbedding","OrderEmbedding.coe_ofStrictMono","OrderEmbedding.ofStrictMono","PartialOrder.toPreorder","Preorder.toLE","RelEmbedding","SemilatticeInf.toPartialOrder","StrictMono","True","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_5","congrArg","congrFun","dite","eq_true","instAddNat","instDistribLatticeOfLinearOrder","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_7","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":114,"type_refs":["DFunLike.coe","Fin","Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","OrderEmbedding","RelEmbedding","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"],"value_dag_size":112,"value_refs":["DFunLike.coe","Fin","Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","OrderEmbedding","RelEmbedding","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_8","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_9","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq","reducibility":null,"statement_dag_size":257,"type_refs":["DFunLike.coe","Eq","Fin","Fin.mk","Fin.val","GetElem?.getElem?","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.length","Nat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Not","OfNat.ofNat","Option","OrderEmbedding","OrderEmbedding.ofStrictMono","RelEmbedding","StrictMono","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","dite","instAddNat","instFunLikeOrderEmbedding","instHAdd","instLEFin","instLENat","instLTNat","instOfNatNat"],"value_dag_size":905,"value_refs":["Bool","Bool.false","Bool.true","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Fin","Fin.mk","Fin.val","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instLinearOrder","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.none","OrderEmbedding","OrderEmbedding.ofStrictMono","PartialOrder.toPreorder","RelEmbedding","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","StrictMono","True","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_3","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4","_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_5","congrArg","dite","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instFunLikeOrderEmbedding","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLEFin","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.NodupEquivFin","name":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_orderEmbedding_getElem?_eq._simp_1_1","namespace":"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_orderEmbedding_getElem?_eq","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some._proof_1_5","namespace":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some","reducibility":null,"statement_dag_size":22,"type_refs":["Fin","Fin.val","LT.lt","Nat","instLTNat"],"value_dag_size":428,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_le","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.le_upper'","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some.match_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some","reducibility":"abbrev","statement_dag_size":397,"type_refs":["And","And.intro","Bool","Bool.not","Bool.true","Eq","Exists","Exists.intro","Fin","GetElem.getElem","LT.lt","List","List.find?_eq_some_iff_getElem._proof_2","List.instGetElemNatLtLength","List.length","List.ofFn","Nat","instLTNat"],"value_dag_size":763,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.not","Bool.true","Eq","Exists","Exists.casesOn","Exists.intro","Fin","GetElem.getElem","LT.lt","List","List.find?_eq_some_iff_getElem._proof_2","List.instGetElemNatLtLength","List.length","List.ofFn","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some.match_1_3","namespace":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some","reducibility":"abbrev","statement_dag_size":176,"type_refs":["And","And.intro","Bool","Bool.true","Eq","Exists","Exists.intro","Fin","LT.lt","Nat","Not","instLTFin"],"value_dag_size":311,"value_refs":["And","And.casesOn","And.intro","Bool","Bool.true","Eq","Exists","Exists.casesOn","Exists.intro","Fin","LT.lt","Nat","Not","instLTFin"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some_of_injective._simp_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some_of_injective","reducibility":null,"statement_dag_size":76,"type_refs":["And","Bool","Bool.true","Eq","Exists","Fin","LT.lt","List.find?","List.ofFn","Nat","Not","Option","Option.some","instLTFin"],"value_dag_size":82,"value_refs":["And","Bool","Bool.true","Eq","Exists","Fin","LT.lt","List.find?","List.find?_ofFn_eq_some","List.ofFn","Nat","Not","Option","Option.some","instLTFin","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some_of_injective._simp_1_2","namespace":"_private.Mathlib.Data.List.OfFn.0.List.find?_ofFn_eq_some_of_injective","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.mem_ofFn'._proof_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.mem_ofFn'","reducibility":null,"statement_dag_size":43,"type_refs":["Fin","Iff","List","List.instMembership","List.ofFn","Membership.mem","Nat","Set","Set.instMembership","Set.range"],"value_dag_size":170,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","False","Fin","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.instMembership","List.mem_ofFn","List.ofFn","Membership.mem","Nat","Not","Set","Set.instMembership","Set.mem_range","Set.range","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_const.match_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_const","reducibility":"abbrev","statement_dag_size":35,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":44,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_fin_repeat._simp_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_fin_repeat","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Fin","List","List.ofFn","List.replicate","Nat"],"value_dag_size":30,"value_refs":["Eq.symm","Fin","List","List.ofFn","List.ofFn_const","List.replicate","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_get.match_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_get","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_getElem_eq_map._proof_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.ofFn_getElem_eq_map","reducibility":null,"statement_dag_size":30,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn._simp_1_1","namespace":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.Pairwise","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":72,"value_refs":["GetElem.getElem","LT.lt","List","List.Pairwise","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn._simp_1_2","namespace":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OfFn","name":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn._simp_1_3","namespace":"_private.Mathlib.Data.List.OfFn.0.List.pairwise_ofFn","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":44,"value_refs":["Fin","Fin.mk","Fin.mk_lt_mk","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag._simp_1_1","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag","reducibility":null,"statement_dag_size":104,"type_refs":["And","Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.offDiag","Membership.mem","Nat","Ne","Prod","Prod.fst","Prod.snd","instLTNat"],"value_dag_size":107,"value_refs":["And","Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_offDiag_iff_getElem","List.offDiag","Membership.mem","Nat","Ne","Prod","Prod.fst","Prod.snd","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag._simp_1_2","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","instLTNat"],"value_dag_size":68,"value_refs":["Eq","Exists","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_iff_getElem","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.of_offDiag._simp_1_1","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.of_offDiag","reducibility":null,"statement_dag_size":45,"type_refs":["BEq","Eq","LE.le","LawfulBEq","List","List.Nodup","List.count","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":49,"value_refs":["BEq","LE.le","LawfulBEq","List","List.Nodup","List.count","List.nodup_iff_count_le_one","Nat","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.of_offDiag._simp_1_2","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.of_offDiag","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Prod","Prod.mk"],"value_dag_size":35,"value_refs":["Prod","Prod.forall","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.offDiag._proof_1_1","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.offDiag","reducibility":null,"statement_dag_size":80,"type_refs":["Classical.decEq","Eq","HMul.hMul","HSub.hSub","LE.le","List","List.Nodup","List.count","Nat","OfNat.ofNat","instBEqOfDecidableEq","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat","ite"],"value_dag_size":2430,"value_refs":["Bool","Bool.true","Classical.byContradiction","Classical.decEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.mul_eq_kk","Int.Internal.Linear.mul_eq_zero_left","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.of_var_eq","Int.Internal.Linear.var_eq","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.natCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Semiring.natCast_mul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Nodup","List.Nodup.count","List.count","List.instDecidableMemOfLawfulBEq","List.instMembership","List.nodup_iff_count","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLawfulBEq","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.Perm.offDiag._simp_1_1","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.Perm.offDiag","reducibility":null,"statement_dag_size":40,"type_refs":["BEq","Eq","LawfulBEq","List","List.Perm","List.count","Nat"],"value_dag_size":46,"value_refs":["BEq","Eq","LawfulBEq","List","List.Perm","List.count","List.perm_iff_count","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite._proof_1_3","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","List","List.count","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1599,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_def'_norm","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.pow","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toAdd","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instHPow","instHSub","instIntCastInt","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instPowNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite._proof_1_4","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","List","List.count","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":209,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","Nat","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instMulNat","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite._proof_1_5","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite","reducibility":null,"statement_dag_size":63,"type_refs":["DecidableEq","Eq","HAdd.hAdd","HMul.hMul","List","List.count","Nat","OfNat.ofNat","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":201,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.count","Nat","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instBEqOfDecidableEq","instHAdd","instHMul","instMulNat","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite._simp_1_1","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite","reducibility":null,"statement_dag_size":50,"type_refs":["BEq","Eq","LawfulBEq","List","List.count","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":56,"value_refs":["BEq","Eq","LawfulBEq","List","List.count","List.count_eq_zero","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite._simp_1_2","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.count_offDiag_eq_mul_sub_ite","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_10","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_11","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Ne"],"value_dag_size":21,"value_refs":["Ne","ne_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_2","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":100,"type_refs":["And","Eq","Exists","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.instGetElemNatLtLength","List.instMembership","List.length","List.zipIdx","Membership.mem","Nat","Prod","Prod.mk","instAddNat","instHAdd","instLTNat"],"value_dag_size":105,"value_refs":["And","Exists","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.exists_mem_zipIdx","List.instGetElemNatLtLength","List.instMembership","List.length","List.zipIdx","Membership.mem","Nat","Prod","Prod.mk","instAddNat","instHAdd","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_3","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":78,"type_refs":["And","Eq","Exists","GetElem.getElem","LT.lt","List","List.eraseIdx","List.instGetElemNatLtLength","List.instMembership","List.length","Membership.mem","Nat","Ne","instLTNat"],"value_dag_size":82,"value_refs":["And","Eq","Exists","GetElem.getElem","LT.lt","List","List.eraseIdx","List.instGetElemNatLtLength","List.instMembership","List.length","List.mem_eraseIdx_iff_getElem","Membership.mem","Nat","Ne","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_4","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_5","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_6","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_7","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":34,"value_refs":["And","Eq.symm","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_8","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem._simp_1_9","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.mem_offDiag_iff_getElem","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.OffDiag","name":"_private.Mathlib.Data.List.OffDiag.0.List.offDiag_cons_perm._simp_1_2","namespace":"_private.Mathlib.Data.List.OffDiag.0.List.offDiag_cons_perm","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HAppend.hAppend","List","List.Perm","List.instAppend","instHAppendOfAppend"],"value_dag_size":42,"value_refs":["HAppend.hAppend","List","List.Perm","List.instAppend","List.perm_append_left_iff","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.cons_cons_of_trans._simp_1_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.cons_cons_of_trans","reducibility":null,"statement_dag_size":41,"type_refs":["And","Eq","IsTrans","List","List.Pairwise","List.cons"],"value_dag_size":48,"value_refs":["And","IsTrans","List","List.Pairwise","List.cons","List.pairwise_cons_cons_iff_of_trans","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head","reducibility":null,"statement_dag_size":37,"type_refs":["LT.lt","List","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.instMembership","List.length","List.length_pos_iff","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_2","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","LT.lt","List","List.cons","List.instMembership","List.length","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":402,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.instMembership","List.length","List.length_pos_of_mem","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_1","cast","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_3","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem","Not"],"value_dag_size":102,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.instMembership","List.ne_nil_of_mem","List.nil","Membership.mem","Not","True","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_4","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head","reducibility":null,"statement_dag_size":53,"type_refs":["List","List.Pairwise","List.head","List.instMembership","List.ne_nil_of_mem","Membership.mem"],"value_dag_size":1084,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq","HEq.refl","HEq.trans","Iff","Iff.mpr","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.leaf","List","List.Pairwise","List.Pairwise.casesOn","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.getElem_cons_zero","List.head","List.head_eq_getElem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_pos_iff","List.length_pos_of_mem","List.mem_cons","List.ne_nil_of_mem","List.nil","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_1","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_of_rel_head_head._proof_1_2","cast","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail","reducibility":null,"statement_dag_size":30,"type_refs":["List","List.instMembership","List.nil","List.tail","Membership.mem","Ne"],"value_dag_size":33,"value_refs":["List","List.instMembership","List.mem_of_mem_tail","List.ne_nil_of_mem","List.tail","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_2","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail","reducibility":null,"statement_dag_size":40,"type_refs":["LT.lt","List","List.instMembership","List.length","List.tail","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.instMembership","List.length","List.length_pos_iff","List.nil","List.tail","Membership.mem","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_1","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_3","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","LT.lt","List","List.cons","List.instMembership","List.length","List.tail","Membership.mem","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":306,"value_refs":["Bool","Bool.true","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.cons","List.instMembership","List.length","List.tail","Membership.mem","Nat","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_2","cast","congrArg","eagerReduce","eq_true","id","instHAdd","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_4","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","List.tail","Membership.mem","Not"],"value_dag_size":105,"value_refs":["Eq","Eq.symm","Eq.trans","False","False.elim","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.ctorIdx","List.instMembership","List.nil","List.tail","Membership.mem","Not","True","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_1","cast","eq_false","eq_true","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_5","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail","reducibility":null,"statement_dag_size":50,"type_refs":["List","List.Pairwise","List.head","List.instMembership","List.mem_of_mem_tail","List.ne_nil_of_mem","List.tail","Membership.mem"],"value_dag_size":868,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq","HEq.refl","HEq.trans","Iff.mpr","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.leaf","List","List.Pairwise","List.Pairwise.casesOn","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.getElem_cons_zero","List.head","List.head_eq_getElem","List.instGetElemNatLtLength","List.instMembership","List.length","List.length_pos_iff","List.mem_of_mem_tail","List.ne_nil_of_mem","List.nil","List.tail","List.tail_cons","Membership.mem","Nat","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_1","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_2","_private.Mathlib.Data.List.Pairwise.0.List.Pairwise.rel_head_tail._proof_1_3","cast","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAdd","instIntCastInt","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_cons_cons_iff_of_trans._simp_1_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_cons_cons_iff_of_trans","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.IsChain","List.Pairwise","Trans"],"value_dag_size":43,"value_refs":["Eq.symm","List","List.IsChain","List.Pairwise","List.isChain_iff_pairwise","Trans","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_cons_cons_iff_of_trans._simp_1_2","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_cons_cons_iff_of_trans","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.IsChain","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.IsChain","List.cons","List.isChain_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LT.lt","List","List.length","List.nil","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":229,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","List","List.length","List.length_nil","List.nil","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_10","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":87,"value_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.instAppend","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_9","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_100","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":105,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":113,"value_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.getLast_eq_getElem._proof_3","List.instAppend","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":66,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":155,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.drop","List.getElem_drop._proof_1","List.length","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":83,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":95,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.getElem_drop._proof_1","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_105","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":56,"type_refs":["LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_106","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":868,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getElem_append._proof_1","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.zero_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_107","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":111,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1118,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_108","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":88,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":100,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_109","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":125,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1239,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getElem_append._proof_1","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_11","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":52,"type_refs":["HAppend.hAppend","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":64,"value_refs":["HAppend.hAppend","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.instAppend","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_8","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_110","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":101,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":331,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.drop","List.instAppend","List.length","List.length_append","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.decLe","Nat.min_def","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","cast","congrArg","eq_true","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instMinNat","instOfNatNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_111","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":103,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":362,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.drop","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.length","List.length_append","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.decLe","Nat.min_def","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","cast","congrArg","eq_true","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instMinNat","instOfNatNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_112","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":70,"type_refs":["Bool","Bool.true","Eq","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":67,"value_refs":["Bool","Bool.true","Eq","List","List.drop","List.head_append._proof_2","List.isEmpty","List.length","List.take","Nat","Not","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_113","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instOfNatNat"],"value_dag_size":168,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LE.le","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.drop","List.instAppend","List.length","List.nil","List.take","List.take_add","Nat","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","cast","eq_true","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_114","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":80,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":190,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","LE.le","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","List","List.drop","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.length","List.nil","List.take","List.take_add","Nat","Not","OfNat.ofNat","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","cast","eq_true","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_115","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":70,"type_refs":["LE.le","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":67,"value_refs":["LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_116","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":83,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":103,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_117","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":86,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_118","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":97,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_119","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":116,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":550,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.decLe","Nat.min_def","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_12","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":177,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_7","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_120","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":95,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":107,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_121","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":133,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":597,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","Nat.decLe","Nat.min_def","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_122","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":102,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":396,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.take","List.take_add","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_123","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":89,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":101,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_124","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":116,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":441,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.take","List.take_add","Nat","Nat.ToInt.add_congr","Nat.ToInt.lt_eq","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_104","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_125","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":100,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":662,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_126","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_127","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":115,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":691,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_128","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":38,"type_refs":["LT.lt","List","List.length","List.take","Nat","instLTNat"],"value_dag_size":535,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_126","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_129","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":92,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":581,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_13","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":52,"type_refs":["HAppend.hAppend","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":152,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","LT.lt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_6","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_130","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_131","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":607,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_132","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":35,"type_refs":["LT.lt","List","List.length","List.take","Nat","instLTNat"],"value_dag_size":480,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_130","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_133","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":112,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":525,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.lt_eq","Nat.decLe","Nat.min_def","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_134","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":83,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":95,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_135","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":125,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":667,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.decLe","Nat.min_def","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_136","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":371,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.instAppend","List.length","List.take","List.take_add","Nat","Nat.ToInt.lt_eq","NatCast.natCast","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_137","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":77,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":89,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_138","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":108,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":504,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.lt_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem_append._proof_1","List.instAppend","List.length","List.take","List.take_add","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.lt_eq","Nat.sub_sub","NatCast.natCast","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_139","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":954,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_14","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":159,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_9","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_140","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":62,"type_refs":["LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_141","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1042,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getElem_append._proof_1","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.zero_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_142","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":119,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1279,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_143","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":94,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":106,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_144","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":136,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1410,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getElem_append._proof_1","List.instAppend","List.length","List.length_append","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_145","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":107,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":992,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_append","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_146","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1020,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.length","List.length_append","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_147","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":110,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1015,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.head_append._proof_1","List.instAppend","List.isEmpty","List.length","List.length_append","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_148","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":55,"type_refs":["Bool","Bool.true","Eq","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","Not"],"value_dag_size":52,"value_refs":["Bool","Bool.true","Eq","List","List.drop","List.head_append._proof_2","List.isEmpty","List.length","List.take","Nat","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_149","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":31,"type_refs":["LT.lt","List","List.length","Nat","instLTNat"],"value_dag_size":97,"value_refs":["Eq","Eq.symm","Eq.trans","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_128","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_132","cast","eq_true","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_15","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":37,"type_refs":["LT.lt","List","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":180,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.rec","Eq.refl","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_self","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_8","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_150","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":95,"type_refs":["GetElem.getElem","LT.lt","List","List.IsInfix","List.getLast","List.head","List.instGetElemNatLtLength","List.length","List.pairwise_iff_forall_infix._proof_2","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":2696,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff.mpr","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.trans","List.IsPrefix.isInfix","List.IsSuffix.isInfix","List.drop","List.drop_suffix","List.getElem_drop","List.getElem_drop._proof_1","List.getElem_take","List.getLast","List.getLast_drop","List.getLast_drop._proof_2","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.head","List.head_eq_getElem","List.instGetElemNatLtLength","List.length","List.length_drop","List.length_pos_iff","List.length_take","List.length_take_le'","List.ne_nil_of_length_pos","List.nil","List.pairwise_iff_forall_infix._proof_2","List.take","List.take_prefix","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.lt_of_lt_of_le","Nat.min_def","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_103","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_117","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_118","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_76","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_77","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","heq_of_eq","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_16","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":70,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_17","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":72,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":207,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_7","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_18","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":38,"type_refs":["LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.mpr_prop","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_19","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":49,"type_refs":["LE.le","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":131,"value_refs":["Eq","Eq.mpr_not","Eq.rec","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.zero_sub","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_6","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_20","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":61,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_21","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":50,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":48,"value_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_22","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":51,"type_refs":["HSub.hSub","LT.lt","List","List.IsInfix","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":712,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_20","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_23","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":72,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":70,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_24","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":75,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_14","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_25","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":168,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_14","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_26","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":53,"type_refs":["HAppend.hAppend","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":231,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_self","OfNat.ofNat","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_11","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_13","cast","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_27","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":85,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_28","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":96,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":116,"value_refs":["Eq.mpr_not","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_11","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_29","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":92,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":104,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_30","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":135,"value_refs":["Eq.mpr_not","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_10","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_31","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","List","List.instAppend","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_32","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":90,"value_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.instAppend","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_25","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_33","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":185,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_24","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_34","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":162,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_25","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_35","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":71,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":83,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_36","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":85,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":230,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_24","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_37","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":74,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_38","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":68,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.IsInfix","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":962,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_37","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_39","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":76,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_4","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":46,"value_refs":["Eq","LT.lt","Lean.Grind.nestedProof","List","List.getLast_eq_getElem._proof_3","List.length","List.nil","List.pairwise_iff_forall_infix._proof_2","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_40","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":78,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":78,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_34","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_41","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":76,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":174,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_34","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_42","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":803,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.instAppend","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_22","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_43","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":86,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":98,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_44","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":127,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":936,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_22","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_45","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":831,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.append_assoc","List.instAppend","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_22","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_46","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":75,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_47","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":117,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":953,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.append_assoc","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_22","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_48","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":110,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_49","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":112,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":141,"value_refs":["Eq.mpr_not","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_32","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_5","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":34,"type_refs":["LT.lt","List","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Eq","Iff.mpr","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_pos_iff","List.nil","List.pairwise_iff_forall_infix._proof_2","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_50","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":81,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":93,"value_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.instAppend","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_41","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_51","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":81,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":191,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_40","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_52","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":64,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_41","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_53","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":77,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":89,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_54","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":91,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":239,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_40","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_55","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":82,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":80,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_56","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":71,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.IsInfix","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1159,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_55","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_57","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":84,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":82,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_58","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":81,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":81,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_52","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_59","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":79,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":180,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_52","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_6","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":50,"type_refs":["HAppend.hAppend","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":50,"value_refs":["LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_5","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_60","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":116,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_61","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":118,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":147,"value_refs":["Eq.mpr_not","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_50","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_62","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1056,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.instAppend","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_38","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_63","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":96,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":108,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_64","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":136,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1151,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_38","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_65","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1084,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.append_assoc","List.instAppend","List.length","Nat","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_38","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_66","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":71,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":83,"value_refs":["Eq.mpr_prop","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_67","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":138,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","LE.le","LT.lt","List","List.IsInfix","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1206,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.mpr_not","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.IsInfix","List.IsInfix.length_le","List.append_assoc","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_38","cast","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_68","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":92,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":417,"value_refs":["Bool","Bool.true","Eq","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instAppend","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_41","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_57","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_69","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":109,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1057,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.instAppend","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_63","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_7","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":58,"type_refs":["HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":57,"value_refs":["HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_4","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_70","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":104,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":810,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.instAppend","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_43","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_71","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":109,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":124,"value_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_append_left'._proof_1","List.instAppend","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_70","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_72","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":108,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","List","List.instAppend","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":245,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.rec","Eq.refl","Eq.trans","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.sub_sub","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_70","congrArg","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_73","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":112,"type_refs":["Eq","GetElem.getElem","HAppend.hAppend","LT.lt","List","List.getLast","List.head","List.instAppend","List.instGetElemNatLtLength","List.length","List.pairwise_iff_forall_infix._proof_2","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":2262,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem","GetElem.getElem","GetElem.getElem.congr_simp","GetElem.getElem.hcongr_8","HAdd.hAdd","HAppend.hAppend","HEq","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff.mpr","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_left'","List.getElem_append_left'._proof_1","List.getElem_append_right'","List.getElem_append_right'._proof_1","List.getLast","List.getLast_eq_getElem","List.getLast_eq_getElem._proof_3","List.head","List.head_eq_getElem","List.instAppend","List.instGetElemNatLtLength","List.length","List.length_pos_iff","List.nil","List.pairwise_iff_forall_infix._proof_2","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_10","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_11","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_21","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_23","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_3","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_4","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_5","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_8","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","heq_of_eq","id","implies_congr","instAddNat","instHAdd","instHAppendOfAppend","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":33,"type_refs":["LE.le","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":55,"value_refs":["Eq.substr","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.pairwise_iff_forall_infix._proof_2","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":68,"type_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":65,"value_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_76","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HAdd.hAdd","LT.lt","List","List.drop","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":84,"value_refs":["Eq","HAdd.hAdd","Iff.mpr","LT.lt","List","List.drop","List.length","List.length_pos_iff","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_77","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":60,"type_refs":["Eq","HAdd.hAdd","List","List.drop","List.nil","List.take","Nat","Ne","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq","HAdd.hAdd","List","List.drop","List.getLast_drop._proof_2","List.ne_nil_of_length_pos","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_78","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.drop","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":61,"value_refs":["Eq","HAdd.hAdd","List","List.drop","List.getLast_eq_getElem._proof_3","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_79","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":42,"type_refs":["LE.le","List","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":39,"value_refs":["LE.le","List","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_8","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":47,"type_refs":["HAppend.hAppend","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":136,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","LT.lt","Lean.Grind.nestedProof","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_5","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_80","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","LE.le","List","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":56,"value_refs":["HAdd.hAdd","LE.le","List","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_81","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":53,"type_refs":["LE.le","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":50,"value_refs":["LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_82","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":42,"type_refs":["LE.le","List","List.drop","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":39,"value_refs":["LE.le","List","List.drop","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_83","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":83,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.drop","List.instAppend","List.isEmpty","List.nil","List.take","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instOfNatNat"],"value_dag_size":87,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.drop","List.getLast_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.take","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_84","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":51,"type_refs":["Bool","Bool.true","Eq","List","List.drop","List.isEmpty","List.nil","List.take","Nat","Ne","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":48,"value_refs":["Bool","Bool.true","Eq","List","List.drop","List.head_append._proof_2","List.isEmpty","List.take","Nat","Not","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_85","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":83,"type_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.drop","List.instAppend","List.isEmpty","List.nil","List.take","Nat","Ne","Not","OfNat.ofNat","instHAppendOfAppend","instOfNatNat"],"value_dag_size":87,"value_refs":["Bool","Bool.true","Eq","HAppend.hAppend","List","List.drop","List.head_append._proof_1","List.instAppend","List.isEmpty","List.nil","List.take","Nat","Not","OfNat.ofNat","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_86","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":46,"type_refs":["Bool","Bool.true","Eq","List","List.drop","List.isEmpty","List.nil","List.take","Nat","Ne","Not"],"value_dag_size":43,"value_refs":["Bool","Bool.true","Eq","List","List.drop","List.head_append._proof_2","List.isEmpty","List.take","Nat","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":98,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":660,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_88","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":97,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":680,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.isEmpty","List.length","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_85","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_89","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":97,"type_refs":["Bool","Bool.true","Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.isEmpty","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":680,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.isEmpty","List.length","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_83","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_9","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":70,"type_refs":["HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","List","List.instAppend","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":160,"value_refs":["Bool","Bool.true","Eq","Eq.rec","Eq.refl","HAdd.hAdd","HAppend.hAppend","HSub.hSub","LT.lt","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.getElem_append_right'._proof_1","List.instAppend","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_4","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_90","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":80,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":65,"value_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_78","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":65,"value_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_77","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_92","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":73,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":65,"value_refs":["HAdd.hAdd","LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_75","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_76","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_93","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":51,"type_refs":["LE.le","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":48,"value_refs":["LE.le","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_94","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":85,"type_refs":["HAppend.hAppend","LE.le","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instHAppendOfAppend","instLENat","instOfNatNat"],"value_dag_size":83,"value_refs":["HAppend.hAppend","LE.le","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_74","instHAppendOfAppend","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_95","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":96,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":747,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_take","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_94","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_96","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":98,"type_refs":["HAdd.hAdd","HAppend.hAppend","LE.le","LT.lt","List","List.drop","List.instAppend","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"],"value_dag_size":125,"value_refs":["Eq","HAdd.hAdd","HAppend.hAppend","Iff.mpr","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.drop","List.instAppend","List.length","List.length_pos_iff","List.nil","List.take","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","instAddNat","instHAdd","instHAppendOfAppend","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_97","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":665,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.instAppend","List.length","List.length_take","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_98","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":79,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.nil","List.take","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":674,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HAppend.hAppend","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_congr","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.drop_append_of_le_length","List.getLast_drop._proof_2","List.instAppend","List.length","List.length_take","List.ne_nil_of_length_pos","List.nil","List.take","List.take_add","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_87","cast","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_99","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":null,"statement_dag_size":77,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.drop","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":80,"value_refs":["Eq","HAdd.hAdd","LE.le","Lean.Grind.nestedProof","List","List.drop","List.getLast_eq_getElem._proof_3","List.length","List.nil","List.take","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix._proof_1_91","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Pairwise","name":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix.match_1_1","namespace":"_private.Mathlib.Data.List.Pairwise.0.List.pairwise_iff_forall_infix","reducibility":"abbrev","statement_dag_size":100,"type_refs":["Eq","Exists","Exists.intro","HAppend.hAppend","List","List.IsInfix","List.instAppend","instHAppendOfAppend"],"value_dag_size":175,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.IsInfix","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add._proof_1_1","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":1513,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add","reducibility":null,"statement_dag_size":55,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":380,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add._proof_1_3","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.drop_of_hasPeriod_add","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":166,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":38,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":760,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_3","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":119,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_4","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","List","List.length","Nat","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":1036,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_5","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":971,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_6","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":34,"type_refs":["HAdd.hAdd","LE.le","List","List.length","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":187,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._proof_1_7","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":63,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":1560,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor._simp_1_1","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.factor","reducibility":null,"statement_dag_size":78,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.HasPeriod","List.instGetElem?NatLtLength","List.length","Nat","Option","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":81,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.HasPeriod","List.hasPeriod_iff_getElem?","List.instGetElem?NatLtLength","List.length","Nat","Option","instAddNat","instHAdd","instHSub","instLTNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd._proof_1_3","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":571,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd._proof_1_4","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":null,"statement_dag_size":36,"type_refs":["HSub.hSub","LT.lt","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":637,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd._proof_1_5","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":null,"statement_dag_size":90,"type_refs":["GT.gt","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","Nat.gcd","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1709,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.gcd","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd._proof_1_8","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","GT.gt","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","Nat.gcd","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1830,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.gcd","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd._simp_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":null,"statement_dag_size":23,"type_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.instDvd"],"value_dag_size":26,"value_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.gcd_eq_left_iff_dvd","Nat.instDvd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd.match_1_6","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.gcd","reducibility":"abbrev","statement_dag_size":82,"type_refs":["Eq","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.drop","List.instAppend","Nat","instHAppendOfAppend"],"value_dag_size":112,"value_refs":["Eq","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.IsPrefix","List.drop","List.instAppend","Nat","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.getElem?_mod._proof_1_1","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.getElem?_mod","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.instLinearOrder","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":753,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.getElem?_mod._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.getElem?_mod","reducibility":null,"statement_dag_size":57,"type_refs":["HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instHSub","instLTNat","instSubNat"],"value_dag_size":954,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append","reducibility":null,"statement_dag_size":34,"type_refs":["LE.le","LT.lt","List","List.length","Nat","instLENat","instLTNat"],"value_dag_size":345,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append._proof_1_3","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append","reducibility":null,"statement_dag_size":73,"type_refs":["GT.gt","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":812,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append._proof_1_4","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append","reducibility":null,"statement_dag_size":40,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":317,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append._proof_1_5","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.HasPeriod.take_append","reducibility":null,"statement_dag_size":79,"type_refs":["GT.gt","HAdd.hAdd","HMod.hMod","LE.le","LT.lt","List","List.length","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instLENat","instLTNat","instOfNatNat"],"value_dag_size":498,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","GT.gt","HAdd.hAdd","HMod.hMod","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMod","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instMod","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMod","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_forall_getElem?_mod._proof_1_1","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_forall_getElem?_mod","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":797,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_forall_getElem?_mod._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_forall_getElem?_mod","reducibility":null,"statement_dag_size":38,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":761,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?._proof_1_2","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?","reducibility":null,"statement_dag_size":38,"type_refs":["HSub.hSub","LT.lt","List","List.length","Nat","instHSub","instLTNat","instSubNat"],"value_dag_size":761,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?._proof_1_3","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":797,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?._proof_1_4","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?","reducibility":null,"statement_dag_size":38,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":380,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.PeriodicityLemma","name":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?._simp_1_5","namespace":"_private.Mathlib.Data.List.PeriodicityLemma.0.List.hasPeriod_iff_getElem?","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","GetElem.getElem","GetElem?.getElem?","LT.lt","List","List.IsPrefix","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","Nat","Option","Option.some","instLTNat"],"value_dag_size":73,"value_refs":["Eq","GetElem.getElem","GetElem?.getElem?","LT.lt","List","List.IsPrefix","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.length","List.prefix_iff_getElem?","Nat","Option","Option.some","instLTNat","propext"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___unexpand_List_foldl_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":279,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesIdent","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List._aux_Mathlib_Data_List_Perm_Basic___unexpand_Relation_Comp_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":253,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.false","Bool.or","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.getArg","Lean.Syntax.isOfKind","Lean.Syntax.matchesNull","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm._simp_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","List","List.Forall₂"],"value_dag_size":29,"value_refs":["Eq","Eq.symm","List","List.Forall₂","List.forall₂_eq_eq_eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm._simp_1_2","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.eq_map_comp_perm","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.Forall₂","List.map"],"value_dag_size":59,"value_refs":["List","List.Forall₂","List.forall₂_map_right_iff","List.map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.forall₂_comp_perm_eq_perm_comp_forall₂.match_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.forall₂_comp_perm_eq_perm_comp_forall₂","reducibility":"abbrev","statement_dag_size":103,"type_refs":["And","And.intro","Exists.intro","List","List.Forall₂","List.Perm","Relation.Comp"],"value_dag_size":169,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","List","List.Forall₂","List.Perm","Relation.Comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.map_append_flatMap_perm._simp_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.map_append_flatMap_perm","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List","List.cons","List.flatMap","List.map","List.nil"],"value_dag_size":43,"value_refs":["Eq.symm","List","List.cons","List.flatMap","List.map","List.map_eq_flatMap","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_comp_perm.match_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_comp_perm","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Exists.intro","List","List.Perm","Relation.Comp"],"value_dag_size":136,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","List","List.Perm","Relation.Comp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_insertIdx_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_insertIdx_iff","reducibility":null,"statement_dag_size":38,"type_refs":["False","GE.ge","LT.lt","List","List.insertIdx","List.length","Nat","instLENat","instLTNat"],"value_dag_size":363,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.insertIdx","List.length","List.length_insertIdx","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","NatCast.natCast","Neg.neg","OfNat.ofNat","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_insertIdx_iff._proof_1_2","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_insertIdx_iff","reducibility":null,"statement_dag_size":39,"type_refs":["GE.ge","LT.lt","List","List.Perm","List.length","Nat","Not","instLENat","instLTNat"],"value_dag_size":341,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Perm","List.Perm.length_eq","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate._simp_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate","reducibility":null,"statement_dag_size":50,"type_refs":["BEq","Eq","LawfulBEq","List","List.count","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":56,"value_refs":["BEq","Eq","LawfulBEq","List","List.count","List.count_eq_zero","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate._simp_1_2","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","Ne"],"value_dag_size":25,"value_refs":["Eq","Ne","Ne.symm","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate._simp_1_3","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","List","List.instHasSubset","List.instMembership","Membership.mem"],"value_dag_size":46,"value_refs":["HasSubset.Subset","List","List.instHasSubset","List.instMembership","List.subset_def","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate._simp_1_4","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.perm_replicate_append_replicate","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.rel_perm_imp.match_1_1","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List.rel_perm_imp","reducibility":"abbrev","statement_dag_size":181,"type_refs":["And","And.intro","Exists.intro","List","List.Forall₂","List.Perm","Relation.Comp","flip"],"value_dag_size":397,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","List","List.Forall₂","List.Perm","Relation.Comp","flip"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«_aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_*__1»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":266,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«_aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_<*>__1»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":288,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.Preresolved.namespace","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.Syntax.node3","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«_aux_Mathlib_Data_List_Perm_Basic___macroRules__private_Mathlib_Data_List_Perm_Basic_0_List_term_∘r__1»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":238,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«term_*_»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":60,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«term_<*>_»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":60,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Perm.Basic","name":"_private.Mathlib.Data.List.Perm.Basic.0.List.«term_∘r_»","namespace":"_private.Mathlib.Data.List.Perm.Basic.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":64,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right","reducibility":null,"statement_dag_size":25,"type_refs":["DecidableEq","List","List.Perm","List.bagInter","List.nil","instBEqOfDecidableEq"],"value_dag_size":179,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.casesOn","Iff","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.Grind.of_forall_eq_false","List","List.Perm","List.bagInter","List.count","List.nil","List.perm_iff_count","Nat","Not","True","congrArg","eq_false","eq_self","forall_congr","funext","instBEqOfDecidableEq","instLawfulBEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right._proof_1_2","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableEq","List","List.Perm","List.bagInter","List.cons","instBEqOfDecidableEq"],"value_dag_size":927,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Perm","List.Perm.count","List.bagInter","List.cons","List.cons_bagInter","List.count","List.count_cons","List.erase","List.instDecidableMemOfLawfulBEq","List.instMembership","List.perm_iff_count","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right._proof_1_3","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","List","List.Perm","List.bagInter","List.cons","instBEqOfDecidableEq"],"value_dag_size":5278,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.Grind.nestedDecidable","Lean.Grind.of_forall_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Perm","List.bagInter","List.cons","List.cons.inj","List.cons_bagInter","List.count","List.count_cons","List.erase","List.erase_comm","List.instDecidableMemOfLawfulBEq","List.instMembership","List.mem_erase_of_ne","List.mem_of_mem_erase","List.perm_iff_count","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instHAdd","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right._proof_1_4","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.bagInter_right","reducibility":null,"statement_dag_size":64,"type_refs":["DecidableEq","List","List.Perm","List.bagInter","instBEqOfDecidableEq"],"value_dag_size":316,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.of_forall_eq_false","List","List.Perm","List.Perm.count","List.bagInter","List.count","List.perm_iff_count","Nat","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq","instLawfulBEq","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.drop_inter._proof_1_1","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.drop_inter","reducibility":null,"statement_dag_size":50,"type_refs":["DecidableEq","Inter.inter","LE.le","List","List.Perm","List.drop","List.instInterOfBEq_batteries","List.length","Nat","Not","instBEqOfDecidableEq","instLENat"],"value_dag_size":509,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Inter.inter","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.Perm","List.count","List.drop","List.drop_eq_nil_of_le","List.instInterOfBEq_batteries","List.inter_nil'","List.length","List.nil","List.perm_iff_count","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instBEqOfDecidableEq","instHAdd","instIntCastInt","instLENat","instLawfulBEq","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.inter_append._simp_1_1","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.inter_append","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Perm.Lattice","name":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.inter_append._simp_1_2","namespace":"_private.Mathlib.Data.List.Perm.Lattice.0.List.Perm.inter_append","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Perm.Subperm","name":"_private.Mathlib.Data.List.Perm.Subperm.0.List.Subperm.append.match_1_1","namespace":"_private.Mathlib.Data.List.Perm.Subperm.0.List.Subperm.append","reducibility":"abbrev","statement_dag_size":114,"type_refs":["And","And.intro","Exists.intro","List","List.Perm","List.Sublist","List.Subperm"],"value_dag_size":259,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","List","List.Perm","List.Sublist","List.Subperm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Perm.Subperm","name":"_private.Mathlib.Data.List.Perm.Subperm.0.List.subperm_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Perm.Subperm.0.List.subperm_iff","reducibility":"abbrev","statement_dag_size":87,"type_refs":["And","And.intro","Exists","Exists.intro","List","List.Perm","List.Sublist"],"value_dag_size":140,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","List","List.Perm","List.Sublist"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.DecEq_eq","namespace":"_private.Mathlib.Data.List.Permutation.0.List","reducibility":null,"statement_dag_size":26,"type_refs":["BEq","DecidableEq","Eq","List","List.instBEq","instBEqOfDecidableEq","instDecidableEqList"],"value_dag_size":194,"value_refs":["BEq","BEq.beq","BEq.mk","Bool","Bool.eq_iff_iff","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.mpr","Iff","Iff.rfl","List","List.beq","List.instBEq","List.instLawfulBEq","beq_iff_eq","congrArg","congr_arg","decide_eq_true_iff","funext","id","instBEqOfDecidableEq","instDecidableEqList","instLawfulBEq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Nat","Nat.succ"],"value_dag_size":21,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self._simp_1_3","namespace":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self","reducibility":null,"statement_dag_size":13,"type_refs":["Eq","Exists","False"],"value_dag_size":13,"value_refs":["Exists","False","eq_false","exists_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self._simp_1_4","namespace":"_private.Mathlib.Data.List.Permutation.0.List.count_permutations'Aux_self","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.getElem_permutations'Aux._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.getElem_permutations'Aux","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq","LT.lt","Nat","Nat.lt_one_iff","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.map_permutations'._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.map_permutations'","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.map","List.permutations'Aux"],"value_dag_size":48,"value_refs":["Eq.symm","List","List.map","List.map_map_permutations'Aux","List.permutations'Aux"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.map_permutationsAux2'._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.map_permutationsAux2'","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.cons","List.map"],"value_dag_size":43,"value_refs":["Eq.symm","List","List.cons","List.map","List.map_cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.map_permutationsAux2'._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.map_permutationsAux2'","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.map","instHAppendOfAppend"],"value_dag_size":61,"value_refs":["Eq.symm","HAppend.hAppend","List","List.instAppend","List.map","List.map_append","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2._simp_1_5","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":null,"statement_dag_size":92,"type_refs":["And","Eq","Exists","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","List.permutationsAux2","Membership.mem","Ne","Prod.snd","id","instHAppendOfAppend"],"value_dag_size":97,"value_refs":["And","Eq","Exists","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.mem_permutationsAux2'","List.nil","List.permutationsAux2","Membership.mem","Ne","Prod.snd","id","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2._simp_1_6","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2._simp_1_7","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2._simp_1_8","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2._simp_1_9","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2.match_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":"abbrev","statement_dag_size":363,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Not","instHAppendOfAppend"],"value_dag_size":955,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2.match_1_3","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_foldr_permutationsAux2","reducibility":"abbrev","statement_dag_size":292,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Not","instHAppendOfAppend"],"value_dag_size":587,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.nil","Membership.mem","Not","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.mem_permutations_of_perm_lemma._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.mem_permutations_of_perm_lemma","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","List","List.Perm","List.nil"],"value_dag_size":25,"value_refs":["Eq","List","List.Perm","List.nil","List.perm_nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_10","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.insertIdx","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":150,"value_refs":["Bool","Bool.true","Eq","Eq.mpr_not","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_4","List.insertIdx","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","Not","OfNat.ofNat","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_11","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","HSub.hSub","LE.le","LT.lt","List","List.insertIdx","List.length","Nat","Not","OfNat.ofNat","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":304,"value_refs":["Bool","Bool.true","Eq","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.insertIdx","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_8","eagerReduce","eq_false","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_12","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","Fin.mk","HAdd.hAdd","LT.lt","List","List.get","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":2932,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.mpr_not","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","Fin.isLt","Fin.mk","Fin.val","GetElem","GetElem.getElem","GetElem.getElem.hcongr_8","HAdd.hAdd","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.get","List.getElem_insertIdx","List.getElem_insertIdx._proof_1","List.getElem_insertIdx._proof_4","List.get_eq_getElem","List.insertIdx","List.instGetElemNatLtLength","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_10","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_11","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_3","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_4","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_5","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_7","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_8","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_9","congrArg","congrFun'","dite","dite_congr","eagerReduce","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_3","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":70,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LT.lt","Lean.Grind.nestedProof","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_4","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":50,"type_refs":["Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.insertIdx","List.length","Nat","instLTNat"],"value_dag_size":48,"value_refs":["Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.insertIdx","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_5","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":37,"type_refs":["Fin.mk","Fin.val","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"],"value_dag_size":35,"value_refs":["Fin.isLt","Fin.mk","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_6","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Fin","HAdd.hAdd","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":72,"value_refs":["Eq","Eq.symm","Fin","HAdd.hAdd","List","List.insertIdx","List.length","Nat","OfNat.ofNat","congrArg","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_7","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":95,"value_refs":["Eq.mpr_prop","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_1","List.insertIdx","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_8","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.insertIdx","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":105,"value_refs":["Eq","Eq.mpr_not","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_4","List.insertIdx","List.length","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_9","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.insertIdx","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":140,"value_refs":["Bool","Bool.true","Eq.mpr_prop","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.nestedProof","List","List.getElem_insertIdx._proof_1","List.insertIdx","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_3","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_3","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_4","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_5","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem._simp_1_6","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_of_notMem","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations_iff","reducibility":"abbrev","statement_dag_size":47,"type_refs":["Exists","Exists.intro","List","List.Duplicate"],"value_dag_size":64,"value_refs":["Exists","Exists.casesOn","Exists.intro","List","List.Duplicate"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.perm_of_mem_permutationsAux._simp_1_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.perm_of_mem_permutationsAux","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.perm_pair._proof_1_11","namespace":"_private.Mathlib.Data.List.Permutation.0.List.perm_pair","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","Iff","List","List.Perm","List.cons","List.nil","List.permutations","Or"],"value_dag_size":555,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","List","List.Perm","List.cons","List.instMembership","List.mem_cons","List.mem_permutations","List.nil","List.not_mem_nil","List.permutations","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutations'Aux_eq_permutationsAux2._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutations'Aux_eq_permutationsAux2","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","List.permutationsAux2","Prod.snd","instHAppendOfAppend"],"value_dag_size":68,"value_refs":["Eq.symm","HAppend.hAppend","List","List.instAppend","List.nil","List.permutationsAux2","List.permutationsAux2_append","Prod.snd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux.rec.match_1"],"value_dag_size":49,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux.rec.match_1"],"value_dag_size":57,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1.splitter","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux.rec.match_1","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.permutationsAux.rec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_1","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","List","List.permutationsAux2.match_1","Prod","Prod.mk"],"value_dag_size":53,"value_refs":["Eq.refl","List","List.permutationsAux2.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_1.splitter","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_1","reducibility":"abbrev","statement_dag_size":39,"type_refs":["List","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["List.permutationsAux2.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3.eq_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux2.match_3"],"value_dag_size":56,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux2.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3.eq_2","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","List","List.cons","List.nil","List.permutationsAux2.match_3"],"value_dag_size":65,"value_refs":["Eq.refl","List","List.cons","List.nil","List.permutationsAux2.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3.splitter","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3","reducibility":"abbrev","statement_dag_size":48,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.permutationsAux2.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2_fst.match_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2_fst","reducibility":"abbrev","statement_dag_size":48,"type_refs":["List","List.cons","List.nil"],"value_dag_size":61,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux_append._simp_1_1","namespace":"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux_append","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.nil","List.permutationsAux2","Prod.snd","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["Eq.symm","HAppend.hAppend","List","List.instAppend","List.nil","List.permutationsAux2","List.permutationsAux2_comp_append","Prod.snd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Permutation","name":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.List.Permutation.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pi","name":"_private.Mathlib.Data.List.Pi.0.Multiset.pi_coe._simp_1_1","namespace":"_private.Mathlib.Data.List.Pi.0.Multiset.pi_coe","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Multiset","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":32,"value_refs":["Eq","Multiset","Multiset.instSingleton","Multiset.singleton_inj","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Pi","name":"_private.Mathlib.Data.List.Pi.0.Multiset.pi_coe._simp_1_3","namespace":"_private.Mathlib.Data.List.Pi.0.Multiset.pi_coe","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.cons","Multiset","Multiset.cons","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq.symm","List","List.cons","Multiset","Multiset.cons","Multiset.cons_coe","Multiset.ofList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Prime","name":"_private.Mathlib.Data.List.Prime.0.Prime.dvd_prod_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Prime.0.Prime.dvd_prod_iff","reducibility":"abbrev","statement_dag_size":156,"type_refs":["And","And.intro","CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Exists","Exists.intro","List","List.instMembership","Membership.mem","MonoidWithZero.toSemigroupWithZero","SemigroupWithZero.toSemigroup","semigroupDvd"],"value_dag_size":223,"value_refs":["And","And.casesOn","And.intro","CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem","MonoidWithZero.toSemigroupWithZero","SemigroupWithZero.toSemigroup","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Prime","name":"_private.Mathlib.Data.List.Prime.0.perm_of_prod_eq_prod.match_1_1","namespace":"_private.Mathlib.Data.List.Prime.0.perm_of_prod_eq_prod","reducibility":"abbrev","statement_dag_size":392,"type_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Eq","List","List.cons","List.instMembership","List.nil","List.prod","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Prime"],"value_dag_size":679,"value_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Eq","List","List.casesOn","List.cons","List.instMembership","List.nil","List.prod","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","Prime"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product._simp_1_1","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product._simp_1_2","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product._simp_1_3","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product","reducibility":null,"statement_dag_size":47,"type_refs":["And","Eq","Prod","Prod.fst","Prod.snd"],"value_dag_size":51,"value_refs":["And","Eq","Prod","Prod.ext_iff","Prod.fst","Prod.snd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product._simp_1_4","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_product","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_1","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_2","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_3","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_4","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_5","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma._simp_1_6","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.mem_sigma","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.product_nil.match_1_1","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.product_nil","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ProdSigma","name":"_private.Mathlib.Data.List.ProdSigma.0.List.sigma_nil.match_1_1","namespace":"_private.Mathlib.Data.List.ProdSigma.0.List.sigma_nil","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.isChain_range._simp_1_1","namespace":"_private.Mathlib.Data.List.Range.0.List.isChain_range","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":45,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.lt_sub_iff_add_lt","instAddNat","instHAdd","instHSub","instLTNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.isChain_range._simp_1_2","namespace":"_private.Mathlib.Data.List.Range.0.List.isChain_range","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HAdd.hAdd","LT.lt","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":36,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.add_lt_add_iff_right","instAddNat","instHAdd","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.isChain_range._simp_1_3","namespace":"_private.Mathlib.Data.List.Range.0.List.isChain_range","reducibility":null,"statement_dag_size":59,"type_refs":["And","Eq","HAppend.hAppend","List","List.IsChain","List.cons","List.instAppend","List.nil","instHAppendOfAppend"],"value_dag_size":66,"value_refs":["And","HAppend.hAppend","List","List.IsChain","List.cons","List.instAppend","List.isChain_append_cons_cons","List.nil","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.isChain_range._simp_1_4","namespace":"_private.Mathlib.Data.List.Range.0.List.isChain_range","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","List.IsChain","List.cons","List.nil","True"],"value_dag_size":27,"value_refs":["List.IsChain","List.IsChain.singleton","List.cons","List.nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.cons","List.nil","List.ranges.match_1","Nat","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","List","List.cons","List.nil","List.ranges.match_1","Nat","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.cons","List.nil","List.ranges.match_1","Nat","Unit"],"value_dag_size":39,"value_refs":["Eq.refl","List","List.cons","List.nil","List.ranges.match_1","Nat","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1.splitter","namespace":"_private.Mathlib.Data.List.Range.0.List.ranges.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":1,"value_refs":["List.ranges.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.ranges_disjoint._proof_1_5","namespace":"_private.Mathlib.Data.List.Range.0.List.ranges_disjoint","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","Exists","False","HAdd.hAdd","LT.lt","List","List.instMembership","Membership.mem","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":313,"value_refs":["And","And.casesOn","Bool","Bool.true","Eq","Eq.mp","Eq.refl","Exists","Exists.casesOn","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Range","name":"_private.Mathlib.Data.List.Range.0.List.ranges_disjoint._simp_1_4","namespace":"_private.Mathlib.Data.List.Range.0.List.ranges_disjoint","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_concat_iff.match_1_1","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_concat_iff","reducibility":"abbrev","statement_dag_size":280,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reduceOption","Option","Option.some","instHAppendOfAppend"],"value_dag_size":584,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.nil","List.reduceOption","Option","Option.some","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_nil_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_nil_iff","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Exists","List","List.instMembership","List.replicate","Membership.mem","Nat","Option","Option.none","id"],"value_dag_size":246,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","List","List.instMembership","List.mem_replicate","List.replicate","Membership.mem","Nat","Ne","Not","OfNat.ofNat","Option","Option.none","True","True.intro","congrArg","eq_false","eq_true","id","id.eq_1","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_singleton_iff.match_1_1","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_eq_singleton_iff","reducibility":"abbrev","statement_dag_size":185,"type_refs":["Eq","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.replicate","Nat","Option","Option.none","Option.some","instHAppendOfAppend"],"value_dag_size":273,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.replicate","Nat","Option","Option.none","Option.some","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_length_lt_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_length_lt_iff","reducibility":null,"statement_dag_size":79,"type_refs":["Bool","Bool.true","Eq","Iff","List","List.cons","List.instMembership","Membership.mem","Not","Option","Option.isSome","Option.none"],"value_dag_size":749,"value_refs":["And","And.casesOn","Bool","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Iff","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Not","Option","Option.casesOn","Option.isSome","Option.isSome_none","Option.isSome_some","Option.none","Option.some","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_true","id","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_map._simp_1_1","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_map","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","True"],"value_dag_size":17,"value_refs":["Eq","True","eq_self_iff_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_mem_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_mem_iff","reducibility":null,"statement_dag_size":63,"type_refs":["And","Eq","Exists","List","List.filterMap","List.instMembership","Membership.mem","Option","Option.some"],"value_dag_size":68,"value_refs":["And","Eq","Exists","List","List.filterMap","List.instMembership","List.mem_filterMap","Membership.mem","Option","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ReduceOption","name":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_mem_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.ReduceOption.0.List.reduceOption_mem_iff","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.dropLast_tail._simp_1_3","namespace":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.dropLast_tail","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List","List.IsRotated","List.cons","List.dropLast","List.getLast","List.nil","Ne","True"],"value_dag_size":38,"value_refs":["List","List.IsRotated","List.IsRotated.cons_getLast_dropLast","List.cons","List.dropLast","List.getLast","List.nil","Ne","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.dropLast_tail.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.dropLast_tail","reducibility":"abbrev","statement_dag_size":153,"type_refs":["Eq","List","List.cons","List.getLast","List.head","List.nil","Ne"],"value_dag_size":294,"value_refs":["Eq","List","List.casesOn","List.cons","List.getLast","List.head","List.nil","Ne"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.trans.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.IsRotated.trans","reducibility":"abbrev","statement_dag_size":101,"type_refs":["Eq","Eq.refl","Exists.intro","List","List.IsRotated","List.rotate","Nat"],"value_dag_size":470,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists.casesOn","Exists.intro","HEq","HEq.refl","List","List.IsRotated","List.rotate","Nat","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HMod.hMod","LT.lt","Nat","Nat.instMod","OfNat.ofNat","True","instHMod","instLTNat","instOfNatNat"],"value_dag_size":40,"value_refs":["HMod.hMod","LT.lt","Nat","Nat.instMod","Nat.mod_lt","OfNat.ofNat","eq_true","instHMod","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr._simp_1_2","namespace":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Option","Option.some"],"value_dag_size":28,"value_refs":["Eq","Option","Option.some","Option.some_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr._simp_1_3","namespace":"_private.Mathlib.Data.List.Rotate.0.List.Nodup.rotate_congr","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","Fin.val","Nat"],"value_dag_size":30,"value_refs":["Eq","Fin","Fin.ext_iff","Fin.val","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.cyclicPermutations_ne_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.cyclicPermutations_ne_nil","reducibility":"abbrev","statement_dag_size":60,"type_refs":["Eq","List","List.cons","List.cyclicPermutations","List.nil"],"value_dag_size":178,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.casesOn","List.cons","List.ctorIdx","List.cyclicPermutations","List.nil","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.getElem?_rotate._proof_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.getElem?_rotate","reducibility":null,"statement_dag_size":103,"type_refs":["Eq","HAdd.hAdd","HMod.hMod","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.instLinearOrder","Nat.instMod","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instHMod","instHSub","instLENat","instLTNat","instSubNat"],"value_dag_size":1451,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.natCast_mod","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.cast","Nat.instLinearOrder","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMod","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_cyclicPermutations_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_cyclicPermutations_iff","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.cyclicPermutations","List.rotate","Nat"],"value_dag_size":32,"value_refs":["Eq.symm","List","List.cyclicPermutations","List.cyclicPermutations_rotate","List.rotate","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range._simp_1_2","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","LT.lt","List","List.instMembership","List.range","Membership.mem","Nat","instLTNat"],"value_dag_size":30,"value_refs":["LT.lt","List","List.instMembership","List.mem_range","List.range","Membership.mem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range._simp_1_3","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range","reducibility":null,"statement_dag_size":46,"type_refs":["And","Eq","Exists","LE.le","List","List.IsRotated","List.length","List.rotate","Nat","instLENat"],"value_dag_size":49,"value_refs":["And","Eq","Exists","LE.le","List","List.IsRotated","List.isRotated_iff_mod","List.length","List.rotate","Nat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range.match_1_4","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range","reducibility":"abbrev","statement_dag_size":110,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","LE.le","List","List.length","List.rotate","Nat","instLENat"],"value_dag_size":169,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","List","List.length","List.rotate","Nat","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range.match_1_6","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mem_map_range","reducibility":"abbrev","statement_dag_size":136,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","HAdd.hAdd","LT.lt","List","List.length","List.rotate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":199,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","LT.lt","List","List.length","List.rotate","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mod.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_iff_mod","reducibility":"abbrev","statement_dag_size":110,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","LE.le","List","List.length","List.rotate","Nat","instLENat"],"value_dag_size":169,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","List","List.length","List.rotate","Nat","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_nil_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_nil_iff","reducibility":"abbrev","statement_dag_size":56,"type_refs":["Eq","Exists.intro","List","List.IsRotated","List.nil","List.rotate","Nat"],"value_dag_size":79,"value_refs":["Eq","Exists.casesOn","Exists.intro","List","List.IsRotated","List.nil","List.rotate","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_reverse_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_reverse_iff","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","List","List.IsRotated","List.reverse"],"value_dag_size":28,"value_refs":["List","List.IsRotated","List.isRotated_reverse_comm_iff","List.reverse","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_singleton_iff.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.isRotated_singleton_iff","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Eq","Exists.intro","List","List.IsRotated","List.cons","List.nil","List.rotate","Nat"],"value_dag_size":97,"value_refs":["Eq","Exists.casesOn","Exists.intro","List","List.IsRotated","List.cons","List.nil","List.rotate","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.length_rotate'.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.length_rotate'","reducibility":"abbrev","statement_dag_size":58,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":87,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.mem_cyclicPermutations_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.mem_cyclicPermutations_iff","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Exists","Fin","List","List.get","List.instMembership","List.length","Membership.mem"],"value_dag_size":44,"value_refs":["Eq","Exists","Fin","List","List.get","List.instMembership","List.length","List.mem_iff_get","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.mem_rotate._simp_1_3","namespace":"_private.Mathlib.Data.List.Rotate.0.List.mem_rotate","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","or_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.mem_rotate.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.mem_rotate","reducibility":"abbrev","statement_dag_size":69,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":100,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_eq_drop_append_take.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_eq_drop_append_take","reducibility":"abbrev","statement_dag_size":106,"type_refs":["HAdd.hAdd","LE.le","List","List.cons","List.length","List.nil","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":178,"value_refs":["HAdd.hAdd","LE.le","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_length_mul.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_length_mul","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_rotate'.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate'_rotate'","reducibility":"abbrev","statement_dag_size":68,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":100,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_rotate'._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_rotate'","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["Eq","List","List.length","List.length_eq_zero_iff","List.nil","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_self_iff_eq_replicate.match_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_self_iff_eq_replicate","reducibility":"abbrev","statement_dag_size":88,"type_refs":["Eq","Exists","Exists.intro","List","List.cons","List.length","List.replicate"],"value_dag_size":114,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","List","List.cons","List.length","List.replicate"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_self_iff_eq_replicate.match_1_3","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate_eq_self_iff_eq_replicate","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate_reverse","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","HMod.hMod","HSub.hSub","List","List.length","List.rotate","Nat","Nat.instMod","instHMod","instHSub","instSubNat"],"value_dag_size":60,"value_refs":["Eq","HMod.hMod","HSub.hSub","List","List.length","List.rotate","List.rotate_eq_iff","Nat","Nat.instMod","instHMod","instHSub","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Rotate","name":"_private.Mathlib.Data.List.Rotate.0.List.rotate_reverse._simp_1_2","namespace":"_private.Mathlib.Data.List.Rotate.0.List.rotate_reverse","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HAdd.hAdd","List","List.rotate","Nat","instAddNat","instHAdd"],"value_dag_size":41,"value_refs":["Eq.symm","HAdd.hAdd","List","List.rotate","List.rotate_rotate","Nat","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.mem_sections._simp_1_1","namespace":"_private.Mathlib.Data.List.Sections.0.List.mem_sections","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","Exists","List","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":66,"value_refs":["And","Exists","List","List.flatMap","List.instMembership","List.mem_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.mem_sections._simp_1_2","namespace":"_private.Mathlib.Data.List.Sections.0.List.mem_sections","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.mem_sections._simp_1_3","namespace":"_private.Mathlib.Data.List.Sections.0.List.mem_sections","reducibility":null,"statement_dag_size":48,"type_refs":["And","Eq","List","List.Forall₂","List.cons"],"value_dag_size":56,"value_refs":["And","List","List.Forall₂","List.cons","List.forall₂_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.mem_sections._simp_1_4","namespace":"_private.Mathlib.Data.List.Sections.0.List.mem_sections","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.rel_sections.match_1_1","namespace":"_private.Mathlib.Data.List.Sections.0.List.rel_sections","reducibility":"abbrev","statement_dag_size":137,"type_refs":["List","List.Forall₂","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":551,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.casesOn","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sections","name":"_private.Mathlib.Data.List.Sections.0.List.rel_sections.match_1_7","namespace":"_private.Mathlib.Data.List.Sections.0.List.rel_sections","reducibility":"abbrev","statement_dag_size":303,"type_refs":["List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit"],"value_dag_size":1259,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Forall₂","List.Forall₂.below","List.Forall₂.below.casesOn","List.Forall₂.below.cons","List.Forall₂.below.nil","List.Forall₂.cons","List.Forall₂.nil","List.cons","List.nil","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.Acc.shortlex","namespace":"_private.Mathlib.Data.List.Shortlex.0.Acc","reducibility":null,"statement_dag_size":62,"type_refs":["Acc","LT.lt","List","List.Shortlex","List.cons","List.length","Nat","instLTNat"],"value_dag_size":1628,"value_refs":["Acc","Acc.intro","Acc.rec","AddCancelCommMonoid.toAddLeftCancelMonoid","AddCommMagma.toAdd","AddCommSemigroup.toAddCommMagma","AddLeftCancelMonoid.toAddLeftCancelSemigroup","AddLeftCancelSemigroup.toIsLeftCancelAdd","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","And.casesOn","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HEq","HEq.refl","Iff.mp","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LT.lt","List","List.Lex","List.Lex.casesOn","List.Lex.cons","List.Lex.nil","List.Lex.rel","List.Shortlex","List.Shortlex.of_lex","List.cons","List.cons.noConfusion","List.length","List.length_cons","List.length_eq_zero_iff._simp_1","List.nil","List.shortlex_def","MulZeroClass.toZero","Nat","Nat.add_eq_zero_iff._simp_1","Nat.instAddCancelCommMonoid","Nat.instAddCommMonoid","Nat.instAddCommSemigroup","Nat.instAddMonoid","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instOne","Nat.instPartialOrder","Nat.instPreorder","Nat.instZeroLEOneClass","Nat.right_eq_add._simp_1","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","True","Zero.toOfNat0","_private.Mathlib.Data.List.Shortlex.0.Acc.shortlex._simp_1_1","addRightReflectLE_of_addLeftReflectLE","and_false","congr","congrArg","contravariant_lt_of_covariant_le","eq_of_heq","id","instAddNat","instHAdd","instIsLeftCancelAddOfAddLeftReflectLE","instIsRightCancelAddOfAddRightReflectLE","instLTNat","instOfNatNat","lt_add_iff_pos_right._simp_1","of_eq_true","one_ne_zero._simp_1","zero_lt_one._simp_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.Acc.shortlex._simp_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.Acc.shortlex","reducibility":null,"statement_dag_size":41,"type_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","instHAdd"],"value_dag_size":47,"value_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","add_left_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left._proof_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left","reducibility":null,"statement_dag_size":44,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":345,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left._simp_1_2","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left","reducibility":null,"statement_dag_size":41,"type_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","instHAdd"],"value_dag_size":47,"value_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","add_left_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left._simp_1_3","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_left","reducibility":null,"statement_dag_size":40,"type_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","instHAdd"],"value_dag_size":46,"value_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","add_right_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_right._proof_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_right","reducibility":null,"statement_dag_size":43,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":360,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_right._proof_1_2","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.append_right","reducibility":null,"statement_dag_size":67,"type_refs":["And","Eq","HAdd.hAdd","LT.lt","List","List.Lex","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":404,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Lex","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.asymm._proof_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.Shortlex.asymm","reducibility":null,"statement_dag_size":20,"type_refs":["List","List.Shortlex","Std.Asymm"],"value_dag_size":67,"value_refs":["InvImage.asymm","LT.lt","List","List.Lex","List.Lex.asymm","List.length","Nat","Nat.instPreorder","Prod","Prod.Lex","Prod.instAsymmLex_mathlib","Prod.mk","Std.Asymm","instAsymmLt","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.not_shortlex_nil_right._simp_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.not_shortlex_nil_right","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","Nat","Or","instLTNat"],"value_dag_size":55,"value_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","List.shortlex_def","Nat","Or","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","Nat","Or","instLTNat"],"value_dag_size":55,"value_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","List.shortlex_def","Nat","Or","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff","reducibility":null,"statement_dag_size":53,"type_refs":["Add","AddRightReflectLT","AddRightStrictMono","Eq","HAdd.hAdd","LT","LT.lt","instHAdd"],"value_dag_size":61,"value_refs":["Add","AddRightReflectLT","AddRightStrictMono","HAdd.hAdd","LT","LT.lt","add_lt_add_iff_right","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff","reducibility":null,"statement_dag_size":41,"type_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","instHAdd"],"value_dag_size":47,"value_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","add_left_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_cons_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.Lex","List.cons","Std.Irrefl"],"value_dag_size":45,"value_refs":["List","List.Lex","List.cons","List.lex_cons_iff","Std.Irrefl","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_iff_lex._simp_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_iff_lex","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","Nat","Or","instLTNat"],"value_dag_size":55,"value_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","List.shortlex_def","Nat","Or","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_nil_or_eq_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_nil_or_eq_nil","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","Nat","Or","instLTNat"],"value_dag_size":55,"value_refs":["And","Eq","LT.lt","List","List.Lex","List.Shortlex","List.length","List.shortlex_def","Nat","Or","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":26,"value_refs":["False","LT.lt","Preorder","Preorder.toLT","lt_self_iff_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Shortlex","name":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Shortlex.0.List.shortlex_singleton_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List.Lex","List.cons","List.nil"],"value_dag_size":36,"value_refs":["List.Lex","List.cons","List.lex_singleton_iff","List.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.NodupKeys.eq_of_mk_mem._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.NodupKeys.eq_of_mk_mem","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","List","List.NodupKeys","List.instMembership","Membership.mem","Sigma","Sigma.mk"],"value_dag_size":376,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.true_imp_eq","List","List.NodupKeys","List.NodupKeys.eq_of_fst_eq","List.instMembership","Membership.mem","Not","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.inj","True","True.intro","eq_false","eq_of_heq","eq_self","eq_true","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.Perm.kunion_left.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.Perm.kunion_left","reducibility":"abbrev","statement_dag_size":129,"type_refs":["List","List.NodupKeys","List.Perm","List.cons","List.nil","Sigma"],"value_dag_size":149,"value_refs":["List","List.NodupKeys","List.Perm","List.casesOn","List.cons","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.Perm.kunion_right._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.Perm.kunion_right","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","List.cons","True"],"value_dag_size":31,"value_refs":["List","List.Perm","List.Perm.swap","List.cons","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":78,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","Eq","HAppend.hAppend","List","List.cons","List.dlookup","List.instAppend","Option","Option.or","Sigma","Sigma.fst","instHAppendOfAppend"],"value_dag_size":480,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","HEq","HEq.refl","HEq.symm","Lean.Grind.nestedProof","List","List.cons","List.cons_append","List.dlookup","List.dlookup_cons_eq","List.instAppend","Not","Option","Option.or","Option.some","Option.some_or","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.dlookup_append._proof_1_1","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append._proof_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_append","reducibility":null,"statement_dag_size":109,"type_refs":["DecidableEq","Eq","HAppend.hAppend","List","List.cons","List.dlookup","List.instAppend","Not","Option","Option.or","Sigma","Sigma.fst","instHAppendOfAppend"],"value_dag_size":366,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.cons_append","List.dlookup","List.dlookup_cons_ne","List.instAppend","Ne","Not","Option","Option.or","Sigma","Sigma.fst","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_cons_ne.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_cons_ne","reducibility":"abbrev","statement_dag_size":64,"type_refs":["Ne","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":92,"value_refs":["Ne","Sigma","Sigma.casesOn","Sigma.fst","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_eq_none._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_eq_none","reducibility":null,"statement_dag_size":54,"type_refs":["Bool","Bool.true","DecidableEq","Eq","List","List.dlookup","List.instMembership","List.keys","Membership.mem","Option.isSome","Sigma"],"value_dag_size":66,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.symm","List","List.dlookup","List.dlookup_isSome","List.instMembership","List.keys","Membership.mem","Option.isSome","Sigma","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_eq_none._simp_1_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_eq_none","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.true","Eq","Option","Option.isNone","Option.none"],"value_dag_size":30,"value_refs":["Bool","Bool.true","Eq","Option","Option.isNone","Option.isNone_iff_eq_none","Option.none","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":78,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome","reducibility":null,"statement_dag_size":73,"type_refs":["Bool","Bool.true","DecidableEq","Eq","Iff","List","List.cons","List.dlookup","List.instMembership","List.keys","Membership.mem","Option.isSome","Sigma","Sigma.fst"],"value_dag_size":473,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.Bool.eq_false_of_not_eq_true'","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_true_left","List","List.cons","List.dlookup","List.dlookup_cons_eq","List.instMembership","List.keys","List.keys_cons","List.mem_cons","Membership.mem","Not","Option","Option.isSome","Option.isSome_some","Option.some","Or","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome._proof_1_1","cast","cast_heq","congrArg","eq_of_heq","eq_true","heq_of_eq","id","noConfusion_of_Nat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome._proof_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_isSome","reducibility":null,"statement_dag_size":99,"type_refs":["Bool","Bool.true","DecidableEq","Eq","Iff","List","List.cons","List.dlookup","List.instMembership","List.keys","Membership.mem","Not","Option.isSome","Sigma","Sigma.fst"],"value_dag_size":376,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_congr","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","List","List.cons","List.dlookup","List.dlookup_cons_ne","List.instMembership","List.keys","List.keys_cons","List.mem_cons","Membership.mem","Ne","Not","Option","Option.isSome","Or","Sigma","Sigma.fst","True","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_kunion_left._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_kunion_left","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_kunion_right._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_kunion_right","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Eq","List.dlookup","List.map","List.nil","Option","Option.map","Sigma","Sigma.map"],"value_dag_size":263,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.dlookup","List.dlookup_nil","List.map","List.map_nil","List.nil","Not","Option","Option.map","Option.map_none","Option.none","Sigma","Sigma.map","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":78,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_5","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":130,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_6","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map","reducibility":null,"statement_dag_size":104,"type_refs":["DecidableEq","Eq","List","List.cons","List.dlookup","List.map","Option","Option.map","Sigma","Sigma.fst","Sigma.map"],"value_dag_size":774,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.symm","HEq.trans","Lean.Grind.nestedProof","List","List.cons","List.dlookup","List.dlookup_cons_eq","List.map","List.map_cons","Not","Option","Option.map","Option.map_some","Option.some","Sigma","Sigma.fst","Sigma.map","Sigma.map.eq_1","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_3","_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_5","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map._proof_1_7","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map","reducibility":null,"statement_dag_size":176,"type_refs":["DecidableEq","Eq","List","List.cons","List.dlookup","List.map","Ne","Not","Option","Option.map","Sigma","Sigma.fst","Sigma.map","Sigma.mk","Sigma.snd"],"value_dag_size":587,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dlookup","List.dlookup_cons_ne","List.map","List.map_cons","Ne","Not","Option","Option.map","Sigma","Sigma.fst","Sigma.map","Sigma.map.eq_1","Sigma.mk","Sigma.mk.inj","Sigma.snd","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map₁._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.dlookup_map₁","reducibility":null,"statement_dag_size":132,"type_refs":["DecidableEq","Eq","Function.Injective","List","List.dlookup","List.map","Option","Option.map","Sigma","Sigma.map","id"],"value_dag_size":272,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Function.Injective","Lean.Grind.imp_eq_of_eq_true_left","List","List.dlookup","List.map","Not","Option","Option.map","Option.map_id_apply","Sigma","Sigma.map","True","True.intro","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_kerase._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_kerase","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_mem_keys._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_mem_keys","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":73,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_mem_keys._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.exists_of_mem_keys","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","Exists","List","List.instMembership","Membership.mem","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":350,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","HEq.symm","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_exists","List","List.instMembership","Membership.mem","Not","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.exists_of_mem_keys._proof_1_1","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sigma.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.head?_lookupAll.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.head?_lookupAll","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Sigma","Sigma.mk","Unit"],"value_dag_size":90,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Sigma.casesOn","Sigma.mk","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_left.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_left","reducibility":"abbrev","statement_dag_size":124,"type_refs":["List","List.cons","List.instMembership","List.keys","List.nil","Membership.mem","Sigma"],"value_dag_size":173,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.keys","List.nil","Membership.mem","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right._simp_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right._simp_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_append_right","reducibility":"abbrev","statement_dag_size":129,"type_refs":["List","List.cons","List.instMembership","List.keys","List.nil","Membership.mem","Not","Sigma"],"value_dag_size":181,"value_refs":["List","List.casesOn","List.cons","List.instMembership","List.keys","List.nil","Membership.mem","Not","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_comm.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_comm","reducibility":"abbrev","statement_dag_size":539,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.mk","instHAppendOfAppend"],"value_dag_size":2029,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.cons","List.instAppend","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.mk","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kerase_of_notMem_keys._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kerase_of_notMem_keys","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_1","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","List","List.kextract.match_1","Option","Prod","Prod.mk","Sigma"],"value_dag_size":71,"value_refs":["Eq.refl","List","List.kextract.match_1","Option","Prod","Prod.mk","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_1","reducibility":"abbrev","statement_dag_size":54,"type_refs":["List","Option","Prod","Prod.mk","Sigma"],"value_dag_size":1,"value_refs":["List.kextract.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3.eq_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","List","List.cons","List.kextract.match_3","List.nil","Sigma","Unit","Unit.unit"],"value_dag_size":53,"value_refs":["Eq.refl","List","List.cons","List.kextract.match_3","List.nil","Sigma","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3.eq_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","List","List.cons","List.kextract.match_3","List.nil","Sigma","Unit"],"value_dag_size":64,"value_refs":["Eq.refl","List","List.cons","List.kextract.match_3","List.nil","Sigma","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3.splitter","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract.match_3","reducibility":"abbrev","statement_dag_size":47,"type_refs":["List","List.cons","List.nil","Sigma","Unit"],"value_dag_size":1,"value_refs":["List.kextract.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kextract_eq_dlookup_kerase.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kextract_eq_dlookup_kerase","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Sigma","Sigma.mk","Unit"],"value_dag_size":90,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Sigma.casesOn","Sigma.mk","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kreplace_of_forall_not._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kreplace_of_forall_not","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":78,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kreplace_of_forall_not._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kreplace_of_forall_not","reducibility":null,"statement_dag_size":93,"type_refs":["DecidableEq","Eq","List","List.instMembership","Membership.mem","Not","Option","Option.none","Option.some","Sigma","Sigma.fst","Sigma.mk","ite"],"value_dag_size":380,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.symm","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.instMembership","Membership.mem","Not","Option","Option.none","Option.some","Or","Or.casesOn","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.kreplace_of_forall_not._proof_1_1","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","ite","ite_cond_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","List","List.cons","List.kunion.match_1","List.nil","Sigma"],"value_dag_size":70,"value_refs":["Eq.refl","List","List.cons","List.kunion.match_1","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","List","List.cons","List.kunion.match_1","List.nil","Sigma"],"value_dag_size":82,"value_refs":["Eq.refl","List","List.cons","List.kunion.match_1","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kunion.match_1","reducibility":"abbrev","statement_dag_size":63,"type_refs":["List","List.cons","List.nil","Sigma"],"value_dag_size":1,"value_refs":["List.kunion.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kunion_kerase.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kunion_kerase","reducibility":"abbrev","statement_dag_size":63,"type_refs":["List","List.cons","List.nil","Sigma"],"value_dag_size":77,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.kunion_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.kunion_nil","reducibility":"abbrev","statement_dag_size":47,"type_refs":["List","List.cons","List.nil","Sigma","Unit"],"value_dag_size":62,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_cons_ne.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_cons_ne","reducibility":"abbrev","statement_dag_size":64,"type_refs":["Ne","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":92,"value_refs":["Ne","Sigma","Sigma.casesOn","Sigma.fst","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_5","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":50,"type_refs":["And","Eq","HEq","Sigma","Sigma.mk"],"value_dag_size":56,"value_refs":["And","Eq","HEq","Sigma","Sigma.mk","Sigma.mk.inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_6","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_7","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_8","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil._simp_1_9","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_eq_nil","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Sigma","Sigma.mk","Unit"],"value_dag_size":90,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Sigma.casesOn","Sigma.mk","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_sublist._simp_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_sublist","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_sublist.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookupAll_sublist","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Sigma","Sigma.mk","Unit"],"value_dag_size":90,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Sigma.casesOn","Sigma.mk","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.lookup_ext._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.lookup_ext","reducibility":null,"statement_dag_size":69,"type_refs":["DecidableEq","Iff","List","List.NodupKeys","List.Perm","List.dlookup","Membership.mem","Option","Option.instMembership","Sigma"],"value_dag_size":725,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_right","List","List.Nodup","List.NodupKeys","List.NodupKeys.nodup","List.Perm","List.dlookup","List.instMembership","List.mem_dlookup_iff","List.mem_ext","Membership.mem","Not","Option","Option.instMembership","Or","Sigma","Sigma.fst","Sigma.mk","Sigma.snd","True","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find","reducibility":null,"statement_dag_size":59,"type_refs":["Decidable.decide","DecidableEq","Eq","List.dlookup","List.find?","List.nil","Option","Option.map","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":203,"value_refs":["Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.dlookup","List.dlookup_nil","List.find?","List.find?_nil","List.nil","Not","Option","Option.map","Option.map_none","Option.none","Sigma","Sigma.fst","Sigma.mk","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":73,"value_refs":["Eq","Eq.rec","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find._proof_1_5","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find","reducibility":null,"statement_dag_size":79,"type_refs":["Decidable.decide","DecidableEq","Eq","List","List.cons","List.dlookup","List.find?","Option","Option.map","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":506,"value_refs":["Bool","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.symm","Lean.Grind.decide_eq_true","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.cons","List.dlookup","List.dlookup_cons_eq","List.filter.match_1","List.filter.match_1.congr_eq_1","List.find?","List.find?_cons","Not","Option","Option.map","Option.map_some","Option.some","PUnit","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","Unit","_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find._proof_1_3","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","heq_of_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find._proof_1_6","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map_dlookup_eq_find","reducibility":null,"statement_dag_size":113,"type_refs":["Decidable.decide","DecidableEq","Eq","List","List.cons","List.dlookup","List.find?","Not","Option","Option.map","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":394,"value_refs":["Bool","Classical.byContradiction","Decidable.decide","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HEq","Lean.Grind.decide_eq_false","Lean.Grind.eq_congr'","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dlookup","List.dlookup_cons_ne","List.filter.match_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","Ne","Not","Option","Option.map","Option.some","PUnit","Sigma","Sigma.fst","Sigma.mk","True","True.intro","Unit","congrArg","eq_false","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map₂_keys._proof_1_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map₂_keys","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","List","List.keys","List.map","List.nil","Sigma","Sigma.map","id"],"value_dag_size":205,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.keys","List.keys_nil","List.map","List.map_nil","List.nil","Not","Sigma","Sigma.map","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.map₂_keys._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.map₂_keys","reducibility":null,"statement_dag_size":100,"type_refs":["Eq","List","List.cons","List.keys","List.map","Sigma","Sigma.map","id"],"value_dag_size":404,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.cons","List.keys","List.keys_cons","List.map","List.map_cons","Not","Sigma","Sigma.fst","Sigma.map","Sigma.map.eq_1","Sigma.mk","Sigma.mk.inj","Sigma.snd","True","True.intro","congr","congrArg","eq_false","eq_true","id","id.eq_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.mem_dlookup_kunion_middle.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.mem_dlookup_kunion_middle","reducibility":"abbrev","statement_dag_size":195,"type_refs":["And","DecidableEq","List","List.dlookup","List.instMembership","List.keys","Membership.mem","Not","Option","Option.instMembership","Or","Or.inl","Or.inr","Sigma"],"value_dag_size":208,"value_refs":["And","DecidableEq","List","List.dlookup","List.instMembership","List.keys","Membership.mem","Not","Option","Option.instMembership","Or","Or.casesOn","Or.inl","Or.inr","Sigma"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.mem_ext._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.mem_ext","reducibility":null,"statement_dag_size":57,"type_refs":["Iff","List","List.Nodup","List.Perm","List.instMembership","Membership.mem","Sigma"],"value_dag_size":302,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","List","List.Nodup","List.Perm","List.instMembership","List.perm_ext_iff_of_nodup","Membership.mem","Not","Sigma","True","True.intro","congrArg","eq_false","eq_true","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.mem_keys.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.mem_keys","reducibility":"abbrev","statement_dag_size":101,"type_refs":["Exists","Exists.intro","List","List.instMembership","Membership.mem","Sigma","Sigma.mk"],"value_dag_size":129,"value_refs":["Exists","Exists.casesOn","Exists.intro","List","List.instMembership","Membership.mem","Sigma","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.mem_keys_kerase_of_ne.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.mem_keys_kerase_of_ne","reducibility":"abbrev","statement_dag_size":554,"type_refs":["And","And.intro","Eq","Eq.refl","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.mk","instHAppendOfAppend"],"value_dag_size":2046,"value_refs":["And","And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","HEq","HEq.refl","List","List.cons","List.instAppend","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.mk","eq_of_heq","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.mem_lookupAll.match_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.mem_lookupAll","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Sigma","Sigma.mk","Unit"],"value_dag_size":90,"value_refs":["List","List.casesOn","List.cons","List.nil","Sigma","Sigma.casesOn","Sigma.mk","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.ne_key._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.ne_key","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","List","List.instMembership","Membership.mem","Not","Sigma","Sigma.fst"],"value_dag_size":127,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","List","List.instMembership","Membership.mem","Not","Sigma","Sigma.fst","eq_false","eq_of_heq","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.ne_key._proof_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.ne_key","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","Iff","List","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.fst"],"value_dag_size":785,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HEq","HEq.refl","HEq.symm","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_true","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","List","List.instMembership","List.keys","List.mem_keys","Membership.mem","Not","Or","Or.casesOn","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.ne_key._proof_1_1","cast","cast_heq","congr","congrArg","eq_false","eq_of_heq","eq_self","eq_true","forall_not_of_not_exists","heq_of_eq","id","implies_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","List","List.NodupKeys","List.Pairwise","Ne","Sigma","Sigma.fst"],"value_dag_size":47,"value_refs":["List","List.NodupKeys","List.Pairwise","List.nodupKeys_iff_pairwise","Ne","Sigma","Sigma.fst","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten._simp_1_3","namespace":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","List","List.Disjoint","List.instMembership","Membership.mem","Ne"],"value_dag_size":50,"value_refs":["List","List.Disjoint","List.disjoint_iff_ne","List.instMembership","Membership.mem","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten._simp_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_flatten","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Sigma","Sigma.mk"],"value_dag_size":40,"value_refs":["Sigma","Sigma.forall","Sigma.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_middle._simp_1_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.nodupKeys_middle","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAppend.hAppend","List","List.Nodup","List.cons","List.instAppend","instHAppendOfAppend"],"value_dag_size":44,"value_refs":["HAppend.hAppend","List","List.Nodup","List.cons","List.instAppend","List.nodup_middle","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.nodup_zipIdx_map_snd._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.nodup_zipIdx_map_snd","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","LT.lt","List.Nodup","List.nodup_range'._auto_1","List.range'","Nat","OfNat.ofNat","True","autoParam","instLTNat","instOfNatNat","optParam"],"value_dag_size":49,"value_refs":["LT.lt","List.Nodup","List.nodup_range'","List.nodup_range'._auto_1","List.range'","Nat","OfNat.ofNat","autoParam","eq_true","instLTNat","instOfNatNat","optParam"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.notMem_keys._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.notMem_keys","reducibility":null,"statement_dag_size":55,"type_refs":["Iff","List","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.mk"],"value_dag_size":476,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","List","List.instMembership","List.keys","List.mem_keys","Membership.mem","Not","Or","Or.casesOn","Sigma","Sigma.mk","True","True.intro","congr","congrArg","eq_false","eq_true","forall_not_of_not_exists","id","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.notMem_keys_of_nodupKeys_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.notMem_keys_of_nodupKeys_cons","reducibility":null,"statement_dag_size":50,"type_refs":["List","List.NodupKeys","List.cons","List.instMembership","List.keys","Membership.mem","Not","Sigma","Sigma.fst"],"value_dag_size":206,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_not","List","List.Nodup","List.NodupKeys","List.NodupKeys.eq_1","List.cons","List.instMembership","List.keys","List.keys_cons","List.nodup_cons","Membership.mem","Not","Sigma","Sigma.fst","True","True.intro","congrArg","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup","reducibility":null,"statement_dag_size":58,"type_refs":["DecidableEq","List","List.dlookup","List.instMembership","List.nil","Membership.mem","Option","Option.instMembership","Sigma","Sigma.mk"],"value_dag_size":168,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.dlookup","List.dlookup_nil","List.instMembership","List.nil","Membership.mem","Not","Option","Option.instMembership","Option.none","Option.not_mem_none","Sigma","Sigma.mk","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup._proof_1_2","namespace":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Sigma","Sigma.fst"],"value_dag_size":78,"value_refs":["Eq","Eq.rec","Eq.symm","HEq","HEq.refl","Sigma","Sigma.fst","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup._proof_1_4","namespace":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup","reducibility":null,"statement_dag_size":82,"type_refs":["DecidableEq","Eq","List","List.cons","List.dlookup","List.instMembership","Membership.mem","Option","Option.instMembership","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":487,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.symm","HEq.trans","Iff","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.dlookup","List.dlookup_cons_eq","List.instMembership","List.mem_cons","Membership.mem","Not","Option","Option.instMembership","Option.mem_some","Option.some","Or","Sigma","Sigma.fst","Sigma.mk","Sigma.mk.hcongr_4","Sigma.snd","True","True.intro","_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup._proof_1_2","cast","cast_heq","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup._proof_1_5","namespace":"_private.Mathlib.Data.List.Sigma.0.List.of_mem_dlookup","reducibility":null,"statement_dag_size":113,"type_refs":["DecidableEq","Eq","List","List.cons","List.dlookup","List.instMembership","Membership.mem","Not","Option","Option.instMembership","Sigma","Sigma.fst","Sigma.mk"],"value_dag_size":343,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","List","List.cons","List.dlookup","List.dlookup_cons_ne","List.instMembership","List.mem_cons","Membership.mem","Ne","Not","Option","Option.instMembership","Or","Sigma","Sigma.fst","Sigma.mk","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.perm_dlookup._simp_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.perm_dlookup","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":39,"value_refs":["Eq","Eq.symm","Membership.mem","Option","Option.instMembership","Option.mem_def","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sigma","name":"_private.Mathlib.Data.List.Sigma.0.List.sublist_dlookup._proof_1_1","namespace":"_private.Mathlib.Data.List.Sigma.0.List.sublist_dlookup","reducibility":null,"statement_dag_size":74,"type_refs":["DecidableEq","List","List.NodupKeys","List.Sublist","List.dlookup","Membership.mem","Option","Option.instMembership","Sigma"],"value_dag_size":458,"value_refs":["Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","Iff","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","List","List.NodupKeys","List.Perm","List.Sublist","List.Sublist.exists_perm_append","List.dlookup","List.dlookup_append","List.instAppend","List.perm_dlookup","Membership.mem","Not","Option","Option.instMembership","Option.mem_def","Option.or","Option.some","Option.some_or","Sigma","True","True.intro","congrArg","eq_false","eq_true","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.eq_of_mem_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.eq_of_mem_iff","reducibility":null,"statement_dag_size":34,"type_refs":["HasSubset.Subset","Iff","List","List.instHasSubset","List.instMembership","Membership.mem"],"value_dag_size":194,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HasSubset.Subset","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","List","List.instHasSubset","List.instMembership","List.subset_def","Membership.mem","Not","True","True.intro","eq_false","forall_congr","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.eq_of_mem_iff._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.eq_of_mem_iff","reducibility":null,"statement_dag_size":34,"type_refs":["HasSubset.Subset","Iff","List","List.instHasSubset","List.instMembership","Membership.mem"],"value_dag_size":197,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HasSubset.Subset","Iff","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","List","List.instHasSubset","List.instMembership","List.subset_def","Membership.mem","Not","True","True.intro","eq_false","forall_congr","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq","reducibility":null,"statement_dag_size":34,"type_refs":["DecidableRel","Eq","List","List.Pairwise","List.insertionSort","List.nil"],"value_dag_size":90,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Pairwise","List.insertionSort","List.insertionSort_nil","List.nil","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableRel","Eq","List","List.Pairwise","List.cons","List.insertionSort"],"value_dag_size":533,"value_refs":["And","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","List","List.Pairwise","List.Pairwise.of_cons","List.casesOn","List.cons","List.insertionSort","List.insertionSort_cons","List.nil","List.orderedInsert","List.orderedInsert_cons","List.orderedInsert_nil","List.pairwise_cons_cons","Not","True","True.intro","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.orderedInsert._proof_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.orderedInsert","reducibility":null,"statement_dag_size":53,"type_refs":["DecidableRel","IsTrans","List","List.Pairwise","List.cons","List.orderedInsert"],"value_dag_size":284,"value_refs":["And","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","IsTrans","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","List","List.IsChain","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.cons","List.isChain_cons_cons","List.orderedInsert","List.orderedInsert_cons","Not","True","True.intro","congrArg","eq_false","eq_true","id","instTransOfIsTrans","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.orderedInsert.match_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.Pairwise.orderedInsert","reducibility":"abbrev","statement_dag_size":59,"type_refs":["List","List.Pairwise","List.cons","List.nil"],"value_dag_size":87,"value_refs":["List","List.Pairwise","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.cons_sublist_orderedInsert._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.cons_sublist_orderedInsert","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableRel","List","List.Sublist","List.cons","List.nil","List.orderedInsert"],"value_dag_size":193,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","List","List.Sublist","List.Sublist.refl","List.cons","List.nil","List.orderedInsert","List.orderedInsert_nil","List.sublist_nil","Not","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.cons_sublist_orderedInsert._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.cons_sublist_orderedInsert","reducibility":null,"statement_dag_size":79,"type_refs":["DecidableRel","List","List.Sublist","List.cons","List.instMembership","List.orderedInsert","Membership.mem"],"value_dag_size":547,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_false_left","List","List.Sublist","List.Sublist.cons","List.cons","List.cons_sublist_cons","List.instMembership","List.mem_cons","List.orderedInsert","List.orderedInsert_cons","List.sublist_cons_iff","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.erase","List.nil","List.orderedInsert","instBEqOfDecidableEq"],"value_dag_size":247,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.congr_simp","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.beq_eq_decide_eq","List","List.cons","List.erase","List.erase_cons","List.nil","List.orderedInsert","List.orderedInsert_nil","Not","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_self","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instDecidableTrue","instLawfulBEq","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.cons","List.erase","List.orderedInsert","Std.Refl","instBEqOfDecidableEq"],"value_dag_size":689,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.congr_simp","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.nestedDecidable","List","List.cons","List.erase","List.erase_cons","List.orderedInsert","List.orderedInsert_cons","Not","Or","Or.casesOn","Std.Refl","Std.Refl.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_of_heq","eq_self","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instDecidableTrue","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.erase","List.nil","List.orderedInsert","instBEqOfDecidableEq"],"value_dag_size":247,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.congr_simp","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.beq_eq_decide_eq","List","List.cons","List.erase","List.erase_cons","List.nil","List.orderedInsert","List.orderedInsert_nil","Not","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_self","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instDecidableTrue","instLawfulBEq","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem","reducibility":null,"statement_dag_size":90,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.cons","List.erase","List.instMembership","List.orderedInsert","Membership.mem","Not","instBEqOfDecidableEq"],"value_dag_size":585,"value_refs":["BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.congr_simp","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.erase","List.erase_cons","List.instMembership","List.mem_cons","List.orderedInsert","List.orderedInsert_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_self","eq_true","id","instBEqOfDecidableEq","instDecidableEqBool","instDecidableTrue","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sort.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.map_insertionSort._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.map_insertionSort","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","List","List.cons","List.instMembership","Membership.mem"],"value_dag_size":47,"value_refs":["And","List","List.cons","List.forall_mem_cons","List.instMembership","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.map_insertionSort._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.map_insertionSort","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.map_orderedInsert._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.map_orderedInsert","reducibility":null,"statement_dag_size":57,"type_refs":["DecidableRel","Eq","List","List.map","List.nil","List.orderedInsert"],"value_dag_size":226,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.cons","List.map","List.map_cons","List.map_nil","List.nil","List.orderedInsert","List.orderedInsert_nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.map_orderedInsert._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.map_orderedInsert","reducibility":null,"statement_dag_size":158,"type_refs":["DecidableRel","Eq","Iff","List","List.cons","List.instMembership","List.map","List.orderedInsert","Membership.mem"],"value_dag_size":1167,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedDecidable","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.instMembership","List.map","List.map_cons","List.mem_cons","List.orderedInsert","List.orderedInsert_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congrArg","congrFun'","eq_false","eq_self","eq_true","forall_congr","id","implies_congr","ite","ite_cond_eq_false","ite_cond_eq_true","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.mem_orderedInsert._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.mem_orderedInsert","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableRel","Eq","Iff","List","List.instMembership","List.nil","List.orderedInsert","Membership.mem","Or"],"value_dag_size":237,"value_refs":["And","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","List","List.cons","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","List.orderedInsert","List.orderedInsert_nil","Membership.mem","Not","Or","congrArg","eq_false","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.mem_orderedInsert._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.mem_orderedInsert","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableRel","Eq","Iff","List","List.cons","List.instMembership","List.orderedInsert","Membership.mem","Or"],"value_dag_size":1535,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","List","List.cons","List.instMembership","List.mem_cons","List.orderedInsert","List.orderedInsert_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.eq_def","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableRel","Eq","List","List.cons","List.nil","List.orderedInsert","Unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","ite"],"value_dag_size":666,"value_refs":["DecidableRel","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","List","List.below","List.brecOn","List.brecOn.eq","List.brecOn.go","List.cons","List.nil","List.orderedInsert","List.orderedInsert._f","List.rec","PProd","PUnit","Unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1.splitter","congrArg","id","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","Unit","Unit.unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","Unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","Unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","Unit","_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["_private.Mathlib.Data.List.Sort.0.List.orderedInsert.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_eq_take_drop._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_eq_take_drop","reducibility":null,"statement_dag_size":67,"type_refs":["Decidable.decide","DecidableRel","Eq","HAppend.hAppend","List","List.cons","List.dropWhile","List.instAppend","List.nil","List.orderedInsert","List.takeWhile","Not","instDecidableNot","instHAppendOfAppend"],"value_dag_size":438,"value_refs":["Bool","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropWhile","List.dropWhile.eq_1","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.orderedInsert","List.orderedInsert_nil","List.takeWhile","List.takeWhile.eq_1","Nat","Not","OfNat.ofNat","PLift","PLift.up","congr","congrArg","congrFun'","decide_not","eagerReduce","funext","id","instDecidableNot","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_eq_take_drop._proof_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_eq_take_drop","reducibility":null,"statement_dag_size":111,"type_refs":["Decidable.decide","DecidableRel","Eq","HAppend.hAppend","List","List.cons","List.dropWhile","List.instAppend","List.orderedInsert","List.takeWhile","Not","instDecidableNot","instHAppendOfAppend"],"value_dag_size":1241,"value_refs":["Bool","Bool.false","Bool.not","Bool.true","Classical.byContradiction","Decidable.decide","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","False.elim","HAppend.hAppend","HEq","Inhabited.default","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.Bool.eq_true_of_not_eq_false","Lean.Grind.Bool.not_eq_of_eq_false","Lean.Grind.alreadyNorm","Lean.Grind.decide_eq_false","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.exists_const","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.not_false","Lean.Grind.of_decide_eq_true","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.cons_append","List.ctorIdx","List.dropWhile","List.dropWhile.eq_2","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.orderedInsert","List.orderedInsert_cons","List.takeWhile","List.takeWhile.eq_2","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","PUnit","PUnit.casesOn","True","True.casesOn","True.intro","Unit","_private.Mathlib.Data.List.Sort.0.List.filter.match_1.splitter","congr","congrArg","congrFun","congrFun'","decide_not","eagerReduce","eq_false","eq_false'","eq_true","funext","heq_eq_eq","id","implies_congr","instDecidableNot","instHAppendOfAppend","instInhabitedPUnit","instNonemptyOfInhabited","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","noConfusion_of_Nat","not_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.erase","List.instMembership","List.nil","List.orderedInsert","Membership.mem","instBEqOfDecidableEq"],"value_dag_size":109,"value_refs":["Classical.byContradiction","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.erase","List.instMembership","List.nil","List.not_mem_nil","List.orderedInsert","Membership.mem","Not","True","True.intro","eq_false","eq_true","id","instBEqOfDecidableEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase","reducibility":null,"statement_dag_size":27,"type_refs":["List","List.Pairwise","List.cons"],"value_dag_size":76,"value_refs":["Eq.mp","Eq.refl","Eq.symm","Eq.trans","Lean.Grind.imp_eq_of_eq_true_left","List","List.Pairwise","List.Pairwise.of_cons","List.cons","True","eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase._proof_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase","reducibility":null,"statement_dag_size":106,"type_refs":["DecidableEq","DecidableRel","Eq","List","List.Pairwise","List.cons","List.erase","List.instMembership","List.orderedInsert","Membership.mem","Std.Antisymm","instBEqOfDecidableEq"],"value_dag_size":2079,"value_refs":["And","BEq.beq","Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidableEq","DecidableRel","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.casesOn","False.elim","HEq","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.beq_eq_decide_eq","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Pairwise.casesOn","List.Pairwise.cons","List.Pairwise.nil","List.Pairwise.of_cons","List.cons","List.cons.noConfusion","List.ctorIdx","List.erase","List.erase_cons","List.erase_nil","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","List.orderedInsert","List.orderedInsert_cons","List.orderedInsert_nil","List.pairwise_cons_cons","Membership.mem","Not","Or","Or.casesOn","Std.Antisymm","Std.Antisymm.casesOn","True","True.intro","_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase._proof_1_2","congr","congrArg","congrFun'","decide_eq_true_eq","eq_false","eq_false'","eq_of_heq","eq_true","heq_eq_eq","id","instBEqOfDecidableEq","instDecidableEqBool","instLawfulBEq","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_length._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_length","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableRel","Eq","HAdd.hAdd","List.length","List.nil","List.orderedInsert","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":147,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","List","List.cons","List.length","List.length_cons","List.nil","List.orderedInsert","List.orderedInsert_nil","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_length._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.orderedInsert_length","reducibility":null,"statement_dag_size":73,"type_refs":["DecidableRel","Eq","HAdd.hAdd","List","List.cons","List.length","List.orderedInsert","Nat","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":577,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","List.orderedInsert","List.orderedInsert_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.pairwise_insertionSort.match_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.pairwise_insertionSort","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.perm_insertionSort._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.perm_insertionSort","reducibility":null,"statement_dag_size":25,"type_refs":["DecidableRel","List.Perm","List.insertionSort","List.nil"],"value_dag_size":117,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Perm","List.Perm.nil","List.insertionSort","List.insertionSort_nil","List.nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.perm_insertionSort._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.perm_insertionSort","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableRel","List","List.Perm","List.cons","List.insertionSort"],"value_dag_size":245,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","List","List.Perm","List.Perm.cons","List.Perm.trans","List.cons","List.insertionSort","List.insertionSort_cons","List.orderedInsert","List.perm_orderedInsert","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.perm_orderedInsert.match_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.perm_orderedInsert","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_5","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_6","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":91,"type_refs":["Fin","Fin.instPartialOrder","Fin.mk","Iff","LE.le","LT.lt","List","List.Pairwise","List.get","List.length","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","instLTNat"],"value_dag_size":2900,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.instPartialOrder","Fin.isLt","Fin.mk","Fin.val","GetElem.getElem","HAdd.hAdd","HEq.trans","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.of_not_lt","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Pairwise","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_4","_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._proof_1_5","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":39,"type_refs":["Antitone","Eq","Fin","Fin.instPartialOrder","List","List.SortedGE","List.get","List.length","PartialOrder.toPreorder","Preorder"],"value_dag_size":42,"value_refs":["Antitone","Fin","Fin.instPartialOrder","List","List.SortedGE","List.get","List.length","List.sortedGE_iff_antitone_get","PartialOrder.toPreorder","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":56,"type_refs":["Antitone","Eq","LE.le","LT.lt","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":61,"value_refs":["Antitone","LE.le","LT.lt","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","antitone_iff_forall_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_iff_pairwise","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_map_ofDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_map_ofDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGE","List.SortedLE","List.map","OrderDual","OrderDual.instPreorder","OrderDual.ofDual","Preorder"],"value_dag_size":884,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLE","OrderDual.instPreorder","OrderDual.ofDual","OrderDual.ofDual_le_ofDual","Preorder","Preorder.toLE","True","True.intro","congrArg","eq_false","eq_true","id","instTransLE","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_map_toDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_map_toDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGE","List.SortedLE","List.map","OrderDual","OrderDual.instPreorder","OrderDual.toDual","Preorder"],"value_dag_size":880,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLE","OrderDual.instPreorder","OrderDual.toDual","OrderDual.toDual_le_toDual","Preorder","Preorder.toLE","True","True.intro","congrArg","eq_false","eq_true","id","instTransLE","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Antitone","Eq","Fin","Fin.instPartialOrder","List","List.SortedGE","List.get","List.length","PartialOrder.toPreorder","Preorder"],"value_dag_size":42,"value_refs":["Antitone","Fin","Fin.instPartialOrder","List","List.SortedGE","List.get","List.length","List.sortedGE_iff_antitone_get","PartialOrder.toPreorder","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_ofFn_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Fin","Fin.mk","LE.le","LT.lt","Nat","instLEFin","instLENat","instLTNat"],"value_dag_size":48,"value_refs":["Fin","Fin.mk","Fin.mk_le_mk","LE.le","LT.lt","Nat","instLEFin","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGE_reverse","reducibility":null,"statement_dag_size":25,"type_refs":["Iff","List","List.SortedGE","List.SortedLE","List.reverse","Preorder"],"value_dag_size":183,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","GE.ge","Iff","LE.le","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.Pairwise","List.SortedGE","List.SortedLE","List.pairwise_reverse","List.reverse","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Preorder","Preorder.toLE","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_5","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_6","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise","reducibility":null,"statement_dag_size":91,"type_refs":["Fin","Fin.instPartialOrder","Fin.mk","Iff","LT.lt","List","List.Pairwise","List.get","List.length","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLT","instLTNat"],"value_dag_size":2900,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.instPartialOrder","Fin.isLt","Fin.mk","Fin.val","GetElem.getElem","HAdd.hAdd","HEq.trans","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.of_not_lt","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Pairwise","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLT","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_4","_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._proof_1_5","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedGT","List.get","List.length","PartialOrder.toPreorder","Preorder","StrictAnti"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedGT","List.get","List.length","List.sortedGT_iff_strictAnti_get","PartialOrder.toPreorder","Preorder","StrictAnti","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_iff_pairwise","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_map_ofDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_map_ofDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGT","List.SortedLT","List.map","OrderDual","OrderDual.instPreorder","OrderDual.ofDual","Preorder"],"value_dag_size":884,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLT","OrderDual.instPreorder","OrderDual.ofDual","OrderDual.ofDual_lt_ofDual","Preorder","Preorder.toLT","True","True.intro","congrArg","eq_false","eq_true","id","instTransLT","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_map_toDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_map_toDual","reducibility":null,"statement_dag_size":59,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGT","List.SortedLT","List.map","OrderDual","OrderDual.instPreorder","OrderDual.toDual","Preorder"],"value_dag_size":923,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLT","OrderDual.instPreorder","OrderDual.toDual","OrderDual.toDual_lt_toDual","Preorder","Preorder.toLT","True","True.intro","congrArg","eq_false","eq_true","id","instTransLT","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedGT","List.get","List.length","PartialOrder.toPreorder","Preorder","StrictAnti"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedGT","List.get","List.length","List.sortedGT_iff_strictAnti_get","PartialOrder.toPreorder","Preorder","StrictAnti","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":44,"value_refs":["Fin","Fin.mk","Fin.mk_lt_mk","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedGT_reverse","reducibility":null,"statement_dag_size":25,"type_refs":["Iff","List","List.SortedGT","List.SortedLT","List.reverse","Preorder"],"value_dag_size":183,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","GT.gt","Iff","LT.lt","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.Pairwise","List.SortedGT","List.SortedLT","List.pairwise_reverse","List.reverse","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Preorder","Preorder.toLT","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_5","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_6","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":91,"type_refs":["Fin","Fin.instPartialOrder","Fin.mk","Iff","LE.le","LT.lt","List","List.Pairwise","List.get","List.length","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","instLTNat"],"value_dag_size":2886,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.instPartialOrder","Fin.isLt","Fin.mk","Fin.val","GetElem.getElem","HAdd.hAdd","HEq.trans","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.of_not_lt","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Pairwise","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_4","_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._proof_1_5","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedLE","List.get","List.length","Monotone","PartialOrder.toPreorder","Preorder"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedLE","List.get","List.length","List.sortedLE_iff_monotone_get","Monotone","PartialOrder.toPreorder","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","LE.le","LT.lt","Monotone","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":61,"value_refs":["LE.le","LT.lt","Monotone","PartialOrder","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","monotone_iff_forall_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_iff_pairwise","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_map_ofDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_map_ofDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGE","List.SortedLE","List.map","OrderDual","OrderDual.instPreorder","OrderDual.ofDual","Preorder"],"value_dag_size":1020,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLE","OrderDual.instPreorder","OrderDual.ofDual","OrderDual.ofDual_le_ofDual","Preorder","Preorder.toLE","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_map_toDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_map_toDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGE","List.SortedLE","List.map","OrderDual","OrderDual.instPreorder","OrderDual.toDual","Preorder"],"value_dag_size":1010,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLE","OrderDual.instPreorder","OrderDual.toDual","OrderDual.toDual_le_toDual","Preorder","Preorder.toLE","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedLE","List.get","List.length","Monotone","PartialOrder.toPreorder","Preorder"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedLE","List.get","List.length","List.sortedLE_iff_monotone_get","Monotone","PartialOrder.toPreorder","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Fin","Fin.mk","LE.le","LT.lt","Nat","instLEFin","instLENat","instLTNat"],"value_dag_size":48,"value_refs":["Fin","Fin.mk","Fin.mk_le_mk","LE.le","LT.lt","Nat","instLEFin","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLE_reverse","reducibility":null,"statement_dag_size":25,"type_refs":["Iff","List","List.SortedGE","List.SortedLE","List.reverse","Preorder"],"value_dag_size":183,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","GE.ge","Iff","LE.le","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.Pairwise","List.SortedGE","List.SortedLE","List.pairwise_reverse","List.reverse","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Preorder","Preorder.toLE","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_5","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise","reducibility":null,"statement_dag_size":64,"type_refs":["Fin.mk","Fin.val","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Fin.isLt","Fin.mk","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_4","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_6","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise","reducibility":null,"statement_dag_size":91,"type_refs":["Fin","Fin.instPartialOrder","Fin.mk","Iff","LT.lt","List","List.Pairwise","List.get","List.length","Nat","PartialOrder.toPreorder","Preorder","Preorder.toLT","instLTNat"],"value_dag_size":2886,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Fin","Fin.instPartialOrder","Fin.isLt","Fin.mk","Fin.val","GetElem.getElem","HAdd.hAdd","HEq.trans","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.lt_eq_true_of_le_k","Lean.Grind.ToInt.of_lt","Lean.Grind.ToInt.of_not_lt","Lean.Grind.ToInt.toInt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLTFinCoOfNatIntCast","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.toInt_fin","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.Pairwise","List.get","List.get_eq_getElem","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.cast","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLT","SemilatticeInf.toPartialOrder","True","_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_4","_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._proof_1_5","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTFin","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedLT","List.get","List.length","PartialOrder.toPreorder","Preorder","StrictMono"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedLT","List.get","List.length","List.sortedLT_iff_strictMono_get","PartialOrder.toPreorder","Preorder","StrictMono","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_iff_pairwise","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_map_ofDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_map_ofDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGT","List.SortedLT","List.map","OrderDual","OrderDual.instPreorder","OrderDual.ofDual","Preorder"],"value_dag_size":1020,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLT","OrderDual.instPreorder","OrderDual.ofDual","OrderDual.ofDual_lt_ofDual","Preorder","Preorder.toLT","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_map_toDual._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_map_toDual","reducibility":null,"statement_dag_size":54,"type_refs":["DFunLike.coe","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Iff","List","List.SortedGT","List.SortedLT","List.map","OrderDual","OrderDual.instPreorder","OrderDual.toDual","Preorder"],"value_dag_size":1010,"value_refs":["And","And.casesOn","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.symm","Eq.trans","Equiv","Equiv.instEquivLike","EquivLike.toFunLike","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","OrderDual","OrderDual.instLT","OrderDual.instPreorder","OrderDual.toDual","OrderDual.toDual_lt_toDual","Preorder","Preorder.toLT","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.instPartialOrder","List","List.SortedLT","List.get","List.length","PartialOrder.toPreorder","Preorder","StrictMono"],"value_dag_size":42,"value_refs":["Fin","Fin.instPartialOrder","List","List.SortedLT","List.get","List.length","List.sortedLT_iff_strictMono_get","PartialOrder.toPreorder","Preorder","StrictMono","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":34,"value_refs":["Fin","Fin.forall_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_ofFn_iff","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Fin","Fin.mk","LT.lt","Nat","instLTFin","instLTNat"],"value_dag_size":44,"value_refs":["Fin","Fin.mk","Fin.mk_lt_mk","LT.lt","Nat","instLTFin","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_reverse._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sortedLT_reverse","reducibility":null,"statement_dag_size":25,"type_refs":["Iff","List","List.SortedGT","List.SortedLT","List.reverse","Preorder"],"value_dag_size":183,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","GT.gt","Iff","LT.lt","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","List","List.Pairwise","List.SortedGT","List.SortedLT","List.pairwise_reverse","List.reverse","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Preorder","Preorder.toLT","congrArg","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sublist_insertionSort'._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sublist_insertionSort'","reducibility":null,"statement_dag_size":44,"type_refs":["DecidableRel","List","List.Perm","List.Sublist","List.insertionSort","List.nil"],"value_dag_size":210,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.iff_eq","List","List.Perm","List.Sublist","List.insertionSort","List.insertionSort_nil","List.nil","List.nil_perm","List.sublist_nil","Not","True","True.intro","congrArg","eq_false","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sublist_insertionSort._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sublist_insertionSort","reducibility":null,"statement_dag_size":35,"type_refs":["DecidableRel","List","List.Sublist","List.insertionSort","List.nil"],"value_dag_size":112,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List","List.Sublist","List.insertionSort","List.insertionSort_nil","List.nil","Not","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sublist_of_subperm_of_pairwise.match_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sublist_of_subperm_of_pairwise","reducibility":"abbrev","statement_dag_size":70,"type_refs":["And","And.intro","Exists.intro","List","List.Perm","List.Sublist","List.Subperm"],"value_dag_size":127,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","List","List.Perm","List.Sublist","List.Subperm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sublist_orderedInsert._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.List.sublist_orderedInsert","reducibility":null,"statement_dag_size":28,"type_refs":["DecidableRel","List.Sublist","List.nil","List.orderedInsert"],"value_dag_size":83,"value_refs":["Classical.byContradiction","DecidableRel","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","List.Sublist","List.nil","List.nil_sublist","List.orderedInsert","Not","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.sublist_orderedInsert._proof_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.List.sublist_orderedInsert","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableRel","List","List.Sublist","List.cons","List.orderedInsert"],"value_dag_size":296,"value_refs":["Classical.byContradiction","DecidableRel","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Iff","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","List","List.Sublist","List.Sublist.cons","List.Sublist.refl","List.cons","List.cons_sublist_cons","List.orderedInsert","List.orderedInsert_cons","Not","Or","Or.casesOn","True","True.intro","congrArg","eq_false","eq_true","id","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.«_aux_Mathlib_Data_List_Sort___macroRules__private_Mathlib_Data_List_Sort_0_List_term_≼__1_1»","namespace":"_private.Mathlib.Data.List.Sort.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":261,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.«_aux_Mathlib_Data_List_Sort___macroRules__private_Mathlib_Data_List_Sort_0_List_term_≼__1»","namespace":"_private.Mathlib.Data.List.Sort.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":261,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.«term_≼__1»","namespace":"_private.Mathlib.Data.List.Sort.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":61,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.List.«term_≼_»","namespace":"_private.Mathlib.Data.List.Sort.0.List","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":61,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGE_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGE_listMap","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.SortedGE","List.SortedLE","List.reverse","Preorder"],"value_dag_size":36,"value_refs":["Eq.symm","List","List.SortedGE","List.SortedLE","List.reverse","List.sortedLE_reverse","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGE_listMap._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGE_listMap","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGT_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGT_listMap","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.SortedGT","List.SortedLT","List.reverse","Preorder"],"value_dag_size":36,"value_refs":["Eq.symm","List","List.SortedGT","List.SortedLT","List.reverse","List.sortedLT_reverse","Preorder","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGT_listMap._simp_1_2","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedGT_listMap","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","List","List.map","List.reverse"],"value_dag_size":37,"value_refs":["Eq.symm","List","List.map","List.map_reverse","List.reverse"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedLE_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedLE_listMap","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LE.le","List","List.Pairwise","List.SortedLE","Preorder","Preorder.toLE"],"value_dag_size":39,"value_refs":["LE.le","List","List.Pairwise","List.SortedLE","List.sortedLE_iff_pairwise","Preorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedLT_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.OrderEmbedding.sortedLT_listMap","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List","List.Pairwise","List.SortedLT","Preorder","Preorder.toLT"],"value_dag_size":39,"value_refs":["LT.lt","List","List.Pairwise","List.SortedLT","List.sortedLT_iff_pairwise","Preorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.RelEmbedding.pairwise_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.RelEmbedding.pairwise_listMap","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.RelEmbedding.pairwise_swap_listMap._simp_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.RelEmbedding.pairwise_swap_listMap","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedGE_listMap._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedGE_listMap","reducibility":null,"statement_dag_size":69,"type_refs":["DistribLattice.toLattice","Iff","Lattice.toSemilatticeInf","LinearOrder","List","List.SortedGE","List.SortedLE","List.map","PartialOrder.toPreorder","Preorder","SemilatticeInf.toPartialOrder","StrictAnti","instDistribLatticeOfLinearOrder"],"value_dag_size":859,"value_refs":["And","And.casesOn","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lattice.toSemilatticeInf","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toPartialOrder","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLE","SemilatticeInf.toPartialOrder","StrictAnti","StrictAnti.le_iff_ge","True","True.intro","congrArg","eq_false","eq_true","id","instDistribLatticeOfLinearOrder","instTransLE","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedGT_listMap._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedGT_listMap","reducibility":null,"statement_dag_size":69,"type_refs":["DistribLattice.toLattice","Iff","Lattice.toSemilatticeInf","LinearOrder","List","List.SortedGT","List.SortedLT","List.map","PartialOrder.toPreorder","Preorder","SemilatticeInf.toPartialOrder","StrictAnti","instDistribLatticeOfLinearOrder"],"value_dag_size":859,"value_refs":["And","And.casesOn","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toPartialOrder","List","List.IsChain","List.IsChain.imp","List.IsChain.pairwise","List.Pairwise","List.Pairwise.isChain","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLT","SemilatticeInf.toPartialOrder","StrictAnti","StrictAnti.lt_iff_gt","True","True.intro","congrArg","eq_false","eq_true","id","instDistribLatticeOfLinearOrder","instTransLT","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedLE_listMap._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedLE_listMap","reducibility":null,"statement_dag_size":69,"type_refs":["DistribLattice.toLattice","Iff","Lattice.toSemilatticeInf","LinearOrder","List","List.SortedGE","List.SortedLE","List.map","PartialOrder.toPreorder","Preorder","SemilatticeInf.toPartialOrder","StrictAnti","instDistribLatticeOfLinearOrder"],"value_dag_size":1000,"value_refs":["And","And.casesOn","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GE.ge","Iff","LE.le","Lattice.toSemilatticeInf","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toPartialOrder","List","List.Pairwise","List.Pairwise.map","List.SortedGE","List.SortedLE","List.map","List.pairwise_map","List.sortedGE_iff_pairwise","List.sortedLE_iff_pairwise","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLE","SemilatticeInf.toPartialOrder","StrictAnti","StrictAnti.le_iff_ge","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","instDistribLatticeOfLinearOrder","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sort","name":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedLT_listMap._proof_1_1","namespace":"_private.Mathlib.Data.List.Sort.0.StrictAnti.sortedLT_listMap","reducibility":null,"statement_dag_size":69,"type_refs":["DistribLattice.toLattice","Iff","Lattice.toSemilatticeInf","LinearOrder","List","List.SortedGT","List.SortedLT","List.map","PartialOrder.toPreorder","Preorder","SemilatticeInf.toPartialOrder","StrictAnti","instDistribLatticeOfLinearOrder"],"value_dag_size":1000,"value_refs":["And","And.casesOn","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.mp","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","GT.gt","Iff","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","LinearOrder","LinearOrder.toPartialOrder","List","List.Pairwise","List.Pairwise.map","List.SortedGT","List.SortedLT","List.map","List.pairwise_map","List.sortedGT_iff_pairwise","List.sortedLT_iff_pairwise","Not","Or","Or.casesOn","PartialOrder.toPreorder","Preorder","Preorder.toLT","SemilatticeInf.toPartialOrder","StrictAnti","StrictAnti.lt_iff_gt","True","True.intro","congrArg","congrFun'","eq_false","eq_true","funext","id","instDistribLatticeOfLinearOrder","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.flatten_splitBy.match_1_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.flatten_splitBy","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.flatten_splitByLoop","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":53,"type_refs":["Bool","Eq","HAppend.hAppend","List","List.cons","List.flatten","List.instAppend","List.nil","List.reverse","List.splitBy.loop","instHAppendOfAppend"],"value_dag_size":830,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","HAppend.hAppend","List","List.append_assoc","List.append_nil","List.cons","List.filter.match_1","List.flatten","List.instAppend","List.nil","List.rec","List.reverse","List.reverse_cons","List.splitBy.loop","List.splitBy.loop.eq_1","True","Unit","_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append","congrArg","congrFun'","eq_self","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1.eq_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1.eq_2","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.getLast?.match_1","List.nil","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.getLast?.match_1","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1.splitter","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.getLast?.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_getLast_head_splitByLoop","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":191,"type_refs":["Bool","Bool.false","Eq","Exists","HAppend.hAppend","List","List.IsChain","List.cons","List.getLast","List.head","List.head?","List.instAppend","List.instMembership","List.nil","List.reverse","List.splitBy.loop","Membership.mem","Ne","Not","Option","Option.instMembership","instHAppendOfAppend"],"value_dag_size":2210,"value_refs":["And","And.intro","Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","HAppend.hAppend","Iff.mp","Iff.mpr","Iff.of_eq","List","List.IsChain","List.append_eq_nil_iff._simp_1","List.append_ne_nil_of_right_ne_nil","List.cons","List.cons_ne_nil","List.cons_ne_self._simp_1","List.filter.match_1","List.getLast","List.getLast_append_of_ne_nil","List.head","List.head?","List.head_append_of_ne_nil","List.instAppend","List.instMembership","List.isChain_cons","List.isChain_reverse","List.mem_cons._simp_1","List.nil","List.nil_eq._simp_1","List.rec","List.reverse","List.reverse_append","List.reverse_cons","List.reverse_eq_nil_iff._simp_1","List.reverse_reverse","List.splitBy.loop","List.splitBy.loop.eq_1","List.splitBy.loop.eq_2","Membership.mem","Ne","Nonempty","Not","Option","Option.instMembership","Option.mem_def._simp_1","Option.some","Option.some.injEq","Or","True","Unit","_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","and_false","congr","congrArg","congrFun'","exists_const._simp_1","exists_prop_congr","false_or","forall_congr","forall_eq'._simp_1","funext","id","implies_congr","instHAppendOfAppend","instInhabitedTrue","instNonemptyOfInhabited","nonempty_prop._simp_1","not_false_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitBy.match_1_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitBy","reducibility":"abbrev","statement_dag_size":77,"type_refs":["Bool","List","List.cons","List.instMembership","List.splitBy","Membership.mem"],"value_dag_size":279,"value_refs":["Bool","Eq","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.casesOn","List.cons","List.ctorIdx","List.instMembership","List.nil","List.splitBy","Membership.mem","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":86,"type_refs":["Bool","Bool.true","Eq","List","List.IsChain","List.head?","List.instMembership","List.nil","List.splitBy.loop","Membership.mem","Option","Option.instMembership"],"value_dag_size":1494,"value_refs":["And","And.intro","Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","False","False.casesOn","HAppend.hAppend","Iff.mp","Iff.mpr","List","List.IsChain","List.append","List.cons","List.filter.match_1","List.head?","List.instAppend","List.instMembership","List.isChain_cons","List.isChain_reverse","List.mem_append","List.mem_reverse","List.mem_singleton","List.nil","List.nil_append","List.not_mem_nil","List.rec","List.reverse","List.reverse_append","List.reverse_cons","List.reverse_nil","List.reverse_reverse","List.reverse_singleton","List.splitBy.loop","List.splitBy.loop.eq_2","Membership.mem","Option","Option.instMembership","Or","Or.casesOn","Unit","_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop._proof_1_4","_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop._proof_1_5","_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append","congrArg","congrFun'","funext","id","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop._proof_1_4","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop","reducibility":null,"statement_dag_size":48,"type_refs":["Bool","Bool.true","Eq","List","List.cons","List.head?","Membership.mem","Option","Option.instMembership"],"value_dag_size":297,"value_refs":["Bool","Bool.ctorIdx","Bool.false","Bool.not_eq_true","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.eq_congr'","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","List","List.cons","List.head?","List.head?_cons","Membership.mem","Not","Option","Option.instMembership","Option.mem_some","Option.some","True","congrArg","eq_of_heq","eq_true","id","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop._proof_1_5","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.isChain_of_mem_splitByLoop","reducibility":null,"statement_dag_size":113,"type_refs":["Bool","Bool.true","Eq","List","List.IsChain","List.head?","List.instMembership","List.nil","List.splitBy.loop","Membership.mem","Option","Option.instMembership"],"value_dag_size":582,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_or_forall","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_false_right","List","List.IsChain","List.IsChain.nil","List.head?","List.instMembership","List.mem_of_mem_head?","List.nil","List.not_mem_nil","List.splitBy.loop","Membership.mem","Not","Option","Option.instMembership","Or","True","True.intro","eq_false","eq_true","forall_congr","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.nil_notMem_splitBy.match_1_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.nil_notMem_splitBy","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.nil_notMem_splitByLoop","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":39,"type_refs":["Bool","List","List.instMembership","List.nil","List.splitBy.loop","Membership.mem","Not"],"value_dag_size":838,"value_refs":["And","Bool","Bool.false","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HAppend.hAppend","List","List.append_eq_nil_iff._simp_1","List.cons","List.cons_ne_self._simp_1","List.filter.match_1","List.instAppend","List.instMembership","List.mem_append","List.mem_cons._simp_1","List.nil","List.nil_eq._simp_1","List.not_mem_nil._simp_1","List.rec","List.reverse","List.reverse_cons","List.reverse_eq_nil_iff._simp_1","List.splitBy.loop","List.splitBy.loop.eq_1","Membership.mem","Not","Or","True","Unit","_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append","and_false","congr","congrArg","congrFun'","false_or","id","instHAppendOfAppend","not_false_eq_true","of_eq_true","or_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1.eq_1","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","List","List.cons","List.nil","List.splitBy.loop.match_1"],"value_dag_size":82,"value_refs":["Eq.refl","List","List.cons","List.nil","List.splitBy.loop.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1.eq_2","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","List","List.cons","List.nil","List.splitBy.loop.match_1"],"value_dag_size":73,"value_refs":["Eq.refl","List","List.cons","List.nil","List.splitBy.loop.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1.splitter","namespace":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy.loop.match_1","reducibility":"abbrev","statement_dag_size":65,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.splitBy.loop.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_append","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":127,"type_refs":["Bool","Bool.false","Bool.true","Eq","HAppend.hAppend","List","List.IsChain","List.cons","List.cons_ne_nil","List.getLast","List.head?","List.instAppend","List.nil","List.reverse","List.splitBy","List.splitBy.loop","Membership.mem","Option","Option.instMembership","instHAppendOfAppend"],"value_dag_size":1912,"value_refs":["And","Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAppend.hAppend","List","List.IsChain","List.append_assoc","List.casesOn","List.cons","List.cons_ne_nil","List.ctorIdx","List.filter.match_1","List.getLast","List.getLast_cons","List.head?","List.instAppend","List.isChain_append_cons_cons._simp_1","List.nil","List.nil_append","List.rec","List.reverse","List.reverse_cons","List.splitBy","List.splitBy.loop","List.splitBy.loop.eq_1","Membership.mem","Not","Option","Option.instMembership","Option.mem_def._simp_1","Option.some","Option.some.injEq","True","Unit","_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append","and_self","congr","congrArg","congrFun'","eq_false'","eq_self","eq_true","forall_congr","forall_eq'._simp_1","id","implies_congr","implies_congr_ctx","implies_true","instHAppendOfAppend","noConfusion_of_Nat","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_eq_append","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":52,"type_refs":["Bool","Eq","HAppend.hAppend","List","List.instAppend","List.nil","List.reverse","List.splitBy.loop","instHAppendOfAppend"],"value_dag_size":811,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.rec","Eq.refl","Eq.symm","Eq.trans","HAppend.hAppend","List","List.append_assoc","List.cons","List.filter.match_1","List.instAppend","List.nil","List.rec","List.reverse","List.reverse_cons","List.splitBy.loop","True","Unit","_private.Mathlib.Data.List.SplitBy.0.List.filter.match_1.splitter","congr","congrArg","congrFun'","eq_self","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitBy","name":"_private.Mathlib.Data.List.SplitBy.0.List.splitBy_append_of_isChain","namespace":"_private.Mathlib.Data.List.SplitBy.0.List","reducibility":null,"statement_dag_size":93,"type_refs":["Bool","Bool.false","Bool.true","Eq","HAppend.hAppend","List","List.IsChain","List.cons","List.getLast","List.head?","List.instAppend","List.nil","List.splitBy","Membership.mem","Ne","Option","Option.instMembership","instHAppendOfAppend"],"value_dag_size":512,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","HAppend.hAppend","List","List.IsChain","List.casesOn","List.cons","List.cons_append","List.getLast","List.head?","List.instAppend","List.nil","List.reverse","List.splitBy","List.splitBy.eq_2","List.splitBy.loop","Membership.mem","Ne","Option","Option.instMembership","_private.Mathlib.Data.List.SplitBy.0.List.splitByLoop_append","absurd","congrArg","eq_self","id","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.length_mem_splitLengths._proof_1_1","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.length_mem_splitLengths","reducibility":null,"statement_dag_size":146,"type_refs":["Eq.mp","GetElem.getElem","LE.le","LT.lt","List","List.instGetElemNatLtLength","List.length","List.length_splitLengths","List.length_splitLengths_getElem_le._proof_1","List.splitLengths","Nat","congrArg","instLENat","instLTNat"],"value_dag_size":465,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","GetElem.getElem","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElemNatLtLength","List.length","List.length_splitLengths","List.length_splitLengths_getElem_le._proof_1","List.splitLengths","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.map_splitLengths_length._simp_1_1","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.map_splitLengths_length","reducibility":null,"statement_dag_size":51,"type_refs":["DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeInf","LinearOrder","Min.min","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":55,"value_refs":["DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeInf","LinearOrder","Min.min","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toMin","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","min_eq_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_1.eq_1","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.splitLengths.match_1","Prod","Prod.mk"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.splitLengths.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_1.splitter","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_1","reducibility":"abbrev","statement_dag_size":32,"type_refs":["List","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["List.splitLengths.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3.eq_1","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","List","List.cons","List.nil","List.splitLengths.match_3","Nat"],"value_dag_size":48,"value_refs":["Eq.refl","List","List.cons","List.nil","List.splitLengths.match_3","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3.eq_2","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","List","List.cons","List.nil","List.splitLengths.match_3","Nat"],"value_dag_size":55,"value_refs":["Eq.refl","List","List.cons","List.nil","List.splitLengths.match_3","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.SplitLengths","name":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3.splitter","namespace":"_private.Mathlib.Data.List.SplitLengths.0.List.splitLengths.match_3","reducibility":"abbrev","statement_dag_size":40,"type_refs":["List","List.cons","List.nil","Nat"],"value_dag_size":1,"value_refs":["List.splitLengths.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_3","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","Membership.mem","instHAppendOfAppend"],"value_dag_size":73,"value_refs":["And","HAppend.hAppend","List","List.Pairwise","List.instAppend","List.instMembership","List.pairwise_append","Membership.mem","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_4","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_5","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_6","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_7","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":"abbrev","statement_dag_size":80,"type_refs":["List","List.Pairwise","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.instMembership","List.nil","Membership.mem","Unit"],"value_dag_size":299,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Pairwise","List.Pairwise.casesOn","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.instMembership","List.nil","Membership.mem","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'.match_1_12","namespace":"_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'","reducibility":"abbrev","statement_dag_size":171,"type_refs":["List","List.Pairwise","List.Pairwise.below","List.Pairwise.below.cons","List.Pairwise.below.nil","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.instMembership","List.nil","Membership.mem","Unit"],"value_dag_size":673,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Pairwise","List.Pairwise.below","List.Pairwise.below.casesOn","List.Pairwise.below.cons","List.Pairwise.below.nil","List.Pairwise.cons","List.Pairwise.nil","List.cons","List.instMembership","List.nil","Membership.mem","Unit","Unit.unit","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.length_of_sublistsLen.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.length_of_sublistsLen","reducibility":"abbrev","statement_dag_size":132,"type_refs":["HAdd.hAdd","List","List.cons","List.instMembership","List.sublistsLen","Membership.mem","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":382,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.casesOn","List.cons","List.ctorIdx","List.instMembership","List.nil","List.sublistsLen","Membership.mem","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.length_sublists'.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.length_sublists'","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.length_sublistsLen.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.length_sublistsLen","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":80,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.map_pure_sublist_sublists._simp_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.map_pure_sublist_sublists","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","List","List.Sublist","List.cons","True"],"value_dag_size":24,"value_refs":["List","List.Sublist","List.cons","List.sublist_cons_self","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'._simp_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'._simp_1_2","namespace":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'._simp_1_3","namespace":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublists'","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublistsLen.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.mem_sublistsLen","reducibility":"abbrev","statement_dag_size":68,"type_refs":["And","And.intro","Eq","List","List.Sublist","List.length","Nat"],"value_dag_size":84,"value_refs":["And","And.casesOn","And.intro","Eq","List","List.Sublist","List.length","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.nodup_sublistsLen._simp_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.nodup_sublistsLen","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.range_bind_sublistsLen_perm._simp_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.range_bind_sublistsLen_perm","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List","List.flatMap","List.map"],"value_dag_size":57,"value_refs":["Eq.symm","List","List.flatMap","List.map","List.map_flatMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.range_bind_sublistsLen_perm._simp_1_2","namespace":"_private.Mathlib.Data.List.Sublists.0.List.range_bind_sublistsLen_perm","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HAppend.hAppend","List","List.cons","List.instAppend","instHAppendOfAppend"],"value_dag_size":42,"value_refs":["Eq.symm","HAppend.hAppend","List","List.cons","List.cons_append","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_2","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_3","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","List","List.Perm","True"],"value_dag_size":17,"value_refs":["List","List.Perm","List.Perm.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_4","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_5","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_6","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'._simp_1_7","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists'","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists._simp_1_2","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists._simp_1_3","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists._simp_1_4","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists._simp_1_5","namespace":"_private.Mathlib.Data.List.Sublists.0.List.revzip_sublists","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublists'_map.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublists'_map","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1","reducibility":null,"statement_dag_size":106,"type_refs":["Eq","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":102,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1","reducibility":null,"statement_dag_size":109,"type_refs":["Eq","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1","reducibility":null,"statement_dag_size":121,"type_refs":["Eq","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":115,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sublistsLenAux.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux.match_1","reducibility":"abbrev","statement_dag_size":94,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["List.sublistsLenAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux_append.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLenAux_append","reducibility":"abbrev","statement_dag_size":129,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":169,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_length.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_length","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_of_length_lt.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_of_length_lt","reducibility":"abbrev","statement_dag_size":68,"type_refs":["And","And.intro","Eq","List","List.Sublist","List.length","Nat"],"value_dag_size":84,"value_refs":["And","And.casesOn","And.intro","Eq","List","List.Sublist","List.length","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_sublist_sublists'.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublistsLen_sublist_sublists'","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":80,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sublists","name":"_private.Mathlib.Data.List.Sublists.0.List.sublists_map.match_1_1","namespace":"_private.Mathlib.Data.List.Sublists.0.List.sublists_map","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym._simp_1_6","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.Nodup","List.cons","List.instMembership","Membership.mem","Not"],"value_dag_size":39,"value_refs":["And","List","List.Nodup","List.cons","List.instMembership","List.nodup_cons","Membership.mem","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym.match_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym","reducibility":"abbrev","statement_dag_size":81,"type_refs":["List","List.Nodup","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":122,"value_refs":["List","List.Nodup","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2._simp_1_4","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","List.Nodup","List.nil","True"],"value_dag_size":13,"value_refs":["List.Nodup","List.nil","List.nodup_nil","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2._simp_1_5","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2._simp_1_6","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2._simp_1_7","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2","reducibility":null,"statement_dag_size":43,"type_refs":["And","Eq","Or","Sym2","Sym2.mk"],"value_dag_size":48,"value_refs":["And","Eq","Or","Sym2","Sym2.eq_iff","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2._simp_1_8","namespace":"_private.Mathlib.Data.List.Sym.0.List.Nodup.sym2","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2._simp_1_4","namespace":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","List","List.Perm","List.cons"],"value_dag_size":32,"value_refs":["List","List.Perm","List.cons","List.perm_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2._simp_1_5","namespace":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":38,"value_refs":["Eq","Eq.symm","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2._simp_1_6","namespace":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List","List.cons","Multiset","Multiset.cons","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq.symm","List","List.cons","Multiset","Multiset.cons","Multiset.cons_coe","Multiset.ofList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2._simp_1_7","namespace":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","Multiset","Multiset.instAdd","Multiset.ofList","instHAdd","instHAppendOfAppend"],"value_dag_size":51,"value_refs":["Eq.symm","HAdd.hAdd","HAppend.hAppend","List","List.instAppend","Multiset","Multiset.coe_add","Multiset.instAdd","Multiset.ofList","instHAdd","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2._simp_1_8","namespace":"_private.Mathlib.Data.List.Sym.0.List.Perm.sym2","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HAdd.hAdd","Multiset","Multiset.cons","Multiset.instAdd","Multiset.instSingleton","Singleton.singleton","instHAdd"],"value_dag_size":42,"value_refs":["Eq.symm","HAdd.hAdd","Multiset","Multiset.cons","Multiset.instAdd","Multiset.instSingleton","Multiset.singleton_add","Singleton.singleton","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Sublist.sym._simp_1_6","namespace":"_private.Mathlib.Data.List.Sym.0.List.Sublist.sym","reducibility":null,"statement_dag_size":17,"type_refs":["Eq","List","List.Sublist","True"],"value_dag_size":17,"value_refs":["List","List.Sublist","List.Sublist.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.Sublist.sym.match_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.Sublist.sym","reducibility":"abbrev","statement_dag_size":130,"type_refs":["List","List.Sublist","List.Sublist.cons","List.Sublist.cons_cons","List.Sublist.slnil","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":561,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","List","List.Sublist","List.Sublist.casesOn","List.Sublist.cons","List.Sublist.cons_cons","List.Sublist.slnil","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","eq_of_heq","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.dedup_sym2._simp_1_4","namespace":"_private.Mathlib.Data.List.Sym.0.List.dedup_sym2","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","List","List.instMembership","List.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":55,"value_refs":["List","List.instMembership","List.mem_sym2_iff","List.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.length_sym.match_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.length_sym","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":80,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.map_mk_disjoint_sym2._simp_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.map_mk_disjoint_sym2","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.instMembership","List.sym2","Membership.mem","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","List","List.instMembership","List.mk_mem_sym2_iff","List.sym2","Membership.mem","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_of_mem_of_mem_sym.match_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_of_mem_of_mem_sym","reducibility":"abbrev","statement_dag_size":233,"type_refs":["HAdd.hAdd","List","List.cons","List.instMembership","List.nil","List.sym","Membership.mem","Nat","Nat.succ","OfNat.ofNat","Sym","Sym.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":387,"value_refs":["HAdd.hAdd","List","List.casesOn","List.cons","List.instMembership","List.nil","List.sym","Membership.mem","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Sym","Sym.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.cons","List.instMembership","Membership.mem","Or"],"value_dag_size":42,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_cons","Membership.mem","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff._simp_1_5","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff._simp_1_6","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff._simp_1_7","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.mem_sym2_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.instMembership","List.sym2","Membership.mem","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","List","List.instMembership","List.mk_mem_sym2_iff","List.sym2","Membership.mem","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.mk_mem_sym2._proof_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.mk_mem_sym2","reducibility":null,"statement_dag_size":140,"type_refs":["And","Eq","Exists","List","List.cons","List.instMembership","List.sym2","Membership.mem","Or","Prod","Prod.mk","Quot","Quot.mk","Sym2","Sym2.Rel","Sym2.mk"],"value_dag_size":1327,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","False","Iff","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_exists","Lean.Grind.not_or","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Lean.Grind.or_eq_of_eq_true_right","List","List.cons","List.instMembership","List.mem_cons","List.sym2","Membership.mem","Not","Or","Or.casesOn","Prod","Prod.fst","Prod.mk","Prod.mk.inj","Prod.snd","Prod.swap","Prod.swap_prod_mk","Quot","Quot.mk","Sym2","Sym2.Rel","Sym2.eq","Sym2.mk","Sym2.rel_iff'","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","false_or","forall_congr","id","implies_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.setOfPred_mem_sym2._simp_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.setOfPred_mem_sym2","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.instMembership","List.sym2","Membership.mem","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","List","List.instMembership","List.mk_mem_sym2_iff","List.sym2","Membership.mem","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1._arg_pusher","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1","reducibility":null,"statement_dag_size":164,"type_refs":["Eq","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":681,"value_refs":["Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","False","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Data.List.Sym.0.List.sym.match_1.eq_2","_private.Mathlib.Data.List.Sym.0.List.sym.match_1.splitter","congr","congrArg","congrFun","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","False","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":239,"value_refs":["Eq","Eq.refl","False","List","List.casesOn","List.cons","List.nil","List.sym.match_1","Nat","Nat.casesOn","Nat.rec","Nat.succ","Nat.zero","OfNat.ofNat","absurd","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1.eq_3","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":71,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sym.match_1","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym.match_1","reducibility":"abbrev","statement_dag_size":61,"type_refs":["Eq","False","List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Eq","False","False.elim","List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.ctorIdx","Nat.succ","OfNat.ofNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1.eq_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","List","List.cons","List.nil","List.sym2.match_1","Unit","Unit.unit"],"value_dag_size":38,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sym2.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1.eq_2","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","List","List.cons","List.nil","List.sym2.match_1","Unit"],"value_dag_size":45,"value_refs":["Eq.refl","List","List.cons","List.nil","List.sym2.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1.splitter","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym2.match_1","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.sym2.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym2_eq_sym_two._simp_1_4","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym2_eq_sym_two","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","List","List.map","List.nil"],"value_dag_size":42,"value_refs":["Eq","List","List.map","List.map_eq_nil_iff","List.nil","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.List.sym_map.match_1_1","namespace":"_private.Mathlib.Data.List.Sym.0.List.sym_map","reducibility":"abbrev","statement_dag_size":55,"type_refs":["List","List.cons","List.nil","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":80,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Sym","name":"_private.Mathlib.Data.List.Sym.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.List.Sym.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.exists_tfae._simp_1_2","namespace":"_private.Mathlib.Data.List.TFAE.0.List.exists_tfae","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":59,"value_refs":["List","List.forall_mem_map","List.instMembership","List.map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.forall_tfae._simp_1_2","namespace":"_private.Mathlib.Data.List.TFAE.0.List.forall_tfae","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":59,"value_refs":["List","List.forall_mem_map","List.instMembership","List.map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_cons_self._simp_1_1","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_cons_self","reducibility":null,"statement_dag_size":28,"type_refs":["And","Eq","Iff","List","List.TFAE","List.cons"],"value_dag_size":32,"value_refs":["And","Iff","List","List.TFAE","List.cons","List.tfae_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff._simp_1_3","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff._simp_1_4","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff._simp_1_5","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff","reducibility":null,"statement_dag_size":37,"type_refs":["Eq"],"value_dag_size":43,"value_refs":["Eq","forall_apply_eq_imp_iff₂","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff._simp_1_6","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_not_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Decidable","Eq","Iff","Not"],"value_dag_size":28,"value_refs":["Decidable","Decidable.not_iff_not","Iff","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle._simp_1_1","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle","reducibility":null,"statement_dag_size":28,"type_refs":["And","Eq","Iff","List","List.TFAE","List.cons"],"value_dag_size":32,"value_refs":["And","Iff","List","List.TFAE","List.cons","List.tfae_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle._simp_1_2","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq","Iff"],"value_dag_size":21,"value_refs":["And","Iff","iff_def","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TFAE","name":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle._simp_1_3","namespace":"_private.Mathlib.Data.List.TFAE.0.List.tfae_of_cycle","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","List","List.IsChain","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.IsChain","List.cons","List.isChain_cons_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_10","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":880,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_11","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":104,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","Not","Option","Option.some","instLTNat"],"value_dag_size":552,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_12","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":195,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1641,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_13","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":112,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","Not","Option","Option.some","instAddNat","instHAdd","instLTNat"],"value_dag_size":628,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.getElem?_drop","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_3","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_14","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":163,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1014,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.getElem?_drop","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_15","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":193,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1667,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_16","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":154,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1159,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.dropLast_nil","List.drop_length","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_17","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":154,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":2181,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.dropLast_nil","List.drop_length","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_18","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":135,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1119,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_19","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":141,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1545,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.getElem?_drop","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_18","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_20","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":174,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1180,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_21","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","GetElem?.getElem?","Iff","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","Option","Option.some","instLTNat"],"value_dag_size":9535,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.dropLast_nil","List.drop_length","List.getElem?_drop","List.getElem?_dropLast","List.getElem?_nil","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","List.nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_17","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_5","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","Option","Option.some","instLTNat"],"value_dag_size":491,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_5","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":155,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":1582,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_6","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":161,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":2003,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.getElem?_drop","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_3","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_5","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_7","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":69,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_8","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":159,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.drop","List.dropLast","List.instGetElem?NatLtLength","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":2238,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropLast","List.getElem?_drop","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_drop","List.length_dropLast","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_5","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_7","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_9","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":72,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":90,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_10","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_11","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":52,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_12","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":105,"value_refs":["Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","List","List.dropLast","List.length","List.length_dropLast","Nat","OfNat.ofNat","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_11","congrArg","eq_true","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_13","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":107,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":648,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","List.length_dropLast","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_10","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_14","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":125,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":569,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_15","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":147,"value_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_14","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_16","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":178,"value_refs":["Eq","Eq.rec","Eq.symm","GetElem?.getElem?","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_dropLast","List.take","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_15","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_17","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":111,"type_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":659,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.length","List.length_dropLast","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_4","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_18","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":131,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.length","List.length_dropLast","List.take","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_19","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":108,"type_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":132,"value_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_17","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_20","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":157,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1316,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.eq_nil_of_length_eq_zero","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.length_take","List.nil","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_21","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":167,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1572,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.eq_nil_of_length_eq_zero","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.length_take","List.nil","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_4","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_22","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":155,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":222,"value_refs":["Eq","Eq.rec","Eq.symm","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_dropLast","List.take","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_20","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_23","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":164,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":191,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_21","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_24","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":171,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1109,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_dropLast","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_23","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_25","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":190,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":984,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_dropLast","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_15","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_26","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","Iff","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":13270,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.lt_unsat_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.eq_nil_of_length_eq_zero","List.getElem?_dropLast","List.getElem?_nil","List.getElem?_take","List.getElem_dropLast","List.getElem_take","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.length_take","List.length_take_le'","List.nil","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.decLt","Nat.lt_of_lt_of_le","Nat.min_def","Nat.not_le_eq","Nat.pred_le","Nat.sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_10","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_13","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_14","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_15","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_16","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_17","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_19","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_23","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_24","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_3","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_4","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_5","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_7","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_8","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","Option","Option.some","instLTNat"],"value_dag_size":491,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":72,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_5","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":880,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropLast","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_dropLast","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_4","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_6","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","Option","Option.some","instLTNat"],"value_dag_size":144,"value_refs":["Eq","Eq.rec","Eq.symm","GetElem?.getElem?","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_dropLast","List.take","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_3","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_7","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":116,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"],"value_dag_size":141,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_5","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_8","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":94,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.length","List.length_take_le'","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_1","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_9","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast","reducibility":null,"statement_dag_size":67,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.dropLast","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":124,"value_refs":["Eq","Eq.rec","Eq.symm","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.dropLast","List.length","List.length_dropLast","List.take","Nat","Nat.lt_of_lt_of_le","Nat.pred_le","Nat.sub","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_take_eq_take_dropLast._proof_1_8","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.drop","List.dropSlice","List.instAppend","List.nil","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"],"value_dag_size":374,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_simp_rhs_suffix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropSlice","List.dropSlice.eq_1","List.drop_nil","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.take","List.take_zero","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","PLift","PLift.up","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.cons","List.drop","List.dropSlice","List.instAppend","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"],"value_dag_size":439,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.MatchCond","Lean.Grind.PreMatchCond","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.drop","List.dropSlice","List.dropSlice.eq_2","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.take","List.take_zero","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","PLift","PLift.up","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.drop","List.dropSlice","List.instAppend","List.nil","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"],"value_dag_size":491,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_erase0","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_rhs_exact","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_lhs_exact","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.dropSlice","List.dropSlice.eq_1","List.drop_nil","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.take","List.take_add","List.take_nil","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","PLift","PLift.up","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.dropSlice_eq","reducibility":null,"statement_dag_size":97,"type_refs":["Eq","HAdd.hAdd","HAppend.hAppend","List","List.cons","List.drop","List.dropSlice","List.instAppend","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"],"value_dag_size":780,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_ai","Lean.Grind.AC.diseq_simp_lhs_prefix","Lean.Grind.AC.diseq_simp_rhs_prefix","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_norm_ai","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_rhs_exact","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.append_assoc","List.cons","List.cons_append","List.drop","List.dropSlice","List.dropSlice.eq_3","List.drop_succ_cons","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.nil","List.take","List.take_add","List.take_succ_cons","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.succ","Nat.succ_eq_add_one","Not","OfNat.ofNat","PLift","PLift.up","congrArg","congrFun'","eagerReduce","forall_congr","id","instAddNat","instHAdd","instHAppendOfAppend","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HSub.hSub","List.dropSlice","List.length","List.nil","Min.min","Nat","OfNat.ofNat","instHSub","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":1328,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropSlice","List.dropSlice.eq_1","List.length","List.length_nil","List.nil","Min.min","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","Nat.sub_zero","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","eagerReduce","id","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","List.dropSlice","List.length","List.nil","Min.min","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":839,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropSlice","List.dropSlice.eq_1","List.length","List.length_nil","List.nil","Min.min","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HSub.hSub","List","List.cons","List.dropSlice","List.length","Min.min","Nat","OfNat.ofNat","instHSub","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":1402,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.MatchCond","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.PreMatchCond","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_false_left","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.ctorIdx","List.drop","List.dropSlice","List.dropSlice.eq_2","List.length","List.length_cons","List.length_drop","List.nil","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","Nat.sub_zero","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","List","List.cons","List.dropSlice","List.length","Min.min","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instMinNat","instOfNatNat","instSubNat"],"value_dag_size":15287,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.dropSlice","List.dropSlice.eq_3","List.length","List.length_cons","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.decLe","Nat.min_def","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice_lt._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.length_dropSlice_lt","reducibility":null,"statement_dag_size":43,"type_refs":["LT.lt","List","List.dropSlice","List.length","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":1793,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropSlice","List.length","List.length_dropSlice","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1.eq_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","List","List.cons","List.nil","List.reverseAux.match_1"],"value_dag_size":49,"value_refs":["Eq.refl","List","List.cons","List.nil","List.reverseAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1.eq_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","List","List.cons","List.nil","List.reverseAux.match_1"],"value_dag_size":57,"value_refs":["Eq.refl","List","List.cons","List.nil","List.reverseAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1.splitter","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.reverseAux.match_1","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":1,"value_refs":["List.reverseAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.span","reducibility":null,"statement_dag_size":55,"type_refs":["Bool","Eq","HAppend.hAppend","List","List.dropWhile","List.instAppend","List.reverse","List.span.loop","List.takeWhile","Prod","Prod.mk","instHAppendOfAppend"],"value_dag_size":70,"value_refs":["Bool","Eq","HAppend.hAppend","List","List.brecOn","List.dropWhile","List.instAppend","List.reverse","List.span.loop","List.takeWhile","Prod","Prod.mk","_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop._f","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop._f","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Bool","Eq","HAppend.hAppend","List","List.below","List.dropWhile","List.instAppend","List.reverse","List.span.loop","List.takeWhile","Prod","Prod.mk","instHAppendOfAppend"],"value_dag_size":651,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","HAppend.hAppend","List","List.append_assoc","List.append_nil","List.below","List.cons","List.dropWhile","List.filter.match_1","List.instAppend","List.nil","List.reverse","List.reverse_cons","List.span.loop","List.takeWhile","Prod","Prod.mk","True","Unit","_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop.match_1_1","congr","congrArg","congrFun'","eq_self","instHAppendOfAppend","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop","reducibility":"abbrev","statement_dag_size":41,"type_refs":["List","List.cons","List.nil"],"value_dag_size":54,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.drop","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail","reducibility":null,"statement_dag_size":58,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":74,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.drop","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":143,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail._proof_1_5","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_drop_eq_drop_tail","reducibility":null,"statement_dag_size":62,"type_refs":["Eq","GetElem?.getElem?","Iff","LT.lt","List","List.drop","List.instGetElem?NatLtLength","List.length","List.tail","Nat","Option","Option.some","instLTNat"],"value_dag_size":320,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GetElem?.getElem?","HAdd.hAdd","Iff","LT.lt","Lean.Grind.eq_congr","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.RArray.branch","Lean.RArray.leaf","List","List.drop","List.getElem?_drop","List.getElem?_tail","List.instGetElem?NatLtLength","List.length","List.tail","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","Option","Option.some","congrArg","eagerReduce","id","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":90,"value_refs":["Eq.substr","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_10","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":134,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_11","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":52,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.tail","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_12","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":125,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":569,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.tail","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_1","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_13","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":120,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":147,"value_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.tail","List.take","Nat","Nat.lt_of_lt_of_le","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_12","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_14","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":129,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HSub.hSub","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Not","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":142,"value_refs":["Eq","GetElem?.getElem?","HSub.hSub","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Nat.add_lt_of_lt_sub","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_13","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_15","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":45,"type_refs":["LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","Not","instLENat","instLTNat"],"value_dag_size":287,"value_refs":["Bool","Bool.true","Eq","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.tail","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_2","eagerReduce","eq_false","id","instAddNat","instHAdd","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_16","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":113,"type_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":678,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_tail","List.tail","List.take","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_17","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":110,"type_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":134,"value_refs":["HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_take_le'","List.tail","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_16","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_18","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":157,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1316,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.eq_nil_of_length_eq_zero","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_tail","List.length_take","List.nil","List.tail","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_2","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_19","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":176,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":1572,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.eq_nil_of_length_eq_zero","List.getElem?_nil","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_tail","List.length_take","List.nil","List.tail","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_20","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":173,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":200,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.tail","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_19","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_21","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","GetElem?.getElem?","HSub.hSub","Iff","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","OfNat.ofNat","Option","Option.some","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":7950,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","False.elim","GetElem.getElem","GetElem?.getElem?","GetElem?.toGetElem","HAdd.hAdd","HEq.trans","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.lt_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_false_of_lt_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_eq_true_of_lt_k","Lean.Grind.Order.le_lt_trans_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.eq_nil_of_length_eq_zero","List.getElem?_nil","List.getElem?_tail","List.getElem?_take","List.getElem_tail","List.getElem_tail._proof_1","List.getElem_take","List.instGetElem?NatLtLength","List.instGetElemNatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_tail","List.length_take","List.length_take_le'","List.nil","List.tail","List.take","Min.min","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.lt_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.add_lt_of_lt_sub","Nat.decLe","Nat.decLt","Nat.lt_of_lt_of_le","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Option.some.inj","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_1","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_10","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_12","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_13","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_14","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_16","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_17","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_2","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_20","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_3","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_4","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_5","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_6","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_8","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_9","congrArg","congrFun'","eagerReduce","eq_false","eq_of_heq","eq_true","forall_prop_domain_congr","getElem?_neg","getElem?_pos","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":143,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_4","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Option","Option.some","instLTNat"],"value_dag_size":491,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.tail","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_2","congrArg","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_5","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":133,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":874,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.instGetElem?NatLtLength","List.instLawfulGetElemNatLtLength","List.length","List.length_tail","List.tail","List.take","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_3","congrArg","congrFun'","eagerReduce","eq_false","eq_true","getElem?_neg","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_6","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":130,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":155,"value_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.instGetElem?NatLtLength","List.length","List.length_take_le'","List.tail","List.take","Nat","Nat.lt_of_lt_of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_5","instAddNat","instHAdd","instHMul","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_7","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","GetElem?.getElem?","HAdd.hAdd","LT.lt","List","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","OfNat.ofNat","Option","Option.some","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":92,"value_refs":["Eq","GetElem?.getElem?","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.instGetElem?NatLtLength","List.length","List.tail","List.take","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","Option","Option.some","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_4","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_8","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":94,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.length","List.length_take_le'","List.tail","List.take","Nat","Nat.lt_of_lt_of_le","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_1","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_9","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","List.tail","List.take","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":89,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.nestedProof","List","List.getElem_tail._proof_1","List.length","List.tail","List.take","Nat","Nat.add_lt_of_lt_sub","OfNat.ofNat","_private.Mathlib.Data.List.TakeDrop.0.List.tail_take_eq_take_tail._proof_1_8","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_eq_take.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_eq_take","reducibility":"abbrev","statement_dag_size":103,"type_refs":["HAdd.hAdd","LE.le","List","List.cons","List.length","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":264,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LE.le","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_left._simp_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_left","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","True","instAddNat","instHAdd","instLENat"],"value_dag_size":28,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.le_add_right","eq_true","instAddNat","instHAdd","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_length.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeD_length","reducibility":"abbrev","statement_dag_size":49,"type_refs":["List","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":61,"value_refs":["List","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_eq_take.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_eq_take","reducibility":"abbrev","statement_dag_size":94,"type_refs":["HAdd.hAdd","LE.le","List","List.cons","List.length","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":253,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LE.le","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_left._simp_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_left","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","True","instAddNat","instHAdd","instLENat"],"value_dag_size":28,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.le_add_right","eq_true","instAddNat","instHAdd","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_length.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_length","reducibility":"abbrev","statement_dag_size":40,"type_refs":["List","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":49,"value_refs":["List","Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_nil.match_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.takeI_nil","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_left_iff","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HSub.hSub","LE.le","Nat","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":40,"value_refs":["Eq","HSub.hSub","LE.le","Nat","Nat.sub_eq_zero_iff_le","OfNat.ofNat","instHSub","instLENat","instOfNatNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_left_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_left_iff","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Or"],"value_dag_size":17,"value_refs":["Or","Or.comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeDrop","name":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_self_iff._proof_1_1","namespace":"_private.Mathlib.Data.List.TakeDrop.0.List.take_eq_self_iff","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","LE.le","List","List.length","List.take","Nat","instLENat"],"value_dag_size":453,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","List.length_take","List.take","Min.min","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.min_def","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff._proof_1_3","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff","reducibility":null,"statement_dag_size":58,"type_refs":["Bool","Eq","False","HAdd.hAdd","LE.le","List","List.dropWhile","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":225,"value_refs":["Bool","Bool.true","Eq","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropWhile","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff._simp_1_1","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LT.lt","Nat","Nat.succ","OfNat.ofNat","True","instLTNat","instOfNatNat"],"value_dag_size":23,"value_refs":["LT.lt","Nat","Nat.succ","Nat.zero_lt_succ","OfNat.ofNat","eq_true","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff._simp_1_2","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.dropWhile_eq_self_iff","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.length_dropWhile_le._proof_1_2","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.length_dropWhile_le","reducibility":null,"statement_dag_size":54,"type_refs":["Bool","HAdd.hAdd","LE.le","List","List.dropWhile","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":293,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.dropWhile","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.TakeWhile","name":"_private.Mathlib.Data.List.TakeWhile.0.List.takeWhile_idem._simp_1_1","namespace":"_private.Mathlib.Data.List.TakeWhile.0.List.takeWhile_idem","reducibility":null,"statement_dag_size":10,"type_refs":["And","Eq"],"value_dag_size":12,"value_refs":["And","and_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ToFinsupp","name":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp._simp_1","namespace":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ToFinsupp","name":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp._simp_2","namespace":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ToFinsupp","name":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp._simp_3","namespace":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ToFinsupp","name":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp_append._proof_1_2","namespace":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp_append","reducibility":null,"statement_dag_size":41,"type_refs":["False","HAdd.hAdd","LT.lt","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","instAddNat","instHAdd"],"value_dag_size":149,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.ToFinsupp","name":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp_apply_fin._proof_1","namespace":"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp_apply_fin","reducibility":null,"statement_dag_size":30,"type_refs":["False","Fin","Fin.val","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":356,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","Fin","Fin.isLt","Fin.val","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_append._proof_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_append","reducibility":null,"statement_dag_size":76,"type_refs":["And","HAppend.hAppend","Iff","List","List.Pairwise","List.Triplewise","List.instAppend","List.instMembership","List.nil","Membership.mem","instHAppendOfAppend"],"value_dag_size":988,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HAppend.hAppend","Iff","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.var","Lean.Grind.AC.eq_expr_seq_seq","Lean.Grind.AC.imp_eq","Lean.Grind.AC.norm_ai","Lean.Grind.AC.refl","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","List","List.Pairwise","List.Pairwise.nil","List.Triplewise","List.Triplewise.nil","List.instAppend","List.instAssociativeHAppend","List.instLawfulIdentityHAppendNil","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Nat","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instHAppendOfAppend","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_append._proof_1_2","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_append","reducibility":null,"statement_dag_size":135,"type_refs":["And","HAppend.hAppend","Iff","List","List.Pairwise","List.Triplewise","List.cons","List.instAppend","List.instMembership","Membership.mem","instHAppendOfAppend"],"value_dag_size":3382,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAppend.hAppend","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_and_eq_true_left","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Lean.Grind.or_of_and_eq_false","List","List.Pairwise","List.Triplewise","List.cons","List.cons_append","List.instAppend","List.instMembership","List.mem_cons","List.pairwise_append","List.pairwise_cons","List.triplewise_cons","Membership.mem","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_self","eq_true","id","instHAppendOfAppend","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_cons._proof_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_cons","reducibility":null,"statement_dag_size":36,"type_refs":["And","Iff","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":1054,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.imp_false_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_right","List","List.Pairwise","List.Triplewise","List.cons","List.cons.noConfusion","List.ctorIdx","List.nil","List.triplewise_iff","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_false'","eq_of_heq","eq_true","false_or","forall_congr","forall_not_of_not_exists","heq_eq_eq","id","implies_congr","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":36,"type_refs":["False","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":595,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_10","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_11","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":55,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":76,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_10","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_12","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":73,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_6","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_13","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":374,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_7","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_14","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":50,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":450,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_7","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_15","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":74,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":154,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_8","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_16","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":72,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":150,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_9","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_17","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","List","List.length","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":134,"value_refs":["Eq","HAdd.hAdd","HSub.hSub","Iff.mp","LT.lt","Lean.Grind.nestedProof","List","List.cons","List.getElem_cons.match_1","List.length","Nat","Nat.succ","Nat.succ_lt_succ_iff","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_18","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":59,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":78,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_19","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":351,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_20","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":62,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":354,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_21","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":77,"value_refs":["Eq.mp","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":57,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_7","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_23","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":110,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":688,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_24","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":105,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":606,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_25","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":76,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_26","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":68,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":73,"value_refs":["HAdd.hAdd","HSub.hSub","LE.le","List","List.length","Nat","OfNat.ofNat","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_6","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_27","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":113,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":764,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_28","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":126,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":837,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_25","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_29","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":131,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":838,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_28","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_30","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":121,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":831,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_26","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_31","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":130,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":642,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_29","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_32","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":119,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":625,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_30","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_33","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":106,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":714,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_34","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":102,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":636,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_35","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":109,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":790,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_36","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":126,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":667,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_29","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_37","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":115,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","List","List.length","Nat","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"],"value_dag_size":650,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_30","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_38","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":189,"type_refs":["And","GetElem.getElem","HAdd.hAdd","LT.lt","List","List.cons","List.instGetElemNatLtLength","List.length","List.triplewise_iff_getElem._proof_2","List.triplewise_iff_getElem._proof_4","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":8596,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.substr","Eq.symm","Eq.trans","False","GetElem.getElem","HAdd.hAdd","HEq","HEq.refl","HEq.trans","HMul.hMul","HSub.hSub","Iff.mp","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.getElem_cons","List.getElem_cons.match_1","List.instGetElemNatLtLength","List.length","List.triplewise_iff_getElem._proof_2","List.triplewise_iff_getElem._proof_4","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.succ","Nat.succ_lt_succ_iff","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_15","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_16","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_17","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_23","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_24","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_25","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_26","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_28","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_29","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_30","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_31","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_32","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_33","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_34","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_36","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_37","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_6","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_7","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_8","_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_9","congr","congrArg","congrFun'","dite","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","forall_prop_domain_congr","id","implies_congr","instAddNat","instDecidableEqNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_39","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":156,"value_refs":["Bool","Bool.true","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.length","List.triplewise_iff_getElem._proof_2","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_40","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":60,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":141,"value_refs":["Bool","Bool.true","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.cons","List.length","List.triplewise_iff_getElem._proof_4","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_41","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Bool","Bool.true","Eq.refl","Eq.substr","Eq.trans","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","Nat.Simproc.add_le_add_le","Nat.decLe","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_42","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_43","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":35,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":326,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_44","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":45,"type_refs":["HAdd.hAdd","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":340,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.length","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_5","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":54,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":105,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.triplewise_iff_getElem._proof_2","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_6","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":53,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":90,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","List.triplewise_iff_getElem._proof_4","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_7","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["Eq.substr","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","List","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_8","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":63,"value_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","List.triplewise_iff_getElem._proof_2","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_9","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":55,"type_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":60,"value_refs":["HAdd.hAdd","LT.lt","List","List.cons","List.length","List.triplewise_iff_getElem._proof_4","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_3","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":35,"type_refs":["False","LT.lt","List","List.length","Nat","Not","instLTNat"],"value_dag_size":488,"value_refs":["Bool","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.symm","Eq.trans","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.instAdd","Int.instLEInt","Int.instNegInt","Int.instSub","Int.sub_nonneg_of_le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.tidy_sat","List","List.cons","List.length","List.nil","Nat","Nat.cast","Nat.le_of_not_lt","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","id","instDecidableEqBool","instHAdd","instHSub","instLTNat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._simp_1_2","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":null,"statement_dag_size":68,"type_refs":["Eq","GetElem.getElem","LT.lt","List","List.Pairwise","List.instGetElemNatLtLength","List.length","Nat","instLTNat"],"value_dag_size":72,"value_refs":["GetElem.getElem","LT.lt","List","List.Pairwise","List.instGetElemNatLtLength","List.length","List.pairwise_iff_getElem","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem.match_1_3","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem","reducibility":"abbrev","statement_dag_size":311,"type_refs":["And","And.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","List.triplewise_iff_getElem._proof_2","List.triplewise_iff_getElem._proof_4","Nat","instLTNat"],"value_dag_size":349,"value_refs":["And","And.casesOn","And.intro","GetElem.getElem","LT.lt","List","List.instGetElemNatLtLength","List.length","List.triplewise_iff_getElem._proof_2","List.triplewise_iff_getElem._proof_4","Nat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_map._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_map","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_map._simp_1_2","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_map","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_pair._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_pair","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse","reducibility":null,"statement_dag_size":76,"type_refs":["And","Eq","HAppend.hAppend","List","List.Pairwise","List.Triplewise","List.instAppend","List.instMembership","Membership.mem","instHAppendOfAppend"],"value_dag_size":81,"value_refs":["And","HAppend.hAppend","List","List.Pairwise","List.Triplewise","List.instAppend","List.instMembership","List.triplewise_append","Membership.mem","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse._simp_1_2","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","List","List.Pairwise","List.reverse"],"value_dag_size":34,"value_refs":["List","List.Pairwise","List.pairwise_reverse","List.reverse","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse._simp_1_3","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse._simp_1_4","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_reverse","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_singleton._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_singleton","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Triplewise","name":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_triple._simp_1_1","namespace":"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_triple","reducibility":null,"statement_dag_size":37,"type_refs":["And","Eq","List","List.Pairwise","List.Triplewise","List.cons"],"value_dag_size":42,"value_refs":["And","List","List.Pairwise","List.Triplewise","List.cons","List.triplewise_cons","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.forall_zipWith._simp_1_3","namespace":"_private.Mathlib.Data.List.Zip.0.List.forall_zipWith","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Nat","Nat.succ"],"value_dag_size":21,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.forall_zipWith.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.forall_zipWith","reducibility":"abbrev","statement_dag_size":98,"type_refs":["Eq","List","List.cons","List.length","List.nil","Nat"],"value_dag_size":369,"value_refs":["Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","List","List.casesOn","List.cons","List.length","List.nil","Nat","Nat.add","Nat.ctorIdx","Nat.succ","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.rightInverse_unzip_zip._proof_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.rightInverse_unzip_zip","reducibility":null,"statement_dag_size":33,"type_refs":["Function.RightInverse","Function.uncurry","List","List.unzip","List.zip","Prod"],"value_dag_size":279,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Function.LeftInverse","Function.LeftInverse.eq_1","Function.RightInverse","Function.RightInverse.eq_1","Function.uncurry","Function.uncurry_apply_pair","Lean.Grind.of_forall_eq_false","List","List.unzip","List.zip","List.zip_unzip","Not","Prod","Prod.fst","Prod.mk","Prod.snd","True","True.intro","congrArg","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_left.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_left","reducibility":"abbrev","statement_dag_size":64,"type_refs":["List","List.cons","List.nil"],"value_dag_size":95,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_mid.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_mid","reducibility":"abbrev","statement_dag_size":64,"type_refs":["List","List.cons","List.nil"],"value_dag_size":95,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_right.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zipWith3_same_right","reducibility":"abbrev","statement_dag_size":64,"type_refs":["List","List.cons","List.nil"],"value_dag_size":95,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zipWith_zipWith_left.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zipWith_zipWith_left","reducibility":"abbrev","statement_dag_size":109,"type_refs":["List","List.cons","List.nil"],"value_dag_size":167,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zipWith_zipWith_right.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zipWith_zipWith_right","reducibility":"abbrev","statement_dag_size":109,"type_refs":["List","List.cons","List.nil"],"value_dag_size":167,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.List.Zip","name":"_private.Mathlib.Data.List.Zip.0.List.zip_swap.match_1_1","namespace":"_private.Mathlib.Data.List.Zip.0.List.zip_swap","reducibility":"abbrev","statement_dag_size":60,"type_refs":["List","List.cons","List.nil"],"value_dag_size":93,"value_refs":["List","List.casesOn","List.cons","List.nil"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.AlgEquiv.mopMatrix._simp_1","namespace":"_private.Mathlib.Data.Matrix.Basic.0.AlgEquiv.mopMatrix","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.evalAddMonoidHom_comp_diagAddMonoidHom._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.evalAddMonoidHom_comp_diagAddMonoidHom","reducibility":null,"statement_dag_size":65,"type_refs":["AddMonoidHom","AddMonoidHom.instFunLike","AddZero","DFunLike.coe","Eq"],"value_dag_size":71,"value_refs":["AddMonoidHom","AddMonoidHom.ext_iff","AddMonoidHom.instFunLike","AddZero","DFunLike.coe","Eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.instFinite._proof_1","namespace":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.instFinite","reducibility":null,"statement_dag_size":26,"type_refs":["Finite","Matrix"],"value_dag_size":35,"value_refs":["Finite","Pi.finite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.proj_comp_diagLinearMap._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.proj_comp_diagLinearMap","reducibility":null,"statement_dag_size":141,"type_refs":["AddCommMonoid","DFunLike.coe","Eq","LinearMap","LinearMap.instFunLike","Module","RingHom","Semiring","Semiring.toNonAssocSemiring"],"value_dag_size":154,"value_refs":["AddCommMonoid","DFunLike.coe","Eq","LinearMap","LinearMap.ext_iff","LinearMap.instFunLike","Module","RingHom","Semiring","Semiring.toNonAssocSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.scalar_comm_iff._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.scalar_comm_iff","reducibility":null,"statement_dag_size":97,"type_refs":["DecidableEq","Distrib.toMul","Eq","Fintype","HMul.hMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.smul","MulZeroClass.toZero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","instHSMul","instSMulOfMul"],"value_dag_size":107,"value_refs":["DecidableEq","Distrib.toMul","Eq.symm","Fintype","HMul.hMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.smul","Matrix.smul_eq_diagonal_mul","MulZeroClass.toZero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","instHSMul","instSMulOfMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basic","name":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.scalar_comm_iff._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Basic.0.Matrix.scalar_comm_iff","reducibility":null,"statement_dag_size":116,"type_refs":["DecidableEq","Distrib.toMul","Eq","Fintype","HMul.hMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.smul","MulOpposite","MulOpposite.instZero","MulOpposite.op","MulZeroClass.toOppositeSMulWithZero","MulZeroClass.toZero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","SMulWithZero.toSMulZeroClass","SMulZeroClass.toSMul","instHSMul"],"value_dag_size":126,"value_refs":["DecidableEq","Distrib.toMul","Eq.symm","Fintype","HMul.hMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.instHMulOfFintypeOfMulOfAddCommMonoid","Matrix.op_smul_eq_mul_diagonal","Matrix.smul","MulOpposite","MulOpposite.instZero","MulOpposite.op","MulZeroClass.toOppositeSMulWithZero","MulZeroClass.toZero","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","NonUnitalNonAssocSemiring.toMulZeroClass","SMulWithZero.toSMulZeroClass","SMulZeroClass.toSMul","instHSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HMul.hMul","Membership.mem","Semigroup","Semigroup.toMul","Set","Set.center","Set.instMembership","instHMul"],"value_dag_size":53,"value_refs":["Eq","HMul.hMul","Membership.mem","Semigroup","Semigroup.mem_center_iff","Semigroup.toMul","Set","Set.center","Set.instMembership","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image.match_1_3","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image","reducibility":"abbrev","statement_dag_size":361,"type_refs":["And","And.intro","DFunLike.coe","DecidableEq","Eq","Exists","Exists.intro","Fintype","HMul.hMul","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","NonUnitalSemiring.toSemigroupWithZero","RingHom","RingHom.instFunLike","Semigroup.toMul","SemigroupWithZero.toSemigroup","Semiring","Semiring.toNonAssocSemiring","Semiring.toNonUnitalSemiring","instHMul"],"value_dag_size":490,"value_refs":["And","And.casesOn","And.intro","DFunLike.coe","DecidableEq","Eq","Exists","Exists.casesOn","Exists.intro","Fintype","HMul.hMul","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","NonUnitalSemiring.toSemigroupWithZero","RingHom","RingHom.instFunLike","Semigroup.toMul","SemigroupWithZero.toSemigroup","Semiring","Semiring.toNonAssocSemiring","Semiring.toNonUnitalSemiring","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image.match_1_5","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.center_eq_scalar_image","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nonempty","Nonempty.intro"],"value_dag_size":29,"value_refs":["Nonempty","Nonempty.casesOn","Nonempty.intro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.diag_single_of_ne.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.diag_single_of_ne","reducibility":"abbrev","statement_dag_size":54,"type_refs":["And","And.intro","Eq"],"value_dag_size":69,"value_refs":["And","And.casesOn","And.intro","Eq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.diagonal_single._proof_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.diagonal_single","reducibility":null,"statement_dag_size":74,"type_refs":["And","DecidableEq","Eq","OfNat.ofNat","Pi.single","Zero","Zero.toOfNat0","instDecidableAnd","ite"],"value_dag_size":473,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_congr'","Lean.Grind.nestedDecidable","Lean.Grind.or_of_and_eq_false","Not","OfNat.ofNat","Or","Or.casesOn","Pi.single","Pi.single_apply","True","True.intro","Zero","Zero.toOfNat0","eq_false","eq_true","id","instDecidableAnd","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.mem_range_scalar_iff_commute_single'.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.mem_range_scalar_iff_commute_single'","reducibility":"abbrev","statement_dag_size":209,"type_refs":["DFunLike.coe","DecidableEq","Eq","Exists.intro","Fintype","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","Membership.mem","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.range"],"value_dag_size":261,"value_refs":["DFunLike.coe","DecidableEq","Eq","Exists.casesOn","Exists.intro","Fintype","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","Membership.mem","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.mem_range_scalar_iff_commute_single.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.mem_range_scalar_iff_commute_single","reducibility":"abbrev","statement_dag_size":209,"type_refs":["DFunLike.coe","DecidableEq","Eq","Exists.intro","Fintype","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","Membership.mem","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.range"],"value_dag_size":261,"value_refs":["DFunLike.coe","DecidableEq","Eq","Exists.casesOn","Exists.intro","Fintype","Matrix","Matrix.nonAssocSemiring","Matrix.scalar","Membership.mem","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring","Set","Set.instMembership","Set.range"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_apply_of_ne._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_apply_of_ne","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_apply_of_ne._simp_1_3","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_apply_of_ne","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_eq_single_vecMulVec_single._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_eq_single_vecMulVec_single","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_mem_matrix._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_mem_matrix","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Matrix","Membership.mem","Set","Set.instMembership","Set.matrix"],"value_dag_size":60,"value_refs":["Matrix","Membership.mem","Set","Set.instMembership","Set.matrix","Set.mem_matrix","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Basis","name":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.sum_sum_single._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Basis.0.Matrix.sum_sum_single","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":56,"value_refs":["And","Eq","Eq.symm","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_mul._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_mul","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Finset","Finset.sigma","Finset.univ","Fintype","Sigma","Sigma.instFintype"],"value_dag_size":55,"value_refs":["Eq.symm","Finset","Finset.sigma","Finset.univ","Finset.univ_sigma_univ","Fintype","Sigma","Sigma.instFintype"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_submatrix_eq_blockDiagonal.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_submatrix_eq_blockDiagonal","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":42,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_2","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Sigma.fst","Sigma.mk"],"value_dag_size":75,"value_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm","Sigma.fst","Sigma.mk","congr_arg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_3","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Sigma.fst","Sigma.mk"],"value_dag_size":60,"value_refs":["Eq","Eq.symm","Sigma.fst","Sigma.mk","congr_arg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_4","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":125,"type_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm","Matrix","Sigma.fst","Sigma.mk","cast","congr_arg"],"value_dag_size":399,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.mpr_prop","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","HEq","HEq.refl","HEq.symm","Lean.Grind.nestedProof","Matrix","Not","Sigma.fst","Sigma.mk","True","True.intro","_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_2","_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_3","cast","cast_heq","congr_arg","eq_false","eq_of_heq","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_5","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","Eq.mpr_prop","Eq.refl","Eq.symm","Matrix","Not","OfNat.ofNat","Sigma.fst","Sigma.mk","Zero","Zero.toOfNat0","cast","congr_arg"],"value_dag_size":153,"value_refs":["Eq","Eq.mp","Eq.mpr_prop","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Matrix","Not","OfNat.ofNat","Sigma.fst","Sigma.mk","True","True.intro","Zero","Zero.toOfNat0","cast","congr_arg","eq_false","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_6","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":105,"type_refs":["Eq","Eq.symm","Matrix","Not","OfNat.ofNat","Sigma.fst","Sigma.mk","Zero","Zero.toOfNat0","cast","congr_arg"],"value_dag_size":141,"value_refs":["Eq","Eq.mp","Eq.symm","Eq.trans","False","False.elim","Matrix","Not","OfNat.ofNat","Sigma.fst","Sigma.mk","True","True.intro","Zero","Zero.toOfNat0","cast","congr_arg","eq_false","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose._proof_1_7","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal'_transpose","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Not","OfNat.ofNat","True","Zero","Zero.toOfNat0","congrArg","eq_self"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_diagonal._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_diagonal","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_diagonal._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_diagonal","reducibility":null,"statement_dag_size":45,"type_refs":["And","Decidable","Eq","instDecidableAnd","ite"],"value_dag_size":54,"value_refs":["And","Decidable","Eq.symm","instDecidableAnd","ite","ite_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_mul._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_mul","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","Finset","Finset.instSProd","Finset.univ","Fintype","Prod","SProd.sprod","instFintypeProd"],"value_dag_size":57,"value_refs":["Eq.symm","Finset","Finset.instSProd","Finset.univ","Finset.univ_product_univ","Fintype","Prod","SProd.sprod","instFintypeProd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_transpose._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_transpose","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Block","name":"_private.Mathlib.Data.Matrix.Block.0.Matrix.ext_iff_blocks.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Block.0.Matrix.ext_iff_blocks","reducibility":"abbrev","statement_dag_size":303,"type_refs":["And","And.intro","Eq","Matrix","Matrix.toBlocks₁₁","Matrix.toBlocks₁₂","Matrix.toBlocks₂₁","Matrix.toBlocks₂₂","Sum"],"value_dag_size":535,"value_refs":["And","And.casesOn","And.intro","Eq","Matrix","Matrix.toBlocks₁₁","Matrix.toBlocks₁₂","Matrix.toBlocks₂₁","Matrix.toBlocks₂₂","Sum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.ColumnRowPartitioned","name":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromCols_inj._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromCols_inj","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Matrix"],"value_dag_size":53,"value_refs":["Eq","Eq.symm","Matrix","Matrix.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.ColumnRowPartitioned","name":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromCols_mulVec._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromCols_mulVec","reducibility":null,"statement_dag_size":121,"type_refs":["Distrib.toAdd","Eq","Fintype","HAdd.hAdd","Matrix","Matrix.fromCols","Matrix.mulVec","NonAssocSemiring.toNonUnitalNonAssocSemiring","Pi.instAdd","Semiring","Semiring.toNonAssocSemiring","Sum","Sum.elim","instDistribOfSemiring","instFintypeSum","instHAdd"],"value_dag_size":134,"value_refs":["Distrib.toAdd","Eq.symm","Fintype","HAdd.hAdd","Matrix","Matrix.fromCols","Matrix.fromCols_mulVec_sumElim","Matrix.mulVec","NonAssocSemiring.toNonUnitalNonAssocSemiring","Pi.instAdd","Semiring","Semiring.toNonAssocSemiring","Sum","Sum.elim","instDistribOfSemiring","instFintypeSum","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.ColumnRowPartitioned","name":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromRows_inj._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.fromRows_inj","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Matrix"],"value_dag_size":53,"value_refs":["Eq","Eq.symm","Matrix","Matrix.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.ColumnRowPartitioned","name":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.vecMul_fromRows._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.ColumnRowPartitioned.0.Matrix.vecMul_fromRows","reducibility":null,"statement_dag_size":121,"type_refs":["Distrib.toAdd","Eq","Fintype","HAdd.hAdd","Matrix","Matrix.fromRows","Matrix.vecMul","NonAssocSemiring.toNonUnitalNonAssocSemiring","Pi.instAdd","Semiring","Semiring.toNonAssocSemiring","Sum","Sum.elim","instDistribOfSemiring","instFintypeSum","instHAdd"],"value_dag_size":134,"value_refs":["Distrib.toAdd","Eq.symm","Fintype","HAdd.hAdd","Matrix","Matrix.fromRows","Matrix.sumElim_vecMul_fromRows","Matrix.vecMul","NonAssocSemiring.toNonUnitalNonAssocSemiring","Pi.instAdd","Semiring","Semiring.toNonAssocSemiring","Sum","Sum.elim","instDistribOfSemiring","instFintypeSum","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.DMatrix","name":"_private.Mathlib.Data.Matrix.DMatrix.0.DMatrix.instSubsingleton._proof_1","namespace":"_private.Mathlib.Data.Matrix.DMatrix.0.DMatrix.instSubsingleton","reducibility":null,"statement_dag_size":25,"type_refs":["DMatrix","Subsingleton"],"value_dag_size":34,"value_refs":["Pi.instSubsingleton","Subsingleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Diagonal","name":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.diagonal_mem_matrix_iff._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.diagonal_mem_matrix_iff","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","Matrix","Membership.mem","Set","Set.instMembership","Set.matrix"],"value_dag_size":60,"value_refs":["Matrix","Membership.mem","Set","Set.instMembership","Set.matrix","Set.mem_matrix","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Diagonal","name":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.one_eq_pi_single._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.one_eq_pi_single","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Diagonal","name":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.row_diagonal._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Diagonal.0.Matrix.row_diagonal","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.commute_diagonal._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.commute_diagonal","reducibility":null,"statement_dag_size":37,"type_refs":["Commute","Eq","HMul.hMul","Mul","instHMul"],"value_dag_size":41,"value_refs":["Commute","Eq","HMul.hMul","Mul","commute_iff_eq","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.isLeftRegular_iff_mulVec_injective._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.isLeftRegular_iff_mulVec_injective","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Function.Injective","Subsingleton","True"],"value_dag_size":25,"value_refs":["Function.Injective","Function.injective_of_subsingleton","Subsingleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.isRightRegular_iff_vecMul_injective._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.isRightRegular_iff_vecMul_injective","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Function.Injective","Subsingleton","True"],"value_dag_size":25,"value_refs":["Function.Injective","Function.injective_of_subsingleton","Subsingleton","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.op_smul_one_eq_diagonal._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.op_smul_one_eq_diagonal","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","Eq","Matrix","Matrix.diagonal","Matrix.one","OfNat.ofNat","One","One.toOfNat1","Zero"],"value_dag_size":61,"value_refs":["DecidableEq","Eq.symm","Matrix","Matrix.diagonal","Matrix.diagonal_one","Matrix.one","OfNat.ofNat","One","One.toOfNat1","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.op_smul_one_eq_diagonal._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.op_smul_one_eq_diagonal","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","Eq","Function.hasSMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.smul","SMulZeroClass","SMulZeroClass.toSMul","Zero","instHSMul"],"value_dag_size":88,"value_refs":["DecidableEq","Eq.symm","Function.hasSMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.diagonal_smul","Matrix.smul","SMulZeroClass","SMulZeroClass.toSMul","Zero","instHSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.pow_col_eq_zero_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.pow_col_eq_zero_of_le","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":678,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.pow_row_eq_zero_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.pow_row_eq_zero_of_le","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":627,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.smul_one_eq_diagonal._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.smul_one_eq_diagonal","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","Eq","Matrix","Matrix.diagonal","Matrix.one","OfNat.ofNat","One","One.toOfNat1","Zero"],"value_dag_size":61,"value_refs":["DecidableEq","Eq.symm","Matrix","Matrix.diagonal","Matrix.diagonal_one","Matrix.one","OfNat.ofNat","One","One.toOfNat1","Zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.smul_one_eq_diagonal._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.smul_one_eq_diagonal","reducibility":null,"statement_dag_size":78,"type_refs":["DecidableEq","Eq","Function.hasSMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.smul","SMulZeroClass","SMulZeroClass.toSMul","Zero","instHSMul"],"value_dag_size":88,"value_refs":["DecidableEq","Eq.symm","Function.hasSMul","HSMul.hSMul","Matrix","Matrix.diagonal","Matrix.diagonal_smul","Matrix.smul","SMulZeroClass","SMulZeroClass.toSMul","Zero","instHSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Matrix"],"value_dag_size":53,"value_refs":["Eq","Eq.symm","Matrix","Matrix.ext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","NoZeroDivisors","OfNat.ofNat","Or","Zero.toOfNat0","instHMul"],"value_dag_size":66,"value_refs":["Eq","HMul.hMul","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","NoZeroDivisors","OfNat.ofNat","Or","Zero.toOfNat0","instHMul","mul_eq_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_3","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_4","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Or"],"value_dag_size":25,"value_refs":["Or","forall_or_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_5","namespace":"_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Or"],"value_dag_size":25,"value_refs":["Or","forall_or_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Mul","name":"_private.Mathlib.Data.Matrix.Mul.0.comp_equiv_dotProduct_comp_equiv._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.Mul.0.comp_equiv_dotProduct_comp_equiv","reducibility":null,"statement_dag_size":113,"type_refs":["DFunLike.coe","Distrib.toMul","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fintype","Function.comp","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","dotProduct"],"value_dag_size":124,"value_refs":["DFunLike.coe","Distrib.toMul","Eq.symm","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","Fintype","Function.comp","NonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toAddCommMonoid","NonUnitalNonAssocSemiring.toDistrib","dotProduct","dotProduct_comp_equiv_symm"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective","reducibility":null,"statement_dag_size":50,"type_refs":["DFunLike.coe","Eq","Option","PEquiv","PEquiv.instFunLikeOption"],"value_dag_size":54,"value_refs":["DFunLike.coe","Eq","Option","PEquiv","PEquiv.ext_iff","PEquiv.instFunLikeOption","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective._simp_1_3","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_injective","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_mul_apply._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_mul_apply","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_toPEquiv_apply._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.toMatrix_toPEquiv_apply","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.transpose_toMatrix_toPEquiv_apply._simp_1_1","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.transpose_toMatrix_toPEquiv_apply","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.PEquiv","name":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.transpose_toMatrix_toPEquiv_apply._simp_1_2","namespace":"_private.Mathlib.Data.Matrix.PEquiv.0.PEquiv.transpose_toMatrix_toPEquiv_apply","reducibility":null,"statement_dag_size":70,"type_refs":["DFunLike.coe","Eq","Equiv","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike"],"value_dag_size":75,"value_refs":["DFunLike.coe","Eq","Equiv","Equiv.eq_symm_apply","Equiv.instEquivLike","Equiv.symm","EquivLike.toFunLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1.eq_1","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1","reducibility":null,"statement_dag_size":91,"type_refs":["Eq","Fin","HAdd.hAdd","Matrix","Matrix.Forall.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq.refl","Fin","HAdd.hAdd","Matrix","Matrix.Forall.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1.eq_2","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Fin","HAdd.hAdd","Matrix","Matrix.Forall.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":92,"value_refs":["Eq.refl","Fin","HAdd.hAdd","Matrix","Matrix.Forall.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1.splitter","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.Forall.match_1","reducibility":"abbrev","statement_dag_size":79,"type_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["Matrix.Forall.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.exists_iff._simp_1_6","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.exists_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Fin","FinVec.Exists","Nat"],"value_dag_size":33,"value_refs":["Exists","Fin","FinVec.Exists","FinVec.exists_iff","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.exists_iff.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.exists_iff","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":113,"value_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.forall_iff._simp_1_6","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.forall_iff","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Fin","FinVec.Forall","Nat"],"value_dag_size":30,"value_refs":["Fin","FinVec.Forall","FinVec.forall_iff","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.forall_iff.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.forall_iff","reducibility":"abbrev","statement_dag_size":78,"type_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":113,"value_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1.eq_1","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Fin","HAdd.hAdd","Matrix","Matrix.transposeᵣ.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":83,"value_refs":["Eq.refl","Fin","HAdd.hAdd","Matrix","Matrix.transposeᵣ.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1.eq_2","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","Fin","HAdd.hAdd","Matrix","Matrix.transposeᵣ.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":86,"value_refs":["Eq.refl","Fin","HAdd.hAdd","Matrix","Matrix.transposeᵣ.match_1","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1.splitter","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":1,"value_refs":["Matrix.transposeᵣ.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Matrix.Reflection","name":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ_eq.match_1_1","namespace":"_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ_eq","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":104,"value_refs":["Fin","HAdd.hAdd","Matrix","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.add_left_inj._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.add_left_inj","reducibility":null,"statement_dag_size":36,"type_refs":["DecidableEq","Eq","Multiset","Multiset.count","Nat"],"value_dag_size":41,"value_refs":["DecidableEq","Eq","Multiset","Multiset.count","Multiset.ext","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.add_right_inj._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.add_right_inj","reducibility":null,"statement_dag_size":36,"type_refs":["DecidableEq","Eq","Multiset","Multiset.count","Nat"],"value_dag_size":41,"value_refs":["DecidableEq","Eq","Multiset","Multiset.count","Multiset.ext","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.le_iff_exists_add.match_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.le_iff_exists_add","reducibility":"abbrev","statement_dag_size":95,"type_refs":["Exists","Exists.intro","HAppend.hAppend","List","List.Perm","List.instAppend","instHAppendOfAppend"],"value_dag_size":121,"value_refs":["Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.Perm","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.le_iff_exists_add.match_1_3","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.le_iff_exists_add","reducibility":"abbrev","statement_dag_size":95,"type_refs":["Eq","Exists","Exists.intro","HAdd.hAdd","Multiset","Multiset.instAdd","instHAdd"],"value_dag_size":121,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","Multiset","Multiset.instAdd","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.mem_sub_of_nodup.match_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.mem_sub_of_nodup","reducibility":"abbrev","statement_dag_size":83,"type_refs":["And","And.intro","Membership.mem","Multiset","Multiset.instMembership","Not"],"value_dag_size":98,"value_refs":["And","And.casesOn","And.intro","Membership.mem","Multiset","Multiset.instMembership","Not"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.rel_add_left._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.rel_add_left","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons","Multiset.rel_cons_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.rel_add_right._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.rel_add_right","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Multiset","Multiset.Rel","flip"],"value_dag_size":46,"value_refs":["Multiset","Multiset.Rel","Multiset.rel_flip","flip","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.AddSub","name":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.sub_le_iff_le_add._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.AddSub.0.Multiset.sub_le_iff_le_add","reducibility":null,"statement_dag_size":46,"type_refs":["DecidableEq","Eq","LE.le","Multiset","Multiset.cons","Multiset.erase","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":51,"value_refs":["DecidableEq","LE.le","Multiset","Multiset.cons","Multiset.erase","Multiset.erase_le_iff_le_cons","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Antidiagonal","name":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.antidiagonal_cons._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.antidiagonal_cons","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Antidiagonal","name":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.map_swap_antidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.map_swap_antidiagonal","reducibility":null,"statement_dag_size":69,"type_refs":["Eq","Function.comp","Prod","Prod.map","Prod.swap"],"value_dag_size":77,"value_refs":["Eq.symm","Function.comp","Prod","Prod.map","Prod.map_comp_swap","Prod.swap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Antidiagonal","name":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Antidiagonal","name":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Antidiagonal","name":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Antidiagonal.0.Multiset.mem_antidiagonal","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","LE.le","List","List.instMembership","Membership.mem","Multiset","Multiset.instPartialOrder","Multiset.ofList","Multiset.powersetAux","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":48,"value_refs":["LE.le","List","List.instMembership","Membership.mem","Multiset","Multiset.instPartialOrder","Multiset.mem_powersetAux","Multiset.ofList","Multiset.powersetAux","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.coe_join.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.coe_join","reducibility":"abbrev","statement_dag_size":36,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":50,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_join._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_join","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_join._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_join","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Exists","Or"],"value_dag_size":33,"value_refs":["Exists","Or","exists_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_product._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_product","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_product.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_product","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Prod","Prod.mk"],"value_dag_size":42,"value_refs":["Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_sigma._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_sigma","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_sigma.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.mem_sigma","reducibility":"abbrev","statement_dag_size":36,"type_refs":["Sigma","Sigma.mk"],"value_dag_size":51,"value_refs":["Sigma","Sigma.casesOn","Sigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.nodup_bind._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.nodup_bind","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Function.onFun","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatMap","List.instMembership","Membership.mem"],"value_dag_size":63,"value_refs":["And","Function.onFun","List","List.Disjoint","List.Nodup","List.Pairwise","List.flatMap","List.instMembership","List.nodup_flatMap","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Bind","name":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.nodup_bind._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Bind.0.Multiset.nodup_bind","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.Pairwise","Multiset.Pairwise","Multiset.ofList","Std.Symm"],"value_dag_size":37,"value_refs":["List","List.Pairwise","Multiset.Pairwise","Multiset.ofList","Multiset.pairwise_coe_iff_pairwise","Std.Symm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.Rel.countP_eq._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.Rel.countP_eq","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":33,"value_refs":["Eq","HAdd.hAdd","Nat","Nat.add_right_inj","instAddNat","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_congr._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_congr","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_eq_card._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_eq_card","reducibility":null,"statement_dag_size":44,"type_refs":["Bool","Bool.true","Eq","List","List.countP","List.instMembership","List.length","Membership.mem","Nat"],"value_dag_size":48,"value_refs":["Bool","Bool.true","Eq","List","List.countP","List.countP_eq_length","List.instMembership","List.length","Membership.mem","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.countP_eq_zero","reducibility":null,"statement_dag_size":50,"type_refs":["Bool","Bool.true","Eq","List","List.countP","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat"],"value_dag_size":54,"value_refs":["Bool","Bool.true","Eq","List","List.countP","List.countP_eq_zero","List.instMembership","Membership.mem","Nat","Not","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_attach._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_attach","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Subtype","Subtype.val"],"value_dag_size":46,"value_refs":["Eq","Subtype","Subtype.ext_iff","Subtype.val","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_eq_card._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_eq_card","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","Membership.mem","Multiset","Multiset.card","Multiset.countP","Multiset.instMembership","Nat"],"value_dag_size":51,"value_refs":["DecidablePred","Eq","Membership.mem","Multiset","Multiset.card","Multiset.countP","Multiset.countP_eq_card","Multiset.instMembership","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_pos._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_pos","reducibility":null,"statement_dag_size":57,"type_refs":["And","DecidablePred","Eq","Exists","LT.lt","Membership.mem","Multiset","Multiset.countP","Multiset.instMembership","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":62,"value_refs":["And","DecidablePred","Exists","LT.lt","Membership.mem","Multiset","Multiset.countP","Multiset.countP_pos","Multiset.instMembership","Nat","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.count_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Multiset","Multiset.cons","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"],"value_dag_size":36,"value_refs":["Eq.symm","Multiset","Multiset.cons","Multiset.cons_zero","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.le_iff_count._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.le_iff_count","reducibility":null,"statement_dag_size":41,"type_refs":["DecidableEq","Eq","LE.le","List","List.Subperm","List.count","Nat","instBEqOfDecidableEq","instLENat"],"value_dag_size":45,"value_refs":["DecidableEq","LE.le","List","List.Subperm","List.count","List.subperm_iff_count","Nat","instBEqOfDecidableEq","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Count","name":"_private.Mathlib.Data.Multiset.Count.0.Multiset.nodup_iff_count_le_one._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Count.0.Multiset.nodup_iff_count_le_one","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","List","List.Nodup","Multiset.Nodup","Multiset.ofList"],"value_dag_size":23,"value_refs":["List","List.Nodup","Multiset.Nodup","Multiset.coe_nodup","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Dedup","name":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.Nodup.le_dedup_iff_le._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.Nodup.le_dedup_iff_le","reducibility":null,"statement_dag_size":44,"type_refs":["And","DecidableEq","Eq","LE.le","Multiset","Multiset.Nodup","Multiset.dedup","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":48,"value_refs":["And","DecidableEq","LE.le","Multiset","Multiset.Nodup","Multiset.dedup","Multiset.instPartialOrder","Multiset.le_dedup","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Dedup","name":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.count_dedup._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.count_dedup","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Dedup","name":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.dedup_ext._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.dedup_ext","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Iff","Membership.mem","Multiset","Multiset.Nodup","Multiset.instMembership"],"value_dag_size":50,"value_refs":["Eq","Iff","Membership.mem","Multiset","Multiset.Nodup","Multiset.Nodup.ext","Multiset.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Dedup","name":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.dedup_map_dedup_eq._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.dedup_map_dedup_eq","reducibility":null,"statement_dag_size":45,"type_refs":["DecidableEq","Eq","Iff","Membership.mem","Multiset","Multiset.dedup","Multiset.instMembership"],"value_dag_size":49,"value_refs":["DecidableEq","Eq","Iff","Membership.mem","Multiset","Multiset.dedup","Multiset.dedup_ext","Multiset.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Dedup","name":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.le_dedup.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Dedup.0.Multiset.le_dedup","reducibility":"abbrev","statement_dag_size":86,"type_refs":["And","And.intro","LE.le","Multiset","Multiset.Nodup","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":109,"value_refs":["And","And.casesOn","And.intro","LE.le","Multiset","Multiset.Nodup","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Defs","name":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.decidableEqPiMultiset._simp_1","namespace":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.decidableEqPiMultiset","reducibility":null,"statement_dag_size":31,"type_refs":["Eq"],"value_dag_size":35,"value_refs":["Eq","funext_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Defs","name":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.leInductionOn.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.leInductionOn","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Exists.intro","LE.le","List","List.Perm","List.Sublist","List.isSetoid","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Quotient.mk"],"value_dag_size":170,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","LE.le","List","List.Perm","List.Sublist","List.isSetoid","Multiset","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Quotient.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Defs","name":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.pairwise_coe_iff_pairwise.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Defs.0.Multiset.pairwise_coe_iff_pairwise","reducibility":"abbrev","statement_dag_size":88,"type_refs":["And","And.intro","Eq","Exists.intro","List","List.Pairwise","Multiset","Multiset.Pairwise","Multiset.ofList"],"value_dag_size":150,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","List","List.Pairwise","Multiset","Multiset.Pairwise","Multiset.ofList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Or","instHAdd"],"value_dag_size":49,"value_refs":["HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.mem_add","Or","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.IsDershowitzMannaLT.trans","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":"regular","statement_dag_size":14,"type_refs":["Multiset","Preorder"],"value_dag_size":82,"value_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.instSingleton","Preorder","Preorder.toLT","Singleton.singleton","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep.eq_1","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","reducibility":null,"statement_dag_size":92,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.instSingleton","Preorder","Preorder.toLT","Singleton.singleton","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","instHAdd"],"value_dag_size":23,"value_refs":["Eq.refl","Multiset","Preorder","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":44,"type_refs":["Acc","LT.lt","Multiset","Multiset.cons","Preorder","Preorder.toLT","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":768,"value_refs":["Acc","Acc.intro","Acc.rec","And","And.casesOn","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.add_cons","Multiset.add_zero","Multiset.cons","Multiset.induction","Multiset.instAdd","Multiset.instMembership","Multiset.instZero","OfNat.ofNat","Or","Or.casesOn","Preorder","Preorder.toLT","Zero.toOfNat0","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt._simp_1_1","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt._simp_1_2","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert","congrArg","forall_congr","id","implies_congr","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Or"],"value_dag_size":42,"value_refs":["Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Or"],"value_dag_size":39,"value_refs":["And","Eq","Or","forall_eq_or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_of_acc_lt","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":41,"type_refs":["Acc","LT.lt","Membership.mem","Multiset","Multiset.instMembership","Preorder","Preorder.toLT","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":562,"value_refs":["Acc","Acc.intro","AddCancelCommMonoid.toAddLeftCancelMonoid","AddLeftCancelMonoid.add_eq_zero._simp_1","AddLeftCancelMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddUnits","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","And","CanonicallyOrderedCommMonoid.toUniqueAddUnits","Eq","Eq.refl","Eq.trans","Exists","False","HAdd","HAdd.hAdd","IsEmpty.forall_iff._simp_1","LT.lt","Membership.mem","Multiset","Multiset.cons","Multiset.induction_on","Multiset.inhabitedMultiset","Multiset.instAdd","Multiset.instAddCancelCommMonoid","Multiset.instCanonicallyOrderedAdd","Multiset.instMembership","Multiset.instPartialOrder","Multiset.instSingleton","Multiset.instZero","Multiset.mem_cons_of_mem","Multiset.mem_cons_self","Multiset.singleton_ne_zero._simp_1","OfNat.ofNat","Preorder","Preorder.toLT","Singleton.singleton","True","Unique.instSubsingleton","Zero.toOfNat0","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_cons_of_acc_lt","and_false","congr","congrArg","congrFun'","eq_comm","exists_const._simp_1","exists_false._simp_1","false_and","forall_congr","funext","implies_congr","implies_true","instHAdd","instIsEmptyFalse","instNonemptyOfInhabited","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_of_oneStep","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":26,"type_refs":["Multiset","Multiset.IsDershowitzMannaLT","Preorder","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":768,"value_refs":["And","And.casesOn","And.intro","EmptyCollection.emptyCollection","Eq","Eq.mpr","Eq.refl","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.IsDershowitzMannaLT","Multiset.instAdd","Multiset.instEmptyCollection","Multiset.instMembership","Multiset.instSingleton","Multiset.instZero","Multiset.mem_singleton._simp_1","Multiset.singleton_ne_zero._simp_1","Ne","Not","OfNat.ofNat","Preorder","Preorder.toLT","Singleton.singleton","True","Zero.toOfNat0","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","congrArg","congrFun'","exists_eq_left._simp_1","forall_congr","funext","id","implies_congr","instHAdd","not_false_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_of_transGen_oneStep","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":30,"type_refs":["Multiset","Multiset.IsDershowitzMannaLT","Preorder","Relation.TransGen","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":921,"value_refs":["And","And.casesOn","EmptyCollection.emptyCollection","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.IsDershowitzMannaLT","Multiset.IsDershowitzMannaLT.trans","Multiset.instAdd","Multiset.instEmptyCollection","Multiset.instMembership","Multiset.instSingleton","Multiset.instZero","Multiset.mem_singleton._simp_1","Multiset.singleton_ne_zero._simp_1","Ne","Not","OfNat.ofNat","Preorder","Preorder.toLT","Relation.TransGen","Relation.TransGen.trans_induction_on","Singleton.singleton","True","Zero.toOfNat0","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","congr","congrArg","congrFun'","eq_self","exists_eq_left._simp_1","forall_congr","funext","id","implies_congr","instHAdd","not_false_eq_true","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Exists","HAdd.hAdd","LT.lt","Membership.mem","Multiset","Multiset.cons","Multiset.instAdd","Multiset.instMembership","Or","Preorder","Preorder.toLT","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","instHAdd"],"value_dag_size":1705,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMagma","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddSemigroup","AddSemigroup.toAdd","And","And.casesOn","And.intro","Classical.propDecidable","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Membership.mem","Multiset","Multiset.cons","Multiset.cons_inj_right._simp_1","Multiset.instAdd","Multiset.instAddCancelCommMonoid","Multiset.instAddLeftMono","Multiset.instAddLeftReflectLE","Multiset.instExistsAddOfLE","Multiset.instMembership","Multiset.instOrderedSub","Multiset.instPartialOrder","Multiset.instSingleton","Multiset.instSub","Multiset.mem_add._simp_1","Multiset.mem_cons._simp_1","Multiset.mem_singleton._simp_1","Multiset.singleton_add","Multiset.singleton_le._simp_1","Ne","Ne.symm","Or","Or.casesOn","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder","Preorder.toLE","Preorder.toLT","Singleton","Singleton.singleton","True","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert._simp_1_1","addRightReflectLE_of_addLeftReflectLE","add_assoc","add_comm","add_left_inj._simp_1","add_tsub_cancel_of_le","congrArg","congrFun'","eq_false","eq_or_ne","eq_self","false_or","id","instHAdd","instHSub","instIsRightCancelAddOfAddRightReflectLE","of_eq_true","or_false","or_true","tsub_add_cancel_of_le","tsub_eq_tsub_of_add_eq_add"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_insert","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_singleton_wf","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":23,"type_refs":["Multiset","Preorder","Preorder.toLT","WellFounded","WellFoundedLT","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":51,"value_refs":["Membership.mem","Multiset","Multiset.instMembership","Preorder","Preorder.toLT","WellFounded.intro","WellFoundedLT","WellFoundedLT.apply","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.acc_oneStep_of_acc_lt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_eq_isDershowitzMannaLT","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","Multiset","Multiset.IsDershowitzMannaLT","Preorder","Relation.TransGen","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":77,"value_refs":["Iff.intro","Multiset","Multiset.IsDershowitzMannaLT","Preorder","Relation.TransGen","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.isDershowitzMannaLT_of_transGen_oneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT","funext","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset","reducibility":null,"statement_dag_size":30,"type_refs":["Multiset","Multiset.IsDershowitzMannaLT","Preorder","Relation.TransGen","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep"],"value_dag_size":2176,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMagma","AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.casesOn","And.intro","And.right","Classical.propDecidable","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","Exists.intro","False","False.elim","HAdd","HAdd.hAdd","HSub.hSub","LT.lt","Membership.mem","Multiset","Multiset.IsDershowitzMannaLT","Multiset.add_cons","Multiset.cons","Multiset.filter","Multiset.filter_le","Multiset.induction_on","Multiset.instAdd","Multiset.instAddCancelCommMonoid","Multiset.instAddLeftMono","Multiset.instAddLeftReflectLE","Multiset.instEmptyCollection","Multiset.instExistsAddOfLE","Multiset.instMembership","Multiset.instOrderedSub","Multiset.instPartialOrder","Multiset.instSingleton","Multiset.instSub","Multiset.instZero","Multiset.mem_cons._simp_1","Multiset.mem_filter._simp_1","Multiset.mem_singleton._simp_1","Multiset.sub_filter_eq_filter_not","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Preorder","Preorder.toLT","Relation.TransGen","Relation.TransGen.single","Relation.TransGen.tail","Singleton.singleton","True","Zero.toOfNat0","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.OneStep","_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT._simp_1_1","add_add_tsub_cancel","add_comm","add_right_comm","and_imp._simp_1","congr","congrArg","congrFun'","eq_false","eq_or_ne","eq_self","exists_eq_left._simp_1","exists_eq_or_imp._simp_1","false_or","forall_congr","funext","id","imp_self._simp_1","implies_congr","implies_true","instDecidableNot","instHAdd","instHSub","not_true_eq_false","of_eq_true","rfl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.DershowitzManna","name":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT","reducibility":null,"statement_dag_size":42,"type_refs":["And","DecidablePred","Eq","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership"],"value_dag_size":48,"value_refs":["And","DecidablePred","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership","Multiset.mem_filter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.count_map_eq_count._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.count_map_eq_count","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.count_map_eq_count._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.count_map_eq_count","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":12,"value_refs":["True","imp_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_add_not._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_add_not","reducibility":null,"statement_dag_size":17,"type_refs":["Decidable","Eq","Not","Or","True"],"value_dag_size":18,"value_refs":["Decidable","Decidable.em","Not","Or","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Exists","Subtype","Subtype.mk"],"value_dag_size":48,"value_refs":["Exists","Subtype","Subtype.exists","Subtype.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_comm._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_comm","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_eq._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_eq","reducibility":null,"statement_dag_size":40,"type_refs":["DecidableEq","Eq","Multiset","Multiset.count","Multiset.filter","Multiset.replicate"],"value_dag_size":47,"value_refs":["DecidableEq","Eq","Eq.symm","Multiset","Multiset.count","Multiset.filter","Multiset.filter_eq'","Multiset.replicate"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_eq._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.le_filter.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.le_filter","reducibility":"abbrev","statement_dag_size":120,"type_refs":["And","And.intro","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":143,"value_refs":["And","And.casesOn","And.intro","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Filter","name":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.map_count_True_eq_filter_card._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Filter.0.Multiset.map_count_True_eq_filter_card","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","Iff"],"value_dag_size":19,"value_refs":["Eq","Iff","eq_iff_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1.eq_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1","reducibility":null,"statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":25,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1.eq_2","namespace":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Bool.false","Bool.true","Eq","List.filter.match_1","Unit","Unit.unit"],"value_dag_size":24,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","List.filter.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1.splitter","namespace":"_private.Mathlib.Data.Multiset.Find.0.List.filter.match_1","reducibility":"abbrev","statement_dag_size":17,"type_refs":["Bool","Bool.false","Bool.true","Unit"],"value_dag_size":1,"value_refs":["List.filter.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_add._proof_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_add","reducibility":null,"statement_dag_size":59,"type_refs":["And","HAdd.hAdd","LE.le","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Set","Set.instLE","Set.ofPred","instHAdd"],"value_dag_size":401,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.mem_add","Not","Or","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","True","True.intro","eq_false","id","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_add._proof_3","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_add","reducibility":null,"statement_dag_size":59,"type_refs":["And","HAdd.hAdd","LE.le","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Set","Set.instLE","Set.ofPred","instHAdd"],"value_dag_size":378,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.of_forall_eq_false","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.mem_add","Not","Or","Set","Set.instLE","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","Set.subset_def","True","True.intro","eq_false","id","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_congr._simp_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_congr","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":25,"value_refs":["And","Eq.symm","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_congr._simp_2","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_congr","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons","reducibility":null,"statement_dag_size":60,"type_refs":["And","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Not","Set.Subsingleton","Set.ofPred"],"value_dag_size":726,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.em","Lean.Grind.false_of_not_eq_self","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Not","Or","Or.casesOn","Set.Subsingleton","Set.ofPred","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_of_heq","eq_true","funext","id","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons","reducibility":null,"statement_dag_size":75,"type_refs":["And","DecidablePred","List","List.cons","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.ofList","Quotient.mk","Set.Subsingleton","Set.ofPred"],"value_dag_size":156,"value_refs":["And","Decidable","DecidablePred","Eq","Eq.rec","Eq.refl","List","List.cons","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.ofList","Quotient.mk","Set.Subsingleton","Set.ofPred","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1_2","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons","reducibility":null,"statement_dag_size":76,"type_refs":["And","DecidablePred","List","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.ofList","Not","Quotient.mk","Set.Subsingleton","Set.ofPred"],"value_dag_size":158,"value_refs":["And","Decidable","DecidablePred","Eq","Eq.rec","Eq.refl","List","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.find?_cons._proof_2","Multiset.instMembership","Multiset.ofList","Not","Quotient","Quotient.mk","Set.Subsingleton","Set.ofPred","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1_4","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons","reducibility":null,"statement_dag_size":275,"type_refs":["And","Decidable","DecidablePred","Eq","Eq.rec","Eq.refl","List","List.cons","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.find?","Multiset.find?_cons._proof_2","Multiset.instMembership","Multiset.ofList","Not","Option","Option.some","Quotient","Quotient.mk","Set.Subsingleton","Set.ofPred","dite","id"],"value_dag_size":644,"value_refs":["And","Bool","Classical.byContradiction","Decidable","Decidable.decide","DecidablePred","Eq","Eq.mp","Eq.rec","Eq.refl","Eq.symm","Eq.trans","False","HEq","Lean.Grind.alreadyNorm","Lean.Grind.decide_eq_false","Lean.Grind.decide_eq_true","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","List","List.cons","List.filter.match_1","List.filter.match_1.congr_eq_1","List.filter.match_1.congr_eq_2","List.find?","List.find?_cons","List.isSetoid","Membership.mem","Multiset","Multiset.cons","Multiset.find?","Multiset.find?_coe","Multiset.find?_cons._proof_2","Multiset.instMembership","Multiset.ofList","Not","Option","Option.some","Or","Or.casesOn","PUnit","Quotient","Quotient.mk","Set.Subsingleton","Set.ofPred","True","True.intro","Unit","_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1_1","_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_cons._proof_1_2","dite","eq_false","eq_true","heq_eq_eq","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_choose._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_choose","reducibility":null,"statement_dag_size":61,"type_refs":["And","DecidablePred","Eq","ExistsUnique","Membership.mem","Multiset","Multiset.choose","Multiset.instMembership"],"value_dag_size":68,"value_refs":["And","DecidablePred","Eq","ExistsUnique","Membership.mem","Multiset","Multiset.choose","Multiset.choose_eq_iff","Multiset.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_none_iff._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_none_iff","reducibility":null,"statement_dag_size":151,"type_refs":["And","DecidablePred","Eq","Iff","Membership.mem","Multiset","Multiset.cons","Multiset.find?","Multiset.find?_cons._proof_2","Multiset.instMembership","Not","Option","Option.none","Option.some","Set.Subsingleton","Set.ofPred","dite"],"value_dag_size":1196,"value_refs":["And","And.casesOn","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.alreadyNorm","Lean.Grind.dite_cond_eq_false'","Lean.Grind.dite_cond_eq_true'","Lean.Grind.em","Lean.Grind.eq_congr","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_propagator","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Membership.mem","Multiset","Multiset.cons","Multiset.find?","Multiset.find?_cons._proof_2","Multiset.instMembership","Multiset.mem_cons","Not","Option","Option.ctorIdx","Option.none","Option.some","Or","Or.casesOn","Set.Subsingleton","Set.ofPred","True","True.intro","congrArg","congrFun'","dite","eq_false","eq_of_heq","eq_self","eq_true","forall_congr","id","noConfusion_of_Nat","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_some_iff._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_some_iff","reducibility":null,"statement_dag_size":68,"type_refs":["And","Eq","Iff","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Option","Option.some"],"value_dag_size":600,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_left","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Not","Option","Option.some","Option.some.noConfusion","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_of_heq","eq_true","heq_eq_eq","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Find","name":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_some_iff._proof_1_2","namespace":"_private.Mathlib.Data.Multiset.Find.0.Multiset.find?_eq_some_iff","reducibility":null,"statement_dag_size":44,"type_refs":["And","Iff","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Not"],"value_dag_size":529,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.symm","Eq.trans","False","False.elim","HEq","HEq.refl","Iff","Lean.Grind._simp_1","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_eq_of_eq_true_right","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership","Multiset.mem_cons","Not","Or","Or.casesOn","True","True.intro","congr","congrArg","eq_false","eq_of_heq","eq_true","id","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.ofList"],"value_dag_size":37,"value_refs":["List","List.instMembership","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.coe_ndinter","reducibility":null,"statement_dag_size":46,"type_refs":["BEq","Bool","Decidable.decide","Eq","LawfulBEq","List","List.elem","List.instDecidableMemOfLawfulBEq","List.instMembership","Membership.mem"],"value_dag_size":53,"value_refs":["BEq","Bool","Decidable.decide","Eq.symm","LawfulBEq","List","List.elem","List.elem_eq_mem","List.instDecidableMemOfLawfulBEq","List.instMembership","Membership.mem"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.disjoint_ndinsert_left._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.disjoint_ndinsert_left","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.le_ndinter._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.le_ndinter","reducibility":null,"statement_dag_size":59,"type_refs":["And","DecidablePred","Eq","LE.le","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":65,"value_refs":["And","DecidablePred","LE.le","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership","Multiset.instPartialOrder","Multiset.le_filter","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.le_ndinter._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.le_ndinter","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.mem_ndinter._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.mem_ndinter","reducibility":null,"statement_dag_size":42,"type_refs":["And","DecidablePred","Eq","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership"],"value_dag_size":48,"value_refs":["And","DecidablePred","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership","Multiset.mem_filter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinsert_le.match_1_1","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinsert_le","reducibility":"abbrev","statement_dag_size":106,"type_refs":["And","And.intro","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":128,"value_refs":["And","And.casesOn","And.intro","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinter_eq_zero_iff_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinter_eq_zero_iff_disjoint","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinter_eq_zero_iff_disjoint._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndinter_eq_zero_iff_disjoint","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le","reducibility":null,"statement_dag_size":53,"type_refs":["And","DecidableEq","Eq","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","Multiset.ndinsert","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":58,"value_refs":["And","DecidableEq","LE.le","Membership.mem","Multiset","Multiset.instMembership","Multiset.instPartialOrder","Multiset.ndinsert","Multiset.ndinsert_le","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.cons","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["And","HasSubset.Subset","Membership.mem","Multiset","Multiset.cons","Multiset.cons_subset","Multiset.instHasSubset","Multiset.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le","reducibility":null,"statement_dag_size":18,"type_refs":["And","Eq"],"value_dag_size":22,"value_refs":["And","and_left_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.FinsetOps","name":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le._simp_1_5","namespace":"_private.Mathlib.Data.Multiset.FinsetOps.0.Multiset.ndunion_le","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.coeEmbedding.match_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.coeEmbedding","reducibility":"abbrev","statement_dag_size":66,"type_refs":["DecidableEq","Fin","Fin.mk","LT.lt","Multiset","Multiset.ToType","Multiset.count","Nat","Sigma.mk","instLTNat"],"value_dag_size":111,"value_refs":["DecidableEq","Fin","Fin.casesOn","Fin.mk","LT.lt","Multiset","Multiset.ToType","Multiset.count","Nat","Sigma.casesOn","Sigma.mk","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.coe_mem._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.coe_mem","reducibility":null,"statement_dag_size":71,"type_refs":["DecidableEq","Fin","Fin.val","LT.lt","Multiset","Multiset.ToType","Multiset.count","Nat","OfNat.ofNat","Sigma.fst","Sigma.snd","instLTNat","instOfNatNat"],"value_dag_size":420,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","Fin","Fin.val","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.IntInterval.co","Lean.Grind.Nat.lt_eq","Lean.Grind.ToInt.ge_lower0","Lean.Grind.ToInt.toInt","Lean.Grind.instToIntFinCoOfNatIntCast","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Multiset","Multiset.ToType","Multiset.count","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.finVal","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.cast","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Sigma.fst","Sigma.snd","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv._simp_4","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv._simp_5","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv._simp_6","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.consEquiv","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._proof_11","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":42,"type_refs":["DecidableEq","LT.lt","Multiset","Multiset.count","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":332,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Multiset","Multiset.count","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_10","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_3","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":94,"type_refs":["And","Eq","Exists","Finset","Finset.disjiUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership"],"value_dag_size":100,"value_refs":["And","Exists","Finset","Finset.disjiUnion","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_disjiUnion","Membership.mem","Set.PairwiseDisjoint","SetLike.coe","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_4","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.toFinset","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Membership.mem","Multiset","Multiset.instMembership","Multiset.mem_toFinset","Multiset.toFinset","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_5","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":79,"type_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership"],"value_dag_size":84,"value_refs":["And","DFunLike.coe","Eq","Exists","Finset","Finset.instSetLike","Finset.map","Finset.mem_map","Function.Embedding","Function.instFunLikeEmbedding","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_6","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_7","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_8","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","Eq.symm","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst._simp_9","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.instFintypeElemProdNatOfPredLtSndCountFst","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._proof_1_7","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":101,"type_refs":["DecidableEq","Eq","False","Finset","Finset.val","GT.gt","HSub.hSub","LE.le","Multiset.card","Multiset.filter","Nat","OfNat.ofNat","Prod","Prod.fst","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":724,"value_refs":["Bool","Bool.true","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.val","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Multiset.card","Multiset.filter","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Prod","Prod.fst","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":48,"type_refs":["DecidableEq","Eq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat"],"value_dag_size":52,"value_refs":["DecidableEq","LE.le","Multiset","Multiset.count","Multiset.instPartialOrder","Multiset.le_iff_count","Nat","PartialOrder.toPreorder","Preorder.toLE","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not"],"value_dag_size":18,"value_refs":["Not","imp_not_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_5","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":45,"value_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.lt_sub_iff_add_lt","instAddNat","instHAdd","instHSub","instLTNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset._simp_1_6","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_fst_le_of_subset_toEnumFinset","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_toEnumFinset_fst._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_toEnumFinset_fst","reducibility":null,"statement_dag_size":36,"type_refs":["DecidablePred","Eq","Finset","Finset.filter","Finset.val","Multiset","Multiset.filter"],"value_dag_size":42,"value_refs":["DecidablePred","Eq.symm","Finset","Finset.filter","Finset.filter_val","Finset.val","Multiset","Multiset.filter"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Exists","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":42,"value_refs":["Exists","Fin","Fin.exists_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","True"],"value_dag_size":33,"value_refs":["Finset","Finset.instSetLike","Finset.mem_univ","Finset.univ","Fintype","Membership.mem","SetLike.instMembership","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.map_univ_coeEmbedding","reducibility":null,"statement_dag_size":34,"type_refs":["And","Eq","Exists"],"value_dag_size":39,"value_refs":["And","Eq","Exists","exists_eq_right_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Fintype","name":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.mem_of_mem_toEnumFinset._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.Fintype.0.Multiset.mem_of_mem_toEnumFinset","reducibility":null,"statement_dag_size":54,"type_refs":["DecidableEq","LT.lt","Multiset","Multiset.count","Nat","OfNat.ofNat","Prod","Prod.fst","Prod.snd","instLTNat","instOfNatNat"],"value_dag_size":356,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Multiset","Multiset.count","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Prod","Prod.fst","Prod.snd","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Multiset.Fold","name":"_private.Mathlib.Data.Multiset.Fold.0.Multiset.«_aux_Mathlib_Data_Multiset_Fold___macroRules__private_Mathlib_Data_Multiset_Fold_0_Multiset_term_*__1»","namespace":"_private.Mathlib.Data.Multiset.Fold.0.Multiset","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":261,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr4","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.Syntax.node2","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Multiset.Fold","name":"_private.Mathlib.Data.Multiset.Fold.0.Multiset.«term_*_»","namespace":"_private.Mathlib.Data.Multiset.Fold.0.Multiset","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.TrailingParserDescr"],"value_dag_size":57,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.ParserDescr.binary","Lean.ParserDescr.cat","Lean.ParserDescr.symbol","Lean.ParserDescr.trailingNode","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Lattice","name":"_private.Mathlib.Data.Multiset.Lattice.0.Multiset.sup_le._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Lattice.0.Multiset.sup_le","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Lattice","name":"_private.Mathlib.Data.Multiset.Lattice.0.Multiset.sup_le._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Lattice.0.Multiset.sup_le","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.exists_multiset_eq_map_quot_mk.match_1_1","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.exists_multiset_eq_map_quot_mk","reducibility":"abbrev","statement_dag_size":96,"type_refs":["Eq","Exists","Exists.intro","Multiset","Multiset.map","Quot","Quot.mk"],"value_dag_size":123,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Multiset","Multiset.map","Quot","Quot.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.foldr_induction'._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.foldr_induction'","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","Membership.mem","Multiset","Multiset.cons","Multiset.instMembership"],"value_dag_size":47,"value_refs":["And","Membership.mem","Multiset","Multiset.cons","Multiset.forall_mem_cons","Multiset.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.induction_on_multiset_quot.match_1_1","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.induction_on_multiset_quot","reducibility":"abbrev","statement_dag_size":103,"type_refs":["Eq","Eq.refl","Exists","Exists.intro","Multiset","Multiset.map","Quot","Quot.mk"],"value_dag_size":298,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","Exists.intro","HEq","HEq.refl","Multiset","Multiset.map","Quot","Quot.mk","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.map_replicate._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.map_replicate","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","List.replicate","Multiset","Multiset.ofList","Multiset.replicate","Nat"],"value_dag_size":30,"value_refs":["Eq.symm","List.replicate","Multiset","Multiset.coe_replicate","Multiset.ofList","Multiset.replicate","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.map_subset_map.match_1_1","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.map_subset_map","reducibility":"abbrev","statement_dag_size":114,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Membership.mem","Multiset","Multiset.instMembership"],"value_dag_size":178,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Membership.mem","Multiset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.MapFold","name":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.rel_map_left._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.rel_map_left","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons","Multiset.rel_cons_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Pairwise","name":"_private.Mathlib.Data.Multiset.Pairwise.0.Multiset.Pairwise.forall.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Pairwise.0.Multiset.Pairwise.forall","reducibility":"abbrev","statement_dag_size":82,"type_refs":["And","And.intro","Eq","Exists.intro","List","List.Pairwise","Multiset","Multiset.Pairwise","Multiset.ofList"],"value_dag_size":142,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","List","List.Pairwise","Multiset","Multiset.Pairwise","Multiset.ofList"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Nodup.pi._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Nodup.pi","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","Membership.mem","Multiset","Multiset.Nodup","Multiset.cons","Multiset.instMembership","Not"],"value_dag_size":39,"value_refs":["And","Membership.mem","Multiset","Multiset.Nodup","Multiset.cons","Multiset.instMembership","Multiset.nodup_cons","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Nodup.pi._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Nodup.pi","reducibility":null,"statement_dag_size":64,"type_refs":["And","Disjoint","Eq","Function.onFun","Membership.mem","Multiset","Multiset.Nodup","Multiset.Pairwise","Multiset.bind","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder"],"value_dag_size":69,"value_refs":["And","Disjoint","Function.onFun","Membership.mem","Multiset","Multiset.Nodup","Multiset.Pairwise","Multiset.bind","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Multiset.nodup_bind","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Pi.cons_swap._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.Pi.cons_swap","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","HEq"],"value_dag_size":24,"value_refs":["Eq","HEq","heq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":36,"value_refs":["Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instSingleton","Multiset.mem_singleton","Singleton.singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi","reducibility":null,"statement_dag_size":60,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership"],"value_dag_size":65,"value_refs":["And","Exists","Membership.mem","Multiset","Multiset.bind","Multiset.instMembership","Multiset.mem_bind","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Pi","name":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Pi.0.Multiset.mem_pi","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.bind_powerset_len._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.bind_powerset_len","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","List.range","Multiset","Multiset.ofList","Multiset.range","Nat"],"value_dag_size":19,"value_refs":["Eq.symm","List.range","Multiset","Multiset.coe_range","Multiset.ofList","Multiset.range","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.bind_powerset_len._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.bind_powerset_len","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","List","List.flatMap","List.map"],"value_dag_size":57,"value_refs":["Eq.symm","List","List.flatMap","List.map","List.map_flatMap"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.map_single_le_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.map_single_le_powerset","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powerset._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powerset","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetAux._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetAux","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.Sublist","List.instMembership","List.length","List.sublistsLen","Membership.mem","Nat"],"value_dag_size":50,"value_refs":["And","Eq","List","List.Sublist","List.instMembership","List.length","List.mem_sublistsLen","List.sublistsLen","Membership.mem","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux.match_1_6","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":"abbrev","statement_dag_size":127,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List","List.Perm","List.Sublist","List.length","Nat"],"value_dag_size":238,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","List","List.Perm","List.Sublist","List.length","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux.match_1_8","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.mem_powersetCardAux","reducibility":"abbrev","statement_dag_size":121,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","List","List.Perm","List.Sublist","List.length","Nat"],"value_dag_size":221,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","List","List.Perm","List.Sublist","List.length","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.nodup_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.nodup_powerset","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","List","List.Nodup","Multiset.Nodup","Multiset.ofList"],"value_dag_size":23,"value_refs":["List","List.Nodup","Multiset.Nodup","Multiset.coe_nodup","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCardAux_perm._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCardAux_perm","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","List.cons","True"],"value_dag_size":31,"value_refs":["List","List.Perm","List.Perm.swap","List.cons","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCard_le_powerset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCard_le_powerset","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCard_mono._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCard_mono","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.revzip_powersetAux'._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.revzip_powersetAux'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Powerset","name":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.revzip_powersetAux._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Powerset.0.Multiset.revzip_powersetAux","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Prod","Prod.mk"],"value_dag_size":44,"value_refs":["Exists","Prod","Prod.exists","Prod.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Replicate","name":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.eq_replicate.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.eq_replicate","reducibility":"abbrev","statement_dag_size":107,"type_refs":["And","And.intro","Eq","Membership.mem","Multiset","Multiset.card","Multiset.instMembership","Nat"],"value_dag_size":124,"value_refs":["And","And.casesOn","And.intro","Eq","Membership.mem","Multiset","Multiset.card","Multiset.instMembership","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Replicate","name":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.le_replicate_iff.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.le_replicate_iff","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","LE.le","Multiset","Multiset.replicate","Nat","instLENat"],"value_dag_size":156,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","LE.le","Multiset","Multiset.replicate","Nat","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Replicate","name":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.nodup_iff_ne_cons_cons.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.nodup_iff_ne_cons_cons","reducibility":"abbrev","statement_dag_size":139,"type_refs":["Eq","Exists","Exists.intro","HAdd.hAdd","Multiset","Multiset.cons","Multiset.instAdd","Multiset.instZero","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":175,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAdd.hAdd","Multiset","Multiset.cons","Multiset.instAdd","Multiset.instZero","OfNat.ofNat","Zero.toOfNat0","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Replicate","name":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.replicate_le_coe.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Replicate.0.Multiset.replicate_le_coe","reducibility":"abbrev","statement_dag_size":111,"type_refs":["And","And.intro","Exists.intro","LE.le","List","List.Perm","List.Sublist","List.replicate","Multiset","Multiset.instPartialOrder","Multiset.ofList","Multiset.replicate","Nat","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":186,"value_refs":["And","And.casesOn","And.intro","Exists.casesOn","Exists.intro","LE.le","List","List.Perm","List.Sublist","List.replicate","Multiset","Multiset.instPartialOrder","Multiset.ofList","Multiset.replicate","Nat","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.Sections","name":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.coe_sections.match_1_1","namespace":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.coe_sections","reducibility":"abbrev","statement_dag_size":36,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":50,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sections","name":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.mem_sections._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.mem_sections","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons"],"value_dag_size":73,"value_refs":["And","Eq","Exists","Multiset","Multiset.Rel","Multiset.cons","Multiset.rel_cons_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sections","name":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.mem_sections._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Sections.0.Multiset.mem_sections","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sum","name":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.inl_mem_disjSum._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.inl_mem_disjSum","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sum","name":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.inr_mem_disjSum._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.inr_mem_disjSum","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sum","name":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.mem_disjSum._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.mem_disjSum","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Or","instHAdd"],"value_dag_size":49,"value_refs":["HAdd.hAdd","Membership.mem","Multiset","Multiset.instAdd","Multiset.instMembership","Multiset.mem_add","Or","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sum","name":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.mem_disjSum._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.Sum.0.Multiset.mem_disjSum","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sym","name":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.mem_sym2_iff._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.mem_sym2_iff","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","List","List.instMembership","List.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike"],"value_dag_size":55,"value_refs":["List","List.instMembership","List.mem_sym2_iff","List.sym2","Membership.mem","SetLike.instMembership","Sym2","Sym2.instSetLike","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sym","name":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.mk_mem_sym2_iff._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.mk_mem_sym2_iff","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","List","List.instMembership","List.sym2","Membership.mem","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","List","List.instMembership","List.mk_mem_sym2_iff","List.sym2","Membership.mem","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sym","name":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.setOfPred_mem_sym2._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.setOfPred_mem_sym2","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.sym2","Sym2","Sym2.mk"],"value_dag_size":49,"value_refs":["And","Membership.mem","Multiset","Multiset.instMembership","Multiset.mk_mem_sym2_iff","Multiset.sym2","Sym2","Sym2.mk","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.Sym","name":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.sym2_mono._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.Sym.0.Multiset.sym2_mono","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.Nodup.add_iff._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.Nodup.add_iff","reducibility":null,"statement_dag_size":48,"type_refs":["And","Disjoint","Eq","HAdd.hAdd","Multiset","Multiset.Nodup","Multiset.instAdd","Multiset.instOrderBot","Multiset.instPartialOrder","instHAdd"],"value_dag_size":51,"value_refs":["And","Disjoint","HAdd.hAdd","Multiset","Multiset.Nodup","Multiset.instAdd","Multiset.instOrderBot","Multiset.instPartialOrder","Multiset.nodup_add","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint","reducibility":null,"statement_dag_size":52,"type_refs":["DecidableEq","Disjoint","Eq","Inter.inter","Multiset","Multiset.instInter","Multiset.instOrderBot","Multiset.instPartialOrder","Multiset.instZero","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":62,"value_refs":["DecidableEq","Disjoint","Eq","Eq.symm","Inter.inter","Multiset","Multiset.instInter","Multiset.instOrderBot","Multiset.instPartialOrder","Multiset.instZero","Multiset.inter_eq_zero_iff_disjoint","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint","reducibility":null,"statement_dag_size":36,"type_refs":["DecidableEq","Eq","Multiset","Multiset.count","Nat"],"value_dag_size":41,"value_refs":["DecidableEq","Eq","Multiset","Multiset.count","Multiset.ext","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Min.min","Nat","OfNat.ofNat","Or","instMinNat","instOfNatNat"],"value_dag_size":36,"value_refs":["Eq","Min.min","Nat","Nat.min_eq_zero_iff","OfNat.ofNat","Or","instMinNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_iff_disjoint","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","Max.max","Nat","Nat.instMax","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq","HAdd.hAdd","Max.max","Nat","Nat.add_eq_max_iff","Nat.instMax","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_right_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_right_of_le","reducibility":null,"statement_dag_size":14,"type_refs":["And","Eq"],"value_dag_size":17,"value_refs":["And","and_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_add_left","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_iff_ne._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_iff_ne","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_iff_ne._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_iff_ne","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Not"],"value_dag_size":18,"value_refs":["Not","imp_not_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_map_map._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.disjoint_map_map","reducibility":null,"statement_dag_size":54,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Ne"],"value_dag_size":57,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_iff_ne","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_add_sub_of_add_eq_add._proof_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_add_sub_of_add_eq_add","reducibility":null,"statement_dag_size":83,"type_refs":["DecidableEq","Eq","False","HAdd.hAdd","HSub.hSub","Min.min","Multiset","Multiset.count","Nat","Not","instAddNat","instHAdd","instHSub","instMinNat","instSubNat"],"value_dag_size":1488,"value_refs":["And","And.left","And.right","Bool","Bool.true","Decidable.decide","DecidableEq","Eq","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HSub.hSub","Int","Int.add_one_le_of_lt","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMin","Int.instNegInt","Int.instSub","Int.min_def","Int.natCast_add","Int.natCast_nonneg","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","LT.lt","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.add_congr","Lean.Omega.Int.lt_of_not_le","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_lt_of_lt","Lean.Omega.Int.ofNat_min","Lean.Omega.Int.ofNat_sub_dichotomy","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.add_eval","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.coordinate_eval_1","Lean.Omega.LinearCombo.coordinate_eval_2","Lean.Omega.LinearCombo.coordinate_eval_3","Lean.Omega.LinearCombo.coordinate_eval_4","Lean.Omega.LinearCombo.coordinate_eval_5","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instAdd","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.sub_eval","Lean.Omega.combo_sat'","Lean.Omega.ite_disjunction","Lean.Omega.tidy_sat","List.cons","List.nil","Min.min","Multiset","Multiset.count","Nat","Nat.cast","Nat.lt_or_gt_of_ne","Neg.neg","Not","OfNat.ofNat","Option.none","Option.some","Or.elim","id","instAddNat","instDecidableEqBool","instHAdd","instHSub","instLENat","instLTNat","instMinNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_eq_zero_iff_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_eq_zero_iff_disjoint","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_eq_zero_iff_disjoint._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.inter_eq_zero_iff_disjoint","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.mem_inter.match_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.mem_inter","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And","And.intro","Membership.mem","Multiset","Multiset.instMembership"],"value_dag_size":93,"value_refs":["And","And.casesOn","And.intro","Membership.mem","Multiset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_add._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_add","reducibility":null,"statement_dag_size":66,"type_refs":["And","Eq","HAppend.hAppend","List","List.Nodup","List.instAppend","List.instMembership","Membership.mem","Ne","instHAppendOfAppend"],"value_dag_size":69,"value_refs":["And","HAppend.hAppend","List","List.Nodup","List.instAppend","List.instMembership","List.nodup_append","Membership.mem","Ne","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_add._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_add","reducibility":null,"statement_dag_size":54,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Ne"],"value_dag_size":57,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_iff_ne","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_union.match_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.nodup_union","reducibility":"abbrev","statement_dag_size":47,"type_refs":["And","And.intro","Multiset","Multiset.Nodup"],"value_dag_size":61,"value_refs":["And","And.casesOn","And.intro","Multiset","Multiset.Nodup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.singleton_disjoint._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.singleton_disjoint","reducibility":null,"statement_dag_size":48,"type_refs":["Disjoint","Eq","Membership.mem","Multiset","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not"],"value_dag_size":51,"value_refs":["Disjoint","Membership.mem","Multiset","Multiset.disjoint_left","Multiset.instMembership","Multiset.instOrderBot","Multiset.instPartialOrder","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.union_add_distrib._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.union_add_distrib","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.UnionInter","name":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.union_add_distrib._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.union_add_distrib","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Multiset","Multiset.instAdd","instHAdd"],"value_dag_size":43,"value_refs":["Eq","HAdd.hAdd","Multiset","Multiset.add_left_inj","Multiset.instAdd","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_four.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_four","reducibility":"abbrev","statement_dag_size":223,"type_refs":["Eq","Exists","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":451,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_one.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_one","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Eq","Exists","Exists.intro","Multiset","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":96,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Multiset","Multiset.instSingleton","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_three.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_three","reducibility":"abbrev","statement_dag_size":173,"type_refs":["Eq","Exists","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":300,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_two.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_eq_two","reducibility":"abbrev","statement_dag_size":129,"type_refs":["Eq","Exists","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"],"value_dag_size":201,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Insert.insert","Multiset","Multiset.instInsert","Multiset.instSingleton","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.card_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Multiset","Multiset.cons","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"],"value_dag_size":36,"value_refs":["Eq.symm","Multiset","Multiset.cons","Multiset.cons_zero","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_eq_cons._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_eq_cons","reducibility":null,"statement_dag_size":27,"type_refs":["And","Eq","Exists"],"value_dag_size":31,"value_refs":["And","Eq","Exists","exists_eq_right'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.cons_subset","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.exists_cons_of_mem.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.exists_cons_of_mem","reducibility":"abbrev","statement_dag_size":139,"type_refs":["Eq","Exists","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","instHAppendOfAppend"],"value_dag_size":212,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HAppend.hAppend","List","List.cons","List.instAppend","instHAppendOfAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.exists_mem_of_ne_zero.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.exists_mem_of_ne_zero","reducibility":"abbrev","statement_dag_size":118,"type_refs":["List","List.cons","List.isSetoid","List.nil","Multiset","Multiset.instZero","Ne","OfNat.ofNat","Quot.mk","Setoid.r","Zero.toOfNat0"],"value_dag_size":174,"value_refs":["List","List.casesOn","List.cons","List.isSetoid","List.nil","Multiset","Multiset.instZero","Ne","OfNat.ofNat","Quot.mk","Setoid.r","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.induction_on'.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.induction_on'","reducibility":"abbrev","statement_dag_size":88,"type_refs":["And","And.intro","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":107,"value_refs":["And","And.casesOn","And.intro","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","List.cons","List.nil","Multiset","Multiset.instSingleton","Multiset.ofList","Singleton.singleton"],"value_dag_size":31,"value_refs":["Eq.symm","List.cons","List.nil","Multiset","Multiset.coe_singleton","Multiset.instSingleton","Multiset.ofList","Singleton.singleton"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LE.le","List","List.Subperm","Multiset","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":41,"value_refs":["LE.le","List","List.Subperm","Multiset","Multiset.coe_le","Multiset.instPartialOrder","Multiset.ofList","PartialOrder.toPreorder","Preorder.toLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","Multiset","Multiset.ofList"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","Multiset","Multiset.coe_eq_coe","Multiset.ofList","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","List","List.Perm","List.cons","List.nil"],"value_dag_size":32,"value_refs":["Eq","List","List.Perm","List.cons","List.nil","List.perm_singleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton._simp_1_5","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.le_singleton","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.Subperm","List.cons","List.nil","Or"],"value_dag_size":36,"value_refs":["Eq","List","List.Subperm","List.cons","List.nil","List.subperm_singleton_iff","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_cons_self._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_cons_self","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["And","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","lt_iff_le_and_ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_iff_cons_le.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_iff_cons_le","reducibility":"abbrev","statement_dag_size":94,"type_refs":["Exists","Exists.intro","LE.le","Multiset","Multiset.cons","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":121,"value_refs":["Exists","Exists.casesOn","Exists.intro","LE.le","Multiset","Multiset.cons","Multiset.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton","reducibility":null,"statement_dag_size":42,"type_refs":["And","Eq","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":46,"value_refs":["And","LE.le","LT.lt","Ne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","lt_iff_le_and_ne","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton._simp_1_2","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Or"],"value_dag_size":27,"value_refs":["And","Or","or_and_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton._simp_1_3","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton","reducibility":null,"statement_dag_size":13,"type_refs":["And","Eq","False","Not"],"value_dag_size":13,"value_refs":["And","Not","and_not_self","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton._simp_1_4","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.lt_singleton","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.mem_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.mem_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Multiset","Multiset.cons","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"],"value_dag_size":36,"value_refs":["Eq.symm","Multiset","Multiset.cons","Multiset.cons_zero","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.rel_cons_left.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.rel_cons_left","reducibility":"abbrev","statement_dag_size":184,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Multiset","Multiset.Rel","Multiset.cons"],"value_dag_size":399,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Multiset","Multiset.Rel","Multiset.cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.rel_flip_aux","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset","reducibility":null,"statement_dag_size":38,"type_refs":["Multiset","Multiset.Rel","flip"],"value_dag_size":112,"value_refs":["Multiset","Multiset.Rel","Multiset.Rel.cons","Multiset.Rel.recOn","Multiset.Rel.zero","flip"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_eq_cons_iff._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_eq_cons_iff","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_inj._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_inj","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Multiset","Multiset.cons","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"],"value_dag_size":36,"value_refs":["Eq.symm","Multiset","Multiset.cons","Multiset.cons_zero","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_le.match_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_le","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Eq","Exists","Exists.intro","Multiset","Multiset.cons"],"value_dag_size":88,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Multiset","Multiset.cons"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Multiset.ZeroCons","name":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_subset._simp_1_1","namespace":"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.singleton_subset","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership"],"value_dag_size":46,"value_refs":["HasSubset.Subset","Membership.mem","Multiset","Multiset.instHasSubset","Multiset.instMembership","Multiset.subset_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe.match_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe","reducibility":"abbrev","statement_dag_size":57,"type_refs":["LE.le","Membership.mem","NNRat","OfNat.ofNat","Rat","Rat.instLE","Rat.instOfNat","Set","Set.instMembership","Subtype.mk"],"value_dag_size":76,"value_refs":["LE.le","Membership.mem","NNRat","OfNat.ofNat","Rat","Rat.instLE","Rat.instOfNat","Set","Set.instMembership","Subtype.casesOn","Subtype.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe.match_1_3","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe","reducibility":"abbrev","statement_dag_size":59,"type_refs":["BddAbove","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instLE","Rat.instNNRatCast","Set","Set.image","Set.instMembership","upperBounds"],"value_dag_size":77,"value_refs":["BddAbove","Exists.casesOn","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instLE","Rat.instNNRatCast","Set","Set.image","Set.instMembership","upperBounds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe.match_1_5","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe","reducibility":"abbrev","statement_dag_size":80,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instNNRatCast","Set","Set.image","Set.instMembership"],"value_dag_size":129,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instNNRatCast","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe.match_1_7","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddAbove_coe","reducibility":"abbrev","statement_dag_size":63,"type_refs":["BddAbove","DistribLattice.toLattice","Exists.intro","Lattice.toSemilatticeInf","Membership.mem","NNRat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instMembership","instDistribLatticeOfLinearOrder","instLinearOrderNNRat","upperBounds"],"value_dag_size":80,"value_refs":["BddAbove","DistribLattice.toLattice","Exists.casesOn","Exists.intro","Lattice.toSemilatticeInf","Membership.mem","NNRat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Set","Set.instMembership","instDistribLatticeOfLinearOrder","instLinearOrderNNRat","upperBounds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddBelow_coe.match_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.bddBelow_coe","reducibility":"abbrev","statement_dag_size":79,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instNNRatCast","Set","Set.image","Set.instMembership"],"value_dag_size":126,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","NNRat","NNRat.cast","Rat","Rat.instNNRatCast","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.divNat_inj._simp_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.divNat_inj","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HMul.hMul","Int","Int.instMul","Nat","Nat.cast","Ne","OfNat.ofNat","Rat","instHMul","instNatCastInt","instOfNatNat","mkRat"],"value_dag_size":68,"value_refs":["Eq","HMul.hMul","Int","Int.instMul","Nat","Nat.cast","Ne","OfNat.ofNat","Rat","Rat.mkRat_eq_iff","instHMul","instNatCastInt","instOfNatNat","mkRat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.num_coe._simp_1_2","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.num_coe","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","Int","Int.instLEInt","LE.le","OfNat.ofNat","Rat","Rat.instLE","Rat.instOfNat","Rat.num","instOfNat"],"value_dag_size":35,"value_refs":["Int","Int.instLEInt","LE.le","OfNat.ofNat","Rat","Rat.instLE","Rat.instOfNat","Rat.num","Rat.num_nonneg","instOfNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.toNNRat_coe_nat._simp_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.NNRat.toNNRat_coe_nat","reducibility":null,"statement_dag_size":98,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","LE.le","Nat","Nat.cast","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","True","Zero.toOfNat0","ZeroLEOneClass"],"value_dag_size":102,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","LE.le","Nat","Nat.cast","Nat.cast_nonneg'","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Zero.toOfNat0","ZeroLEOneClass","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.instPosMulMono._simp_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.instPosMulMono","reducibility":null,"statement_dag_size":83,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HSub.hSub","LE","LE.le","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub"],"value_dag_size":89,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddRightMono","AddZero.toAdd","AddZeroClass.toAddZero","HSub.hSub","LE","LE.le","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub","propext","sub_nonneg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_add._simp_1_2","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_add","reducibility":null,"statement_dag_size":102,"type_refs":["AddLeftMono","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LE.le","OfNat.ofNat","Preorder","Preorder.toLE","True","Zero.toOfNat0","instHAdd"],"value_dag_size":108,"value_refs":["AddLeftMono","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","HAdd.hAdd","LE.le","OfNat.ofNat","Preorder","Preorder.toLE","Zero.toOfNat0","add_nonneg","eq_true","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_le_toNNRat_iff._simp_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_le_toNNRat_iff","reducibility":null,"statement_dag_size":46,"type_refs":["DistribLattice.toLattice","Eq","LE.le","Lattice.toSemilatticeInf","NNRat","NNRat.cast","PartialOrder.toPreorder","Preorder.toLE","Rat","Rat.instLE","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat"],"value_dag_size":54,"value_refs":["DistribLattice.toLattice","Eq.symm","LE.le","Lattice.toSemilatticeInf","NNRat","NNRat.cast","NNRat.coe_le_coe","PartialOrder.toPreorder","Preorder.toLE","Rat","Rat.instLE","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_lt_toNNRat_iff'._simp_1_1","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_lt_toNNRat_iff'","reducibility":null,"statement_dag_size":46,"type_refs":["DistribLattice.toLattice","Eq","LT.lt","Lattice.toSemilatticeInf","NNRat","NNRat.cast","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.instLT","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat"],"value_dag_size":54,"value_refs":["DistribLattice.toLattice","Eq.symm","LT.lt","Lattice.toSemilatticeInf","NNRat","NNRat.cast","NNRat.coe_lt_coe","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.instLT","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_mul._simp_1_2","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_mul","reducibility":null,"statement_dag_size":94,"type_refs":["Eq","HMul.hMul","LE.le","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","PosMulMono","Preorder","Preorder.toLE","True","Zero.toOfNat0","instHMul"],"value_dag_size":100,"value_refs":["HMul.hMul","LE.le","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","PosMulMono","Preorder","Preorder.toLE","Zero.toOfNat0","eq_true","instHMul","mul_nonneg"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Defs","name":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_pos._simp_1_2","namespace":"_private.Mathlib.Data.NNRat.Defs.0.Rat.toNNRat_pos","reducibility":null,"statement_dag_size":46,"type_refs":["DistribLattice.toLattice","Eq","LT.lt","Lattice.toSemilatticeInf","NNRat","NNRat.cast","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.instLT","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat"],"value_dag_size":54,"value_refs":["DistribLattice.toLattice","Eq.symm","LT.lt","Lattice.toSemilatticeInf","NNRat","NNRat.cast","NNRat.coe_lt_coe","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.instLT","Rat.instNNRatCast","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder","instLinearOrderNNRat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.IsRat.natCeil._simp_1_1","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.IsRat.natCeil","reducibility":null,"statement_dag_size":134,"type_refs":["DivInvMonoid.toDiv","Eq","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","LE.le","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","PosMulReflectLT","Preorder.toLE","True","Zero.toOfNat0","instHDiv"],"value_dag_size":140,"value_refs":["DivInvMonoid.toDiv","GroupWithZero","GroupWithZero.toDivInvMonoid","GroupWithZero.toMonoidWithZero","HDiv.hDiv","LE.le","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","PosMulReflectLT","Preorder.toLE","Zero.toOfNat0","div_nonneg","eq_true","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_1","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":154,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":157,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_2","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":129,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":132,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_3","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":101,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":104,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_4","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":101,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":104,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_5","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":111,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":114,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_6","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":137,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":140,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._proof_7","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":null,"statement_dag_size":111,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"],"value_dag_size":114,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","PLift","PLift.down","Prod","Prod.fst","Prod.snd","Qq.Quoted","Qq.Quoted.unsafeMk","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._sparseCasesOn_3","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil.match_1","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":"abbrev","statement_dag_size":233,"type_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","List.cons","List.nil","Mathlib.Meta.NormNum.Result","Mathlib.Meta.NormNum.Result'.isBool","Mathlib.Meta.NormNum.Result'.isNNRat","Mathlib.Meta.NormNum.Result'.isNat","Mathlib.Meta.NormNum.Result'.isNegNNRat","Mathlib.Meta.NormNum.Result'.isNegNat","Qq.Quoted","Rat"],"value_dag_size":281,"value_refs":["Bool","Lean.Expr","Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.mkStr4","List.cons","List.nil","Mathlib.Meta.NormNum.Result","Mathlib.Meta.NormNum.Result'.casesOn","Mathlib.Meta.NormNum.Result'.isBool","Mathlib.Meta.NormNum.Result'.isNNRat","Mathlib.Meta.NormNum.Result'.isNat","Mathlib.Meta.NormNum.Result'.isNegNNRat","Mathlib.Meta.NormNum.Result'.isNegNat","Qq.Quoted","Rat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNRat.Floor","name":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil.match_3","namespace":"_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil","reducibility":"abbrev","statement_dag_size":84,"type_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Mathlib.Meta.NormNum.Result","OfNat.ofNat","Qq.Quoted"],"value_dag_size":145,"value_refs":["Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Mathlib.Meta.NormNum.Result","Nat.hasNotBit","OfNat.ofNat","Qq.Quoted","_private.Mathlib.Data.NNRat.Floor.0.Mathlib.Meta.NormNum.evalNatCeil._sparseCasesOn_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Basic","name":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.bddAbove_natCast_image_iff._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.bddAbove_natCast_image_iff","reducibility":null,"statement_dag_size":90,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","FloorSemiring","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.floor","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLENat","instMulZeroClassOfSemiring"],"value_dag_size":97,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","FloorSemiring","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.floor","Nat.le_floor_iff","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Basic","name":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iInf._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iInf","reducibility":null,"statement_dag_size":92,"type_refs":["BddBelow","ConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderInf.toInfSet","ConditionallyCompletePartialOrderSup.toPartialOrder","Eq","LE.le","Nonempty","PartialOrder.toPreorder","Preorder.toLE","Set.range","iInf"],"value_dag_size":99,"value_refs":["BddBelow","ConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderInf.toInfSet","ConditionallyCompletePartialOrderSup.toPartialOrder","LE.le","Nonempty","PartialOrder.toPreorder","Preorder.toLE","Set.range","iInf","le_ciInf_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Basic","name":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iInf._simp_1_2","namespace":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iInf","reducibility":null,"statement_dag_size":66,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","FloorSemiring","LE.le","Nat","Nat.cast","Nat.ceil","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","instLENat"],"value_dag_size":78,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq.symm","FloorSemiring","LE.le","Nat","Nat.cast","Nat.ceil","Nat.ceil_le","NonAssocSemiring.toAddCommMonoidWithOne","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Basic","name":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iSup._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iSup","reducibility":null,"statement_dag_size":100,"type_refs":["BddAbove","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","ConditionallyCompletePartialOrderSup.toSupSet","Eq","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set.range","iSup"],"value_dag_size":106,"value_refs":["BddAbove","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","ConditionallyCompletePartialOrderSup.toSupSet","LE.le","PartialOrder.toPreorder","Preorder.toLE","Set.range","ciSup_le_iff'","iSup","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Basic","name":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iSup._simp_1_2","namespace":"_private.Mathlib.Data.NNReal.Basic.0.NNReal.natCast_iSup","reducibility":null,"statement_dag_size":90,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","FloorSemiring","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.floor","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLENat","instMulZeroClassOfSemiring"],"value_dag_size":103,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq.symm","FloorSemiring","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.floor","Nat.le_floor_iff","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","instLENat","instMulZeroClassOfSemiring","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._proof_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._proof_2","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._sparseCasesOn_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._sparseCasesOn_6","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal.match_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal.match_4","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal.match_6","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal","reducibility":"abbrev","statement_dag_size":178,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":393,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._sparseCasesOn_6","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealNNAbs._sparseCasesOn_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealNNAbs","reducibility":"abbrev","statement_dag_size":29,"type_refs":["Nat.hasNotBit","Option","Option.ctorIdx","Option.some"],"value_dag_size":88,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.rec","Option.some","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealNNAbs.match_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealNNAbs","reducibility":"abbrev","statement_dag_size":116,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Option","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":140,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Nat.hasNotBit","Option","Option.ctorIdx","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealNNAbs._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal._proof_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal._proof_2","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal.match_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalRealToNNReal","reducibility":"abbrev","statement_dag_size":178,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","Option.some","Qq.Quoted","Qq.Quoted.unsafeMk"],"value_dag_size":393,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Level","Lean.Level.succ","Lean.Level.zero","Lean.Literal.natVal","Lean.Name.anonymous","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.Name.str","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Option.some.noConfusion","Qq.Quoted","Qq.Quoted.unsafeMk","_private.Mathlib.Data.NNReal.Defs.0.Mathlib.Meta.Positivity.evalNNRealtoReal._sparseCasesOn_6","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.Bound.coe_lt_coe_of_lt","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.Bound","reducibility":null,"statement_dag_size":28,"type_refs":["LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT"],"value_dag_size":33,"value_refs":["Iff.mpr","LT.lt","NNReal","NNReal.coe_lt_coe","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.Bound.coe_pos_of_pos","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.Bound","reducibility":null,"statement_dag_size":40,"type_refs":["LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0"],"value_dag_size":44,"value_refs":["Iff.mpr","LT.lt","NNReal","NNReal.coe_pos","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe.match_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe","reducibility":"abbrev","statement_dag_size":59,"type_refs":["LE.le","Membership.mem","NNReal","OfNat.ofNat","Real","Real.instLE","Real.instZero","Set","Set.instMembership","Subtype.mk","Zero.toOfNat0"],"value_dag_size":78,"value_refs":["LE.le","Membership.mem","NNReal","OfNat.ofNat","Real","Real.instLE","Real.instZero","Set","Set.instMembership","Subtype.casesOn","Subtype.mk","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe.match_1_3","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe","reducibility":"abbrev","statement_dag_size":56,"type_refs":["BddAbove","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Real.instLE","Set","Set.image","Set.instMembership","upperBounds"],"value_dag_size":74,"value_refs":["BddAbove","Exists.casesOn","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Real.instLE","Set","Set.image","Set.instMembership","upperBounds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe.match_1_5","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe","reducibility":"abbrev","statement_dag_size":77,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Set","Set.image","Set.instMembership"],"value_dag_size":126,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe.match_1_7","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddAbove_coe","reducibility":"abbrev","statement_dag_size":51,"type_refs":["BddAbove","Exists.intro","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","upperBounds"],"value_dag_size":68,"value_refs":["BddAbove","Exists.casesOn","Exists.intro","Membership.mem","NNReal","NNReal.instPartialOrder","PartialOrder.toPreorder","Preorder.toLE","Set","Set.instMembership","upperBounds"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddBelow_coe.match_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.bddBelow_coe","reducibility":"abbrev","statement_dag_size":76,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Set","Set.image","Set.instMembership"],"value_dag_size":123,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","NNReal","NNReal.toReal","Real","Set","Set.image","Set.instMembership"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.iSup_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.iSup_eq_zero","reducibility":null,"statement_dag_size":99,"type_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bot.bot","CanonicallyOrderedAdd","DistribLattice.toLattice","Eq","Lattice.toSemilatticeInf","LinearOrder","OfNat.ofNat","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Zero.toOfNat0","instDistribLatticeOfLinearOrder"],"value_dag_size":106,"value_refs":["AddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Bot.bot","CanonicallyOrderedAdd","DistribLattice.toLattice","Eq.symm","Lattice.toSemilatticeInf","LinearOrder","OfNat.ofNat","OrderBot","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Zero.toOfNat0","bot_eq_zero'","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.iSup_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.iSup_eq_zero","reducibility":null,"statement_dag_size":45,"type_refs":["Bot.bot","Eq","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":55,"value_refs":["Bot.bot","Eq","Eq.symm","LE.le","OrderBot","OrderBot.toBot","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_bot_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.instIsStrictOrderedModule._proof_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.instIsStrictOrderedModule","reducibility":null,"statement_dag_size":110,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","IsStrictOrderedModule","Module","Module.toDistribMulAction","NNReal","NNReal.instPartialOrder","NNReal.instSMulOfReal","NNReal.instZero","PartialOrder","PartialOrder.toPreorder","Real","Real.instMonoid","Real.instPreorder","Real.instZero","Real.semiring","SMulZeroClass.toSMul"],"value_dag_size":101,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DistribMulAction.toDistribSMul","DistribSMul.toSMulZeroClass","IsStrictOrderedModule","Module","Module.toDistribMulAction","Module.toMulActionWithZero","MulActionWithZero.toSMulWithZero","Nonneg.instIsStrictOrderedModule","PartialOrder","PartialOrder.toPreorder","Real","Real.instMonoid","Real.instMonoidWithZero","Real.instPreorder","Real.instZero","Real.partialOrder","Real.semiring","SMulZeroClass.toSMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.lt_iff_exists_rat_btwn.match_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.lt_iff_exists_rat_btwn","reducibility":"abbrev","statement_dag_size":108,"type_refs":["And","And.intro","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","NNReal","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"],"value_dag_size":153,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","DivisionRing.toRatCast","Exists","Exists.casesOn","Exists.intro","Field.toDivisionRing","LT.lt","Lattice.toSemilatticeInf","NNReal","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Real","Real.instField","Real.linearOrder","SemilatticeInf.toPartialOrder","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.lt_iff_exists_rat_btwn.match_1_3","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.lt_iff_exists_rat_btwn","reducibility":"abbrev","statement_dag_size":114,"type_refs":["And","And.intro","Exists","Exists.intro","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"],"value_dag_size":201,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","NNReal","NNReal.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Rat","Rat.cast","Rat.instLE","Rat.instOfNat","Real","Real.instRatCast","Real.toNNReal"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.sSup_of_not_bddAbove._proof_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.NNReal.sSup_of_not_bddAbove","reducibility":null,"statement_dag_size":53,"type_refs":["BddAbove","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","Eq","NNReal","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instPartialOrder","NNReal.instZero","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Set","SupSet.sSup","Zero.toOfNat0"],"value_dag_size":253,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoid.toAddZeroClass","AddMonoidWithOne.toAddMonoid","AddZero.toZero","AddZeroClass.toAddZero","BddAbove","Bot.bot","Classical.byContradiction","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompleteLattice.toLattice","ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice","ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder","ConditionallyCompleteLinearOrderBot.toOrderBot","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toPartialOrder","ConditionallyCompletePartialOrderSup.toSupSet","DistribLattice.toLattice","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Lattice.toSemilatticeInf","Lattice.toSemilatticeSup","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.not_eq_of_eq_false","NNReal","NNReal.instBot","NNReal.instCanonicallyOrderedAdd","NNReal.instConditionallyCompleteLinearOrderBot","NNReal.instLinearOrder","NNReal.instOrderBot","NNReal.instPartialOrder","NNReal.instSemiring","NNReal.instZero","NonAssocSemiring.toAddCommMonoidWithOne","Not","OfNat.ofNat","OrderBot.toBot","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SemilatticeSup.toPartialOrder","Semiring.toNonAssocSemiring","Set","Set.instEmptyCollection","SupSet.sSup","True","True.intro","Zero.toOfNat0","bot_eq_zero'","csSup_empty","csSup_of_not_bddAbove","eq_false","eq_true","id","instDistribLatticeOfLinearOrder","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.natCast_lt_toNNReal._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.natCast_lt_toNNReal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.nnabs_pos._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.nnabs_pos","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0"],"value_dag_size":50,"value_refs":["Eq.symm","LT.lt","NNReal","NNReal.coe_pos","NNReal.instPartialOrder","NNReal.instZero","NNReal.toReal","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","Real.instZero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.nnreal_trichotomy._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.nnreal_trichotomy","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.one_lt_toNNReal._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.one_lt_toNNReal","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_add._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_add","reducibility":null,"statement_dag_size":102,"type_refs":["AddLeftMono","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LE.le","OfNat.ofNat","Preorder","Preorder.toLE","True","Zero.toOfNat0","instHAdd"],"value_dag_size":108,"value_refs":["AddLeftMono","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","HAdd.hAdd","LE.le","OfNat.ofNat","Preorder","Preorder.toLE","Zero.toOfNat0","add_nonneg","eq_true","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_eq_toNNReal_iff._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_eq_toNNReal_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","NNReal","NNReal.toReal","Real"],"value_dag_size":29,"value_refs":["Eq","Eq.symm","NNReal","NNReal.coe_inj","NNReal.toReal","Real","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff'._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff'._simp_1_2","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff'","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","LE.le","NNReal","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE"],"value_dag_size":39,"value_refs":["Eq.symm","LE.le","NNReal","NNReal.coe_le_coe","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff_of_pos._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff_of_pos","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","LE.le","NNReal","NNReal.instPartialOrder","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instZero","Real.toNNReal","Zero.toOfNat0"],"value_dag_size":46,"value_refs":["LE.le","NNReal","NNReal.instPartialOrder","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Real","Real.instLE","Real.instZero","Real.toNNReal","Real.toNNReal_le_toNNReal_iff'","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_lt_natCast'._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_lt_natCast'","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_lt_one._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_lt_one","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Defs","name":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_pos._simp_1_1","namespace":"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_pos","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","LT.lt","NNReal","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT"],"value_dag_size":39,"value_refs":["Eq.symm","LT.lt","NNReal","NNReal.coe_lt_coe","NNReal.instPartialOrder","NNReal.toReal","PartialOrder.toPreorder","Preorder.toLT","Real","Real.instLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.NNReal.Star","name":"_private.Mathlib.Data.NNReal.Star.0.instStarModuleNNRealReal._simp_1","namespace":"_private.Mathlib.Data.NNReal.Star.0.instStarModuleNNRealReal","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","Nonempty"],"value_dag_size":20,"value_refs":["Nonempty","forall_const","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Basic","name":"_private.Mathlib.Data.Nat.Basic.0.Nat.dvd_sub_self_left._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Basic.0.Nat.dvd_sub_self_left","reducibility":null,"statement_dag_size":44,"type_refs":["HSub.hSub","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":635,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instLinearOrder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Basic","name":"_private.Mathlib.Data.Nat.Basic.0.Nat.dvd_sub_self_left._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Basic.0.Nat.dvd_sub_self_left","reducibility":null,"statement_dag_size":50,"type_refs":["HSub.hSub","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","Ne","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":659,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Basic","name":"_private.Mathlib.Data.Nat.Basic.0.Nat.pow_left_injective._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Basic.0.Nat.pow_left_injective","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Basic","name":"_private.Mathlib.Data.Nat.Basic.0.Nat.pow_right_injective._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Basic.0.Nat.pow_right_injective","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BinaryRec","name":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.binaryRec_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.binaryRec_eq","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BinaryRec","name":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_eq_zero_iff","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":32,"value_refs":["Eq.symm","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BinaryRec","name":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_lt_two_pow_succ_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_lt_two_pow_succ_iff","reducibility":null,"statement_dag_size":65,"type_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","Iff","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":874,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Nat.pow_one","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.iff_eq","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.mulR","Nat.Internal.Linear.Expr.var","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BinaryRec","name":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_lt_two_pow_succ_iff._proof_1_2","namespace":"_private.Mathlib.Data.Nat.BinaryRec.0.Nat.bit_lt_two_pow_succ_iff","reducibility":null,"statement_dag_size":67,"type_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","Iff","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":948,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Nat.pow_one","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.iff_eq","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.mulR","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congr","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BitIndices","name":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sorted._simp_1_1","namespace":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sorted","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List","List.Pairwise","List.SortedLT","Preorder","Preorder.toLT"],"value_dag_size":39,"value_refs":["LT.lt","List","List.Pairwise","List.SortedLT","List.sortedLT_iff_pairwise","Preorder","Preorder.toLT","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BitIndices","name":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sorted._simp_1_2","namespace":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sorted","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.Pairwise","List.map"],"value_dag_size":48,"value_refs":["List","List.Pairwise","List.map","List.pairwise_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BitIndices","name":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sum_map_two_pow._simp_1_1","namespace":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sum_map_two_pow","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":42,"value_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.lt_iff_add_one_le","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.BitIndices","name":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sum_map_two_pow._simp_1_2","namespace":"_private.Mathlib.Data.Nat.BitIndices.0.Nat.bitIndices_sum_map_two_pow","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.binaryRec_decreasing._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.binaryRec_decreasing","reducibility":null,"statement_dag_size":24,"type_refs":["LT.lt","Nat","Nat.div2","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":512,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.div2","Nat.div2.eq_1","Nat.instDiv","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":142,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":132,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add'","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Bool","Bool.false","Bool.true","Nat"],"value_dag_size":44,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":142,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":132,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_add","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Bool","Bool.false","Bool.true","Nat"],"value_dag_size":44,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le","reducibility":null,"statement_dag_size":51,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":314,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le","reducibility":null,"statement_dag_size":34,"type_refs":["HMul.hMul","LE.le","Nat","OfNat.ofNat","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":271,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_le","reducibility":"abbrev","statement_dag_size":49,"type_refs":["Bool","Bool.false","Bool.true","LE.le","Nat","instLENat"],"value_dag_size":60,"value_refs":["Bool","Bool.casesOn","Bool.false","Bool.true","LE.le","Nat","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit","reducibility":null,"statement_dag_size":34,"type_refs":["HMul.hMul","LT.lt","Nat","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":354,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","HMul.hMul","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":392,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit","reducibility":null,"statement_dag_size":27,"type_refs":["HMul.hMul","LE.le","Nat","OfNat.ofNat","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":116,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit","reducibility":null,"statement_dag_size":42,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":120,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_ne_zero","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HMul.hMul","Nat","Ne","Not","OfNat.ofNat","instHMul","instMulNat","instOfNatNat"],"value_dag_size":219,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMul","Int.instNegInt","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_ne_zero._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bit_ne_zero","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":95,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LT.lt","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat","Nat.boddDiv2.match_1","Prod","Prod.mk"],"value_dag_size":38,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat","Nat.boddDiv2.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1","reducibility":null,"statement_dag_size":40,"type_refs":["Bool","Bool.false","Bool.true","Eq","Nat","Nat.boddDiv2.match_1","Prod","Prod.mk"],"value_dag_size":38,"value_refs":["Bool","Bool.false","Bool.true","Eq.refl","Nat","Nat.boddDiv2.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_1","reducibility":"abbrev","statement_dag_size":28,"type_refs":["Bool","Bool.false","Bool.true","Nat","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["Nat.boddDiv2.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3.eq_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.boddDiv2.match_3","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.boddDiv2.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3.eq_2","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.boddDiv2.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.boddDiv2.match_3","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3.splitter","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.boddDiv2.match_3","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.boddDiv2.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bodd_add._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bodd_add","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","instAddNat","instHAdd"],"value_dag_size":32,"value_refs":["Eq.symm","HAdd.hAdd","Nat","Nat.add_assoc","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.bodd_eq_one_and_ne_zero.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.bodd_eq_one_and_ne_zero","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_add","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_false.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_false","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_sub._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_sub","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HDiv.hDiv","Nat","Nat.div2","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq.symm","HDiv.hDiv","Nat","Nat.div2","Nat.div2_val","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_sub.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft'_sub","reducibility":"abbrev","statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":195,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LE.le","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft_sub._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.shiftLeft_sub","reducibility":null,"statement_dag_size":25,"type_refs":["Bool.false","Eq","HShiftLeft.hShiftLeft","Nat","Nat.instShiftLeft","Nat.shiftLeft'","instHShiftLeftOfShiftLeft"],"value_dag_size":29,"value_refs":["Bool.false","Eq.symm","HShiftLeft.hShiftLeft","Nat","Nat.instShiftLeft","Nat.shiftLeft'","Nat.shiftLeft'_false","instHShiftLeftOfShiftLeft"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.Nat.testBit_bit_succ._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Bits.0.Nat.testBit_bit_succ","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HDiv.hDiv","Nat","Nat.div2","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq.symm","HDiv.hDiv","Nat","Nat.div2","Nat.div2_val","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"]}
+{"definition_height":10,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0._aux_Mathlib_Data_Nat_Bits___macroRules__private_Mathlib_Data_Nat_Bits_0_termBxor_1","namespace":"_private.Mathlib.Data.Nat.Bits.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.Macro"],"value_dag_size":190,"value_refs":["Applicative.toPure","Bind.bind","Bool","Bool.true","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Eq","Lean.Macro.Context","Lean.Macro.Exception","Lean.Macro.Exception.unsupportedSyntax","Lean.Macro.State","Lean.Macro.instMonadQuotationMacroM","Lean.Macro.instMonadRefMacroM","Lean.MacroM","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.Name.mkStr2","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.Preresolved","Lean.Syntax.Preresolved.decl","Lean.Syntax.getArg","Lean.Syntax.ident","Lean.Syntax.isOfKind","Lean.SyntaxNodeKind","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.addMacroScope","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","String","String.toRawSubstring'","instDecidableEqBool","instMonadExceptOfMonadExceptOf","instOfNatNat","ite"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0._aux_Mathlib_Data_Nat_Bits___unexpand_Bool_xor_1","namespace":"_private.Mathlib.Data.Nat.Bits.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.PrettyPrinter.Unexpander"],"value_dag_size":179,"value_refs":["Applicative.toPure","Bind.bind","Bool.false","Bool.or","EStateM","EStateM.instMonad","EStateM.instMonadExceptOfOfBacktrackable","EStateM.nonBacktrackable","Lean.MacroScope","Lean.MonadQuotation.getContext","Lean.MonadQuotation.getCurrMacroScope","Lean.MonadQuotation.toMonadRef","Lean.MonadRef.mkInfoFromRefPos","Lean.Name","Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.Name.mkStr1","Lean.PrettyPrinter.UnexpandM","Lean.PrettyPrinter.instMonadQuotationUnexpandM","Lean.SourceInfo","Lean.Syntax","Lean.Syntax.atom","Lean.Syntax.isOfKind","Lean.Syntax.node1","Lean.SyntaxNodeKind","Lean.TSyntax","Lean.TSyntax.mk","Lean.TSyntax.raw","Lean.withRef","List.cons","List.nil","Monad.toBind","MonadExcept.throw","Nat","OfNat.ofNat","PUnit","Pure.pure","ReaderT.instApplicativeOfMonad","ReaderT.instMonad","ReaderT.instMonadExceptOf","Unit","Unit.unit","cond","instMonadExceptOfMonadExceptOf","instOfNatNat"]}
+{"definition_height":2,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Bits","name":"_private.Mathlib.Data.Nat.Bits.0.termBxor","namespace":"_private.Mathlib.Data.Nat.Bits.0","reducibility":"regular","statement_dag_size":1,"type_refs":["Lean.ParserDescr"],"value_dag_size":42,"value_refs":["Lean.Name.anonymous","Lean.Name.mkNum","Lean.Name.mkStr","Lean.ParserDescr.node","Lean.ParserDescr.symbol","Nat","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise.eq_1","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise","reducibility":null,"statement_dag_size":149,"type_refs":["Bool","Bool.false","Bool.true","Decidable.decide","Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","Nat","Nat.bitwise","Nat.instDiv","Nat.instMod","OfNat.ofNat","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHDiv","instHMod","instOfNatNat","ite"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Bool.true","Decidable.decide","Eq","Eq.refl","Eq.trans","HAdd.hAdd","HDiv.hDiv","HMod.hMod","Nat","Nat.bitwise","Nat.instDiv","Nat.instMod","OfNat.ofNat","_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise.eq_def","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHDiv","instHMod","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise.eq_def","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise","reducibility":null,"statement_dag_size":149,"type_refs":["Bool","Bool.false","Bool.true","Decidable.decide","Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","Nat","Nat.bitwise","Nat.instDiv","Nat.instMod","OfNat.ofNat","instAddNat","instDecidableEqBool","instDecidableEqNat","instHAdd","instHDiv","instHMod","instOfNatNat","ite"],"value_dag_size":1,"value_refs":["_private.Init.Data.Nat.Bitwise.Basic.0.Nat.bitwise.eq_def"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_bit'._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_bit'","reducibility":null,"statement_dag_size":43,"type_refs":["Bool","Bool.true","Eq","HMod.hMod","Nat","Nat.bit","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":46,"value_refs":["Bool","Bool.true","Eq","HMod.hMod","Nat","Nat.bit","Nat.bit_mod_two_eq_one_iff","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_bit'._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_bit'","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HDiv.hDiv","Nat","Nat.div2","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq.symm","HDiv.hDiv","Nat","Nat.div2","Nat.div2_val","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_zero_right._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.bitwise_zero_right","reducibility":null,"statement_dag_size":33,"type_refs":["Decidable","Eq","ite"],"value_dag_size":39,"value_refs":["Decidable","Eq","ite","ite_eq_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","HAdd.hAdd","HMod.hMod","Iff","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instOfNatNat"],"value_dag_size":2489,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_false","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Even","HMod.hMod","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq","Even","HMod.hMod","Nat","Nat.even_iff","Nat.instMod","OfNat.ofNat","instAddNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor.eq_1","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor","reducibility":null,"statement_dag_size":19,"type_refs":["Bool","Eq","Nat","Nat.bitwise","Nat.xor","bne","instBEqOfDecidableEq","instDecidableEqBool"],"value_dag_size":8,"value_refs":["Eq.refl","Nat","Nat.xor"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAdd.hAdd","HMod.hMod","Iff","Nat","Nat.instMod","OfNat.ofNat","instAddNat","instHAdd","instHMod","instOfNatNat"],"value_dag_size":1431,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._proof_1_7","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","HMod.hMod","Iff","Nat","Nat.instMod","Not","OfNat.ofNat","instAddNat","instHAdd","instHMod","instOfNatNat"],"value_dag_size":1385,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":41,"type_refs":["Bool","Bool.false","Eq","HMod.hMod","Nat","Nat.instMod","Nat.testBit","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":43,"value_refs":["Bool","Bool.false","Eq","HMod.hMod","Nat","Nat.instMod","Nat.mod_two_eq_zero_iff_testBit_zero","Nat.testBit","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HMod.hMod","HXor.hXor","Iff","Nat","Nat.instMod","Nat.instXorOp","Not","OfNat.ofNat","instHMod","instHXorOfXorOp","instOfNatNat"],"value_dag_size":62,"value_refs":["Eq","HMod.hMod","HXor.hXor","Iff","Nat","Nat.instMod","Nat.instXorOp","Nat.xor_mod_two_eq_one","Not","OfNat.ofNat","instHMod","instHXorOfXorOp","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":35,"type_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq"],"value_dag_size":41,"value_refs":["BEq","BEq.beq","Bool","Bool.true","Eq","LawfulBEq","beq_iff_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":27,"type_refs":["Bool","Decidable","Decidable.decide","Eq","Iff"],"value_dag_size":33,"value_refs":["Bool","Decidable","Decidable.decide","Eq","Iff","decide_eq_decide","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_mod_two_eq","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HMod.hMod","Nat","Nat.instMod","Ne","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":43,"value_refs":["Eq","HMod.hMod","Nat","Nat.instMod","Nat.mod_two_ne_zero","Ne","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_one_of_even._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_one_of_even","reducibility":null,"statement_dag_size":81,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":86,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Distrib.toMul","Eq.symm","HAdd.hAdd","HMul.hMul","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","OfNat.ofNat","instHAdd","instHMul","instOfNatAtLeastTwo","instOfNatNat","mul_two"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_one_of_odd._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_one_of_odd","reducibility":null,"statement_dag_size":152,"type_refs":["Bool","Bool.false","Bool.true","Decidable.decide","Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HSub.hSub","Nat","Nat.instDiv","Nat.instMod","Nat.instSemiring","Odd","OfNat.ofNat","True","bne","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instDecidableEqNat","instDecidableTrue","instHAdd","instHDiv","instHMod","instHSub","instOfNatNat","instSubNat","ite"],"value_dag_size":993,"value_refs":["Bool","Bool.false","Bool.not","Bool.not_eq_false","Bool.true","Classical.byContradiction","Decidable.decide","Decidable.decide.congr_simp","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.norm_eq","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instDiv","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.bne_eq_decide_not_eq","Lean.Grind.bool_eq_to_prop","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_of_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Simproc.add_eq_gt","Nat.Simproc.add_sub_le","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.mod_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ctorIdx","Nat.decLe","Nat.decLt","Nat.instDiv","Nat.instMod","Nat.instSemiring","Nat.odd_iff","NatCast.natCast","Neg.neg","Not","Odd","OfNat.ofNat","True","bne","congr","congrArg","congrFun'","decide_eq_true_eq","decide_not","eagerReduce","eq_false'","eq_self","eq_true","id","instAddNat","instBEqOfDecidableEq","instDecidableEqBool","instDecidableEqNat","instDecidableNot","instDecidableTrue","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instLTNat","instLawfulBEqBool","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","noConfusion_of_Nat","not_decide_eq_true","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Bitwise","name":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_range.match_1_1","namespace":"_private.Mathlib.Data.Nat.Bitwise.0.Nat.xor_range","reducibility":"abbrev","statement_dag_size":68,"type_refs":["Eq","Fin","Fin.instOfNat","Nat","Nat.instNeZeroSucc","OfNat.ofNat","instOfNatNat"],"value_dag_size":932,"value_refs":["Eq","Eq.ndrec","Eq.refl","False","False.elim","Fin","Fin.casesOn","Fin.instOfNat","Fin.mk","HAdd.hAdd","HEq","HEq.refl","LT.lt","Nat","Nat.Internal.elimOffset","Nat.add","Nat.casesOn","Nat.ctorIdx","Nat.instNeZeroSucc","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Cast.Basic","name":"_private.Mathlib.Data.Nat.Cast.Basic.0.Nat.cast_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Basic.0.Nat.cast_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Cast.Basic","name":"_private.Mathlib.Data.Nat.Cast.Basic.0.eq_natCast'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Basic.0.eq_natCast'","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":221,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.succ","Nat.unaryCast.match_1","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.Nat.unaryCast.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.unaryCast.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.nsmul_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.nsmul_one","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four","reducibility":null,"statement_dag_size":68,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":72,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat","one_add_one_eq_two"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four","reducibility":null,"statement_dag_size":36,"type_refs":["AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Eq","Nat","Nat.cast","OfNat.ofNat","One.toOfNat1","instOfNatNat"],"value_dag_size":40,"value_refs":["AddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Eq.symm","Nat","Nat.cast","Nat.cast_one","OfNat.ofNat","One.toOfNat1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four","reducibility":null,"statement_dag_size":80,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":84,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat","three_add_one_eq_four"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Defs","name":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Cast.Defs.0.two_add_two_eq_four","reducibility":null,"statement_dag_size":80,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat"],"value_dag_size":84,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","OfNat.ofNat","One.toOfNat1","instHAdd","instOfNatAtLeastTwo","instOfNatNat","two_add_one_eq_three"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.NeZero","name":"_private.Mathlib.Data.Nat.Cast.NeZero.0.NeZero.one_le._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.NeZero.0.NeZero.one_le","reducibility":null,"statement_dag_size":33,"type_refs":["LE.le","Nat","Ne","OfNat.ofNat","Zero.ofOfNat0","Zero.toOfNat0","instLENat","instOfNatNat"],"value_dag_size":144,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","Ne","Not","OfNat.ofNat","True","True.intro","Zero.ofOfNat0","Zero.toOfNat0","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"_private.Mathlib.Data.Nat.Cast.Order.Basic.0.Nat.cast_nonpos._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Basic.0.Nat.cast_nonpos","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Iff","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":93,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Iff","LE.le","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.le_zero_eq","Not","OfNat.ofNat","True","congrArg","congrFun'","eq_self","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Basic","name":"_private.Mathlib.Data.Nat.Cast.Order.Basic.0.Nat.cast_pos'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Basic.0.Nat.cast_pos'","reducibility":null,"statement_dag_size":142,"type_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LT.lt","Nat","Nat.cast","NeZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","True","Zero.toOfNat0","ZeroLEOneClass","instHAdd"],"value_dag_size":147,"value_refs":["AddLeftMono","AddMonoid.toAddSemigroup","AddMonoid.toAddZeroClass","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","AddSemigroup.toAdd","AddZero.toZero","AddZeroClass.toAddZero","HAdd.hAdd","LT.lt","Nat","Nat.cast","Nat.cast_add_one_pos","NeZero","OfNat.ofNat","One.toOfNat1","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","ZeroLEOneClass","eq_true","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Field","name":"_private.Mathlib.Data.Nat.Cast.Order.Field.0.Nat.cast_inv_le_one._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Field.0.Nat.cast_inv_le_one","reducibility":null,"statement_dag_size":67,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Eq","IsOrderedRing","LE.le","MulZeroClass.toZero","Nat","Nat.cast","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","True","Zero.toOfNat0","instMulZeroClassOfSemiring"],"value_dag_size":70,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","IsOrderedRing","LE.le","MulZeroClass.toZero","Nat","Nat.cast","Nat.cast_nonneg","NonAssocSemiring.toAddCommMonoidWithOne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Semiring","Semiring.toNonAssocSemiring","Zero.toOfNat0","eq_true","instMulZeroClassOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Cast.Order.Field","name":"_private.Mathlib.Data.Nat.Cast.Order.Field.0.Nat.cast_inv_le_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Field.0.Nat.cast_inv_le_one","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.cast_eq_neg_cast._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.cast_eq_neg_cast","reducibility":null,"statement_dag_size":74,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd"],"value_dag_size":78,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","eq_neg_iff_add_eq_zero","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.cast_eq_neg_cast._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.cast_eq_neg_cast","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.neg_cast_eq_cast._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.neg_cast_eq_cast","reducibility":null,"statement_dag_size":74,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd"],"value_dag_size":78,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHAdd","neg_eq_iff_add_eq_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.Order.Ring","name":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.neg_cast_eq_cast._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Cast.Order.Ring.0.Nat.neg_cast_eq_cast","reducibility":null,"statement_dag_size":55,"type_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq","HAdd.hAdd","Nat","Nat.cast","instAddNat","instHAdd"],"value_dag_size":61,"value_refs":["AddMonoid.toAddSemigroup","AddMonoidWithOne","AddMonoidWithOne.toAddMonoid","AddMonoidWithOne.toNatCast","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","Nat","Nat.cast","Nat.cast_add","instAddNat","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Icc._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Icc","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Preorder","Set.Ici","Set.OrdConnected","True"],"value_dag_size":24,"value_refs":["Preorder","Set.Ici","Set.OrdConnected","Set.ordConnected_Ici","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ici._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ici","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","IsUpperSet","Preorder","Preorder.toLE","Set.Ici","True"],"value_dag_size":27,"value_refs":["IsUpperSet","Preorder","Preorder.toLE","Set.Ici","eq_true","isUpperSet_Ici"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ico._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ico","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Preorder","Set.Ici","Set.OrdConnected","True"],"value_dag_size":24,"value_refs":["Preorder","Set.Ici","Set.OrdConnected","Set.ordConnected_Ici","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioc._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioc","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Preorder","Set.Ici","Set.OrdConnected","True"],"value_dag_size":24,"value_refs":["Preorder","Set.Ici","Set.OrdConnected","Set.ordConnected_Ici","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioi._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioi","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","IsUpperSet","Preorder","Preorder.toLE","Set.Ici","True"],"value_dag_size":27,"value_refs":["IsUpperSet","Preorder","Preorder.toLE","Set.Ici","eq_true","isUpperSet_Ici"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Cast.SetInterval","name":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioo._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ioo","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","Preorder","Set.Ici","Set.OrdConnected","True"],"value_dag_size":24,"value_refs":["Preorder","Set.Ici","Set.OrdConnected","Set.ordConnected_Ici","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1","reducibility":null,"statement_dag_size":87,"type_refs":["Eq","Function.onFun","List","List.Pairwise","List.cons","List.nil","Nat","Nat.Coprime","Nat.chineseRemainderOfList.match_1"],"value_dag_size":85,"value_refs":["Eq.refl","Function.onFun","List","List.Pairwise","List.cons","List.nil","Nat","Nat.Coprime","Nat.chineseRemainderOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1","reducibility":null,"statement_dag_size":105,"type_refs":["Eq","Function.onFun","List","List.Pairwise","List.cons","List.nil","Nat","Nat.Coprime","Nat.chineseRemainderOfList.match_1"],"value_dag_size":101,"value_refs":["Eq.refl","Function.onFun","List","List.Pairwise","List.cons","List.nil","Nat","Nat.Coprime","Nat.chineseRemainderOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList.match_1","reducibility":"abbrev","statement_dag_size":82,"type_refs":["Function.onFun","List","List.Pairwise","List.cons","List.nil","Nat","Nat.Coprime"],"value_dag_size":1,"value_refs":["Nat.chineseRemainderOfList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod._simp_1_5","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","List","List.instMembership","List.prod","Membership.mem","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NoZeroDivisors","Nontrivial","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":86,"value_refs":["Eq","List","List.instMembership","List.prod","List.prod_eq_zero_iff","Membership.mem","MonoidWithZero","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulOneClass","MulZeroOneClass.toMulZeroClass","NoZeroDivisors","Nontrivial","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod._simp_1_6","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod._simp_1_7","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_lt_prod","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_modEq_unique._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.chineseRemainderOfList_modEq_unique","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nat","Nat.ModEq","OfNat.ofNat","True","instOfNatNat"],"value_dag_size":22,"value_refs":["Nat","Nat.ModEq","Nat.modEq_one","OfNat.ofNat","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nat","Nat.ModEq","OfNat.ofNat","True","instOfNatNat"],"value_dag_size":22,"value_refs":["Nat","Nat.ModEq","Nat.modEq_one","OfNat.ofNat","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","List","List.instMembership","List.prod","Membership.mem","Nat","Nat.Coprime","Nat.instOne","instMulNat"],"value_dag_size":37,"value_refs":["List","List.instMembership","List.prod","Membership.mem","Nat","Nat.Coprime","Nat.coprime_list_prod_right_iff","Nat.instOne","instMulNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","List","List.instMembership","List.map","Membership.mem"],"value_dag_size":62,"value_refs":["And","Eq","Exists","List","List.instMembership","List.map","List.mem_map","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_4","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Exists","Exists.intro"],"value_dag_size":39,"value_refs":["Exists","Exists.intro","forall_exists_index","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_5","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_6","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff","reducibility":null,"statement_dag_size":37,"type_refs":["Eq"],"value_dag_size":43,"value_refs":["Eq","forall_apply_eq_imp_iff₂","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ChineseRemainder","name":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_prod_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_prod_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nat","Nat.ModEq","OfNat.ofNat","True","instOfNatNat"],"value_dag_size":22,"value_refs":["Nat","Nat.ModEq","Nat.modEq_one","OfNat.ofNat","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.add_one_mul_choose_eq.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.add_one_mul_choose_eq","reducibility":"abbrev","statement_dag_size":44,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":75,"value_refs":["Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Eq","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":479,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.refl","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":48,"value_refs":["Eq.refl","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq.refl","Nat","Nat.choose.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose.match_1","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.choose.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_one_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_one_iff","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Iff","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.choose","Nat.instLinearOrder","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","instOfNatNat"],"value_dag_size":967,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.choose","Nat.choose_mono","Nat.choose_succ_self_right","Nat.choose_zero_right","Nat.instLinearOrder","Nat.instPreorder","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_one_iff._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_one_iff","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","Iff","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.choose","Nat.instLinearOrder","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","instOfNatNat"],"value_dag_size":714,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.choose","Nat.choose_eq_zero_of_lt","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","True","congr","congrArg","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instNatCastNat","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_zero_of_lt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_eq_zero_of_lt","reducibility":"abbrev","statement_dag_size":78,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":124,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_middle._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_middle","reducibility":null,"statement_dag_size":67,"type_refs":["HDiv.hDiv","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instDiv","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","instHDiv","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":767,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instDiv","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_middle_of_le_half_left","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat","reducibility":null,"statement_dag_size":39,"type_refs":["HDiv.hDiv","LE.le","Nat","Nat.choose","Nat.instDiv","OfNat.ofNat","instHDiv","instLENat","instOfNatNat"],"value_dag_size":110,"value_refs":["HAdd.hAdd","HDiv.hDiv","LE.le","LE.le.trans","LT.lt","Nat","Nat.choose","Nat.choose_le_succ_of_lt_half_left","Nat.decreasingInduction","Nat.instDiv","Nat.instPreorder","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instLENat","instLTNat","instOfNatNat","le_refl"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_succ._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_succ","reducibility":null,"statement_dag_size":23,"type_refs":["LE.le","Nat","Nat.choose","Nat.succ","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":336,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_norm_expr","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.choose","Nat.choose_zero_right","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_succ._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_le_succ","reducibility":null,"statement_dag_size":36,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.choose","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":381,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.choose","Nat.choose_succ_succ","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HMul.hMul","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.choose","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","instHMul","instHSub","instLENat","instMulNat","instSubNat"],"value_dag_size":1593,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.mul_eq_zero_left","Int.Internal.Linear.mul_eq_zero_right","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Internal.Linear.of_var_eq","Int.Internal.Linear.var_eq","Int.Nonneg.mul","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.choose","Nat.choose_eq_zero_of_lt","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul","reducibility":null,"statement_dag_size":88,"type_refs":["Eq","HMul.hMul","HSub.hSub","LE.le","LinearOrder.toPartialOrder","Nat","Nat.choose","Nat.factorial","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instHMul","instHSub","instLENat","instMulNat","instSubNat"],"value_dag_size":1686,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.le_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.choose","Nat.choose_mul_factorial_mul_factorial","Nat.factorial","Nat.instLinearOrder","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","HMul.hMul","HSub.hSub","LE.le","LinearOrder.toPartialOrder","Nat","Nat.choose","Nat.factorial","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instHMul","instHSub","instLENat","instMulNat","instSubNat"],"value_dag_size":1683,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.choose","Nat.factorial","Nat.instLinearOrder","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add","reducibility":null,"statement_dag_size":64,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","Nat.choose","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":426,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.mul_congr","Nat.ToInt.of_diseq","Nat.choose","Nat.factorial","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":168,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.factorial","Not","OfNat.ofNat","True","congrArg","congrFun'","eagerReduce","eq_self","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add","reducibility":null,"statement_dag_size":63,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":373,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.norm_int","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.factorial","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","Nat.choose","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":424,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.norm_int","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.choose","Nat.factorial","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_add","reducibility":null,"statement_dag_size":71,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","Nat.choose","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":395,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.norm_int","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.choose","Nat.factorial","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_factorial_mul_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_factorial_mul_factorial","reducibility":"abbrev","statement_dag_size":78,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":121,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_right._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_mul_right","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LT.lt","Nat","Nat.choose","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq","LT.lt","Nat","Nat.choose","Nat.choose_eq_zero_iff","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_ne_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_ne_zero_iff","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LT.lt","Nat","Nat.choose","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq","LT.lt","Nat","Nat.choose","Nat.choose_eq_zero_iff","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_pos.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_pos","reducibility":"abbrev","statement_dag_size":77,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":122,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_self._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_self","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","Nat","Nat.choose","OfNat.ofNat","instOfNatNat"],"value_dag_size":65,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Nat","Nat.choose","Nat.choose_zero_right","Not","OfNat.ofNat","True","True.intro","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_self._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_self","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.choose","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":438,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.true_imp_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.choose","Nat.choose_eq_zero_of_lt","Nat.choose_succ_succ","Nat.decLe","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","congr","congrArg","eagerReduce","id","implies_congr","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_succ_self_right.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_succ_self_right","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.multichoose_eq.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.multichoose_eq","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Basic","name":"_private.Mathlib.Data.Nat.Choose.Basic.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Choose.Basic.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Central","name":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.centralBinom_lt_four_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.centralBinom_lt_four_pow","reducibility":null,"statement_dag_size":37,"type_refs":["HMul.hMul","LT.lt","Nat","Ne","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":309,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Central","name":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.centralBinom_strictMono._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.centralBinom_strictMono","reducibility":null,"statement_dag_size":33,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.centralBinom","Nat.instPreorder","OfNat.ofNat","Preorder.toLT","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":750,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.true_imp_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.centralBinom","Nat.centralBinom.eq_1","Nat.choose","Nat.choose_pos","Nat.choose_succ_succ","Nat.instPreorder","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLT","True","congr","congrArg","congrFun'","eagerReduce","id","implies_congr","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Central","name":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.four_pow_le_two_mul_self_mul_centralBinom.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Central.0.Nat.four_pow_le_two_mul_self_mul_centralBinom","reducibility":"abbrev","statement_dag_size":88,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":161,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","HMul.hMul","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":388,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":39,"value_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul","reducibility":null,"statement_dag_size":54,"type_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":59,"value_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.filter_eq_empty_iff","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_of_lt_three_mul","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_prime_pow_add_factorization._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_prime_pow_add_factorization","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_prime_pow_add_factorization._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_choose_prime_pow_add_factorization","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_factorial","reducibility":"abbrev","statement_dag_size":78,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.log","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":107,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.log","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_factorial_mul_succ._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_factorial_mul_succ","reducibility":null,"statement_dag_size":45,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":415,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Nonneg.add","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_le_factorization_choose_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.factorization_le_factorization_choose_add","reducibility":"abbrev","statement_dag_size":96,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":155,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.prod_pow_factorization_centralBinom._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.prod_pow_factorization_centralBinom","reducibility":null,"statement_dag_size":27,"type_refs":["HMul.hMul","LE.le","Nat","OfNat.ofNat","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":116,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Factorization","name":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.sub_one_mul_factorization_factorial._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Factorization.0.Nat.sub_one_mul_factorization_factorial","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","Finset.range","Finset.sum","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","List.sum","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.digits","Nat.instAddCommMonoid","Nat.instDiv","Nat.instMonoid","Nat.instMulZeroClass","Nat.log","Nat.succ","OfNat.ofNat","instAddNat","instHDiv","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":103,"value_refs":["Eq.symm","Finset.range","Finset.sum","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","List.sum","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.digits","Nat.instAddCommMonoid","Nat.instDiv","Nat.instMonoid","Nat.instMulZeroClass","Nat.log","Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits","Nat.succ","OfNat.ofNat","instAddNat","instHDiv","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":43,"type_refs":["AddGroupWithOne.toIntCast","CommRing.toRing","Eq","Int","Int.ModEq","Int.cast","Nat","Nat.cast","Ring.toAddGroupWithOne","ZMod","ZMod.commRing","instNatCastInt"],"value_dag_size":53,"value_refs":["AddGroupWithOne.toIntCast","CommRing.toRing","Eq","Eq.symm","Int","Int.ModEq","Int.cast","Nat","Nat.cast","Ring.toAddGroupWithOne","ZMod","ZMod.commRing","ZMod.intCast_eq_intCast_iff","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":77,"type_refs":["DFunLike.coe","Eq","Nat","Polynomial","Polynomial.coeff","Polynomial.map","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring"],"value_dag_size":86,"value_refs":["DFunLike.coe","Eq.symm","Nat","Polynomial","Polynomial.coeff","Polynomial.coeff_map","Polynomial.map","RingHom","RingHom.instFunLike","Semiring","Semiring.toNonAssocSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HMul.hMul","HPow.hPow","Monoid","Monoid.toNPow","NPow.toPow","Nat","instHMul","instHPow","instMulNat"],"value_dag_size":56,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Monoid","Monoid.toNPow","NPow.toPow","Nat","instHMul","instHPow","instMulNat","pow_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":87,"type_refs":["And","Eq","Finset","Finset.instSProd","Finset.instSetLike","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership"],"value_dag_size":92,"value_refs":["And","Finset","Finset.instSProd","Finset.instSetLike","Finset.mem_product","Membership.mem","Prod","Prod.fst","Prod.snd","SProd.sprod","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div._simp_1_8","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":null,"statement_dag_size":61,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq","HMul.hMul","Nat","Nat.cast","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"],"value_dag_size":67,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toMul","Eq.symm","HMul.hMul","Nat","Nat.cast","Nat.cast_mul","NonAssocSemiring","NonAssocSemiring.toAddCommMonoidWithOne","NonAssocSemiring.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistrib","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div.match_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mod_mul_choose_div","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Nat","Prod","Prod.mk"],"value_dag_size":33,"value_refs":["Nat","Prod","Prod.casesOn","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mul_prod_range_choose._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mul_prod_range_choose","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Int","Int.ModEq","True"],"value_dag_size":15,"value_refs":["Int","Int.ModEq","Int.ModEq.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mul_prod_range_choose.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_choose_mul_prod_range_choose","reducibility":"abbrev","statement_dag_size":19,"type_refs":["Nat","Nat.succ","Nat.zero","Unit"],"value_dag_size":31,"value_refs":["Nat","Nat.casesOn","Nat.succ","Nat.zero","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_prod_range_choose._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_modEq_prod_range_choose","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Int","Int.ModEq","True"],"value_dag_size":15,"value_refs":["Int","Int.ModEq","Int.ModEq.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_mul_mul_modEq_choose._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_mul_mul_modEq_choose","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","IsBotZeroClass","LT.lt","NeZero","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","True","Zero","Zero.toOfNat0"],"value_dag_size":59,"value_refs":["IsBotZeroClass","LT.lt","NeZero","NeZero.pos","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_mul_mul_modEq_choose._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_mul_mul_modEq_choose","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Int","Int.ModEq","True"],"value_dag_size":15,"value_refs":["Int","Int.ModEq","Int.ModEq.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_pow_mul_pow_mul_modEq_choose._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.choose_pow_mul_pow_mul_modEq_choose","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Int","Int.ModEq","True"],"value_dag_size":15,"value_refs":["Int","Int.ModEq","Int.ModEq.refl","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.eq_pow_multiplicity_of_choose_modEq_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.eq_pow_multiplicity_of_choose_modEq_zero","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","Finset","Finset.Icc","Finset.instSetLike","HMul.hMul","HPow.hPow","HSub.hSub","LT.lt","Membership.mem","Monoid.toNPow","Monoid.toSemigroup","NPow.toPow","Nat","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instPreorder","Ne","OfNat.ofNat","Semigroup.toMul","SetLike.instMembership","instHMul","instHPow","instHSub","instLTNat","instOfNatNat","instSubNat","multiplicity"],"value_dag_size":1311,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.mul_eq_zero_left","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Internal.Linear.of_var_eq","Int.Internal.Linear.var_eq","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Monoid.toNPow","Monoid.toSemigroup","NPow.toPow","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.pow_congr","Nat.decLe","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instPreorder","Nat.le_of_dvd","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","Semigroup.toMul","SemilatticeInf.toPartialOrder","SetLike.instMembership","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","ite","ite_cond_eq_true","ite_congr","multiplicity","of_decide_eq_true","of_eq_false","of_eq_true","pow_multiplicity_dvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.eq_pow_multiplicity_of_choose_modEq_zero._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.eq_pow_multiplicity_of_choose_modEq_zero","reducibility":null,"statement_dag_size":37,"type_refs":["False","HAdd.hAdd","LE.le","Nat","Nat.instMonoid","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat","multiplicity"],"value_dag_size":107,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","False","HAdd.hAdd","LE.le","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.instMonoid","OfNat.ofNat","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instOfNatNat","multiplicity"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_minFac_of_isPrimePow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_minFac_of_isPrimePow","reducibility":null,"statement_dag_size":64,"type_refs":["And","CommMonoidWithZero.toMonoidWithZero","Eq","HSub.hSub","IsPrimePow","LE.le","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instCommMonoidWithZero","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","Zero.toOfNat0","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1054,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","CommMonoidWithZero.toMonoidWithZero","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","IsPrimePow","IsPrimePow.two_le","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.instCommMonoidWithZero","Nat.instPreorder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Zero.toOfNat0","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow","reducibility":null,"statement_dag_size":51,"type_refs":["Finset","Finset.Icc","Finset.instSetLike","HSub.hSub","LT.lt","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","SetLike.instMembership","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":760,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.decLe","Nat.instLocallyFiniteOrder","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congrArg","congrFun'","eagerReduce","eq_false","eq_true","eq_true_of_decide","id","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_false","of_eq_true","true_and"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow","reducibility":null,"statement_dag_size":82,"type_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Eq","Finset","Finset.gcd","Finset.instSetLike","Membership.mem","MonoidWithZero.toSemigroupWithZero","NormalizedGCDMonoid","SemigroupWithZero.toSemigroup","SetLike.instMembership","semigroupDvd"],"value_dag_size":89,"value_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Finset","Finset.dvd_gcd_iff","Finset.gcd","Finset.instSetLike","Membership.mem","MonoidWithZero.toSemigroupWithZero","NormalizedGCDMonoid","SemigroupWithZero.toSemigroup","SetLike.instMembership","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.gcd_choose_eq_one_of_not_isPrimePow","reducibility":null,"statement_dag_size":27,"type_refs":["Dvd.dvd","Eq","Nat","Nat.ModEq","Nat.instDvd","OfNat.ofNat","instOfNatNat"],"value_dag_size":35,"value_refs":["Dvd.dvd","Eq.symm","Nat","Nat.ModEq","Nat.instDvd","Nat.modEq_zero_iff_dvd","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_dvd_gcd_choose_of_isPrimePow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_dvd_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.Icc","Finset.instSetLike","HSub.hSub","Membership.mem","Nat","Nat.instLocallyFiniteOrder","Nat.instPreorder","Not","OfNat.ofNat","SetLike.instMembership","instHSub","instOfNatNat","instSubNat"],"value_dag_size":278,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instLocallyFiniteOrder","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","SetLike.instMembership","True","eagerReduce","eq_true","id","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_dvd_gcd_choose_of_isPrimePow._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_dvd_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","Finset","Finset.Icc","Finset.instSetLike","HPow.hPow","HSub.hSub","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instPreorder","Nat.minFac","Not","OfNat.ofNat","SetLike.instMembership","instHPow","instHSub","instOfNatNat","instSubNat"],"value_dag_size":945,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instPreorder","Nat.minFac","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":40,"type_refs":["HSub.hSub","LT.lt","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":957,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Icc","Finset.instSetLike","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.minFac_sq_ndvd_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":64,"type_refs":["And","CommMonoidWithZero.toMonoidWithZero","Eq","HSub.hSub","IsPrimePow","LE.le","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.instCommMonoidWithZero","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","Zero.toOfNat0","instHSub","instOfNatNat","instSubNat"],"value_dag_size":1054,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","CommMonoidWithZero.toMonoidWithZero","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","IsPrimePow","IsPrimePow.two_le","LE.le","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_and","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Nat","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.instCommMonoidWithZero","Nat.instPreorder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","Zero.toOfNat0","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":50,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.mem_primeFactors","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":82,"type_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Eq","Finset","Finset.gcd","Finset.instSetLike","Membership.mem","MonoidWithZero.toSemigroupWithZero","NormalizedGCDMonoid","SemigroupWithZero.toSemigroup","SetLike.instMembership","semigroupDvd"],"value_dag_size":89,"value_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Finset","Finset.dvd_gcd_iff","Finset.gcd","Finset.instSetLike","Membership.mem","MonoidWithZero.toSemigroupWithZero","NormalizedGCDMonoid","SemigroupWithZero.toSemigroup","SetLike.instMembership","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Lucas","name":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Lucas.0.Choose.primeFactors_gcd_choose_of_isPrimePow","reducibility":null,"statement_dag_size":27,"type_refs":["Dvd.dvd","Eq","Nat","Nat.ModEq","Nat.instDvd","OfNat.ofNat","instOfNatNat"],"value_dag_size":35,"value_refs":["Dvd.dvd","Eq.symm","Nat","Nat.ModEq","Nat.instDvd","Nat.modEq_zero_iff_dvd","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_eq_sum_piAntidiag._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_eq_sum_piAntidiag","reducibility":null,"statement_dag_size":94,"type_refs":["CommMonoid","CommMonoid.toCommSemigroup","CommMonoid.toMonoid","CommSemigroup.toCommMagma","Commute.all","Eq","Finset","Finset.instSetLike","Finset.noncommProd","Finset.prod","Membership.mem","Ne","Set","Set.instMembership","SetLike.coe"],"value_dag_size":101,"value_refs":["CommMonoid","CommMonoid.toCommSemigroup","CommMonoid.toMonoid","CommSemigroup.toCommMagma","Commute.all","Eq.symm","Finset","Finset.instSetLike","Finset.noncommProd","Finset.noncommProd_eq_prod","Finset.prod","Membership.mem","Ne","Set","Set.instMembership","SetLike.coe"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_eq_sum_piAntidiag_of_commute._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_eq_sum_piAntidiag_of_commute","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_of_commute._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_of_commute","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Subsingleton","True"],"value_dag_size":25,"value_refs":["Eq","Subsingleton","True","eq_iff_true_of_subsingleton","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_of_commute._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finset.sum_pow_of_commute","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finsupp.multinomial_eq_of_support_subset._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Finsupp.multinomial_eq_of_support_subset","reducibility":null,"statement_dag_size":96,"type_refs":["CommMonoid.toMonoid","DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","Nat","Nat.factorial","Nat.instCommMonoid","Nat.instMulZeroClass","Not","OfNat.ofNat","One.toOfNat1","SetLike.instMembership"],"value_dag_size":362,"value_refs":["Bool","Bool.true","Classical.byContradiction","CommMonoid.toMonoid","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.RArray","Lean.RArray.leaf","Membership.mem","Monoid.toMulOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroClass.toZero","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.factorial","Nat.factorial_eq_one","Nat.instCommMonoid","Nat.instMulZeroClass","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","One.toOfNat1","SetLike.instMembership","Zero.toOfNat0","eagerReduce","eq_false","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.List.toFinsupp_sum.match_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.List.toFinsupp_sum","reducibility":"abbrev","statement_dag_size":31,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":45,"value_refs":["List","List.casesOn","List.cons","List.nil","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial._proof_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial","reducibility":null,"statement_dag_size":74,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":77,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial._proof_2","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial","reducibility":null,"statement_dag_size":61,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":64,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","PLift","PLift.down","Qq.Quoted","Qq.QuotedDefEq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial._sparseCasesOn_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial.match_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial.match_4","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.evalMultinomial","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial._simp_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HMul.hMul","Semigroup","Semigroup.toMul","instHMul"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","mul_assoc"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial_pos","reducibility":null,"statement_dag_size":90,"type_refs":["Eq","HMul.hMul","LT.lt","MulPosReflectLT","MulPosStrictMono","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Preorder","Preorder.toLT","Zero.toOfNat0","instHMul"],"value_dag_size":98,"value_refs":["HMul.hMul","LT.lt","MulPosReflectLT","MulPosStrictMono","MulZeroClass","MulZeroClass.toMul","MulZeroClass.toZero","OfNat.ofNat","Preorder","Preorder.toLT","Zero.toOfNat0","instHMul","mul_pos_iff_of_pos_right","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial_singleton._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Multiset.multinomial_singleton","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Multiset","Multiset.cons","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"],"value_dag_size":36,"value_refs":["Eq.symm","Multiset","Multiset.cons","Multiset.cons_zero","Multiset.instSingleton","Multiset.instZero","OfNat.ofNat","Singleton.singleton","Zero.toOfNat0"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter","reducibility":null,"statement_dag_size":102,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Nat","Nat.instAddCommMonoid","Not","OfNat.ofNat","SDiff.sdiff","SetLike.instMembership","Zero.toOfNat0","instOfNatNat"],"value_dag_size":231,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Membership.mem","Nat","Nat.instAddCommMonoid","Not","OfNat.ofNat","SDiff.sdiff","SetLike.instMembership","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter","reducibility":null,"statement_dag_size":102,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Nat","Nat.instAddCommMonoid","Not","OfNat.ofNat","SDiff.sdiff","SetLike.instMembership","Zero.toOfNat0","instOfNatNat"],"value_dag_size":231,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Membership.mem","Nat","Nat.instAddCommMonoid","Not","OfNat.ofNat","SDiff.sdiff","SetLike.instMembership","True","True.intro","Zero.toOfNat0","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter._proof_1_6","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_eq_on_inter","reducibility":null,"statement_dag_size":81,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":207,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.iff_eq","Membership.mem","Nat","Not","SetLike.instMembership","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_sdiff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_sdiff","reducibility":null,"statement_dag_size":70,"type_refs":["DecidableEq","Eq","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","LE.le","Membership.mem","Nat","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","instOfNatNat"],"value_dag_size":263,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instPartialOrder","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Finset.subset_iff","Iff","LE.le","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Membership.mem","Nat","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","SDiff.sdiff","SetLike.instMembership","True","True.intro","eq_true","id","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Multinomial","name":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_sdiff._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Multinomial.0.Nat.multinomial_congr_of_sdiff","reducibility":null,"statement_dag_size":68,"type_refs":["DecidableEq","Eq","Finset","Finset.instInter","Finset.instSetLike","Inter.inter","Membership.mem","Nat","SetLike.instMembership"],"value_dag_size":197,"value_refs":["And","Classical.byContradiction","DecidableEq","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.iff_eq","Membership.mem","Nat","Not","SetLike.instMembership","True","True.intro","eq_false","eq_true","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Finset.prod_antidiagonal_pow_choose_succ._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Finset.prod_antidiagonal_pow_choose_succ","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Finset.sum_powerset_neg_one_pow_card._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Finset.sum_powerset_neg_one_pow_card","reducibility":null,"statement_dag_size":36,"type_refs":["EmptyCollection.emptyCollection","Eq","Finset","Finset.card","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":45,"value_refs":["EmptyCollection.emptyCollection","Eq","Eq.symm","Finset","Finset.card","Finset.card_eq_zero","Finset.instEmptyCollection","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Int.alternating_sum_range_choose_eq_choose._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Int.alternating_sum_range_choose_eq_choose","reducibility":null,"statement_dag_size":108,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.instAddCommMonoid","Int.instMonoid","Int.instMul","Int.instNegInt","Monoid.toNPow","NPow.toPow","Nat","Nat.choose","Nat.succ","NatCast.natCast","Neg.neg","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instNatCastInt","instOfNat","instOfNatNat"],"value_dag_size":497,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulR","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.norm_eq","Int.instAdd","Int.instAddCommMonoid","Int.instMonoid","Int.instMul","Int.instNatPow","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Int.pow_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.Semiring.toAdd","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.cast","Nat.choose","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instNatCastInt","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.choose_middle_le_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.choose_middle_le_pow","reducibility":null,"statement_dag_size":69,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","HAdd.hAdd","HMul.hMul","LE.le","Nat","Nat.choose","Nat.instAddCommMonoid","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":143,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Lean.Grind.intro_with_eq","Nat","Nat.Simproc.add_eq_gt","Nat.choose","Nat.decLt","Nat.instAddCommMonoid","Nat.instPreorder","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","Preorder.toLE","Zero.toOfNat0","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_Icc_choose._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_Icc_choose","reducibility":null,"statement_dag_size":46,"type_refs":["HAdd.hAdd","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":337,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_Icc_choose._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_Icc_choose","reducibility":null,"statement_dag_size":41,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.instPartialOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":272,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.instPartialOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway","reducibility":null,"statement_dag_size":46,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":166,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.decLe","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway","reducibility":null,"statement_dag_size":55,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":783,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.toAdd","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Simproc.add_sub_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_choose_halfway","reducibility":null,"statement_dag_size":44,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":163,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.decLe","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_multichoose._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.Nat.sum_range_multichoose","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Finset.range","Finset.sum","HAdd.hAdd","Nat","Nat.choose","Nat.instAddCommMonoid","Nat.multichoose","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":550,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.instSetLike","Finset.range","Finset.sum","Finset.sum_congr","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.forall_imp_eq_or","Lean.Grind.intro_with_eq","Lean.Grind.true_imp_eq","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_le","Nat.choose","Nat.choose_symm_of_eq_add","Nat.decLe","Nat.instAddCommMonoid","Nat.multichoose","Nat.multichoose_eq","Nat.sum_range_add_choose","Not","OfNat.ofNat","Or","Or.casesOn","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Sum","name":"_private.Mathlib.Data.Nat.Choose.Sum.0.sub_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Sum.0.sub_pow","reducibility":null,"statement_dag_size":65,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":722,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.decLe","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Choose.Vandermonde","name":"_private.Mathlib.Data.Nat.Choose.Vandermonde.0.Nat.add_choose_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Choose.Vandermonde.0.Nat.add_choose_eq","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","True"],"value_dag_size":11,"value_refs":["True","imp_true_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_iff_forall._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_iff_forall","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_injective._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_injective","reducibility":null,"statement_dag_size":22,"type_refs":["LT.lt","Nat","Ne","Not","instLTNat"],"value_dag_size":483,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.nat_eq","Lean.Grind.instCommRingInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_lt_count_succ_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_lt_count_succ_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","HAdd.hAdd","Iff","LT.lt","Nat","Nat.count","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":858,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.count","Nat.count_succ","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_monotone._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_monotone","reducibility":null,"statement_dag_size":44,"type_refs":["DecidablePred","HAdd.hAdd","LE.le","Nat","Nat.count","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":319,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.count","Nat.count_succ","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_ne_iff_exists._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_ne_iff_exists","reducibility":null,"statement_dag_size":42,"type_refs":["DecidablePred","Eq","LT.lt","Nat","Nat.count","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":47,"value_refs":["DecidablePred","Eq","LT.lt","Nat","Nat.count","Nat.count_iff_forall_not","Not","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ","reducibility":null,"statement_dag_size":53,"type_refs":["DecidablePred","Eq","HAdd.hAdd","Nat","Nat.count","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat","ite"],"value_dag_size":636,"value_refs":["Bool","Bool.true","Classical.byContradiction","Decidable.decide","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HAppend.hAppend","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.countP","List.countP_append","List.countP_cons","List.countP_nil","List.instAppend","List.nil","List.range","List.range_succ","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.count","Nat.count.eq_1","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","decide_eq_true_eq","eagerReduce","id","instAddNat","instDecidableEqBool","instHAdd","instHAppendOfAppend","instNatCastInt","instOfNat","instOfNatNat","ite","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ_eq_count_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ_eq_count_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","HAdd.hAdd","Iff","Nat","Nat.count","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":632,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.count","Nat.count_succ","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ_eq_succ_count_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.count_succ_eq_succ_count_iff","reducibility":null,"statement_dag_size":45,"type_refs":["DecidablePred","Eq","HAdd.hAdd","Iff","Nat","Nat.count","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":642,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.mul","Lean.Grind.CommRing.Stepwise.simp","Lean.Grind.CommRing.Stepwise.unsat_eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.instIsCharPQOfAddRightCancel","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsCharPNatOfNat","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.count","Nat.count_succ","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.exists_of_count_lt_count._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.exists_of_count_lt_count","reducibility":null,"statement_dag_size":74,"type_refs":["AddSemigroup.toAdd","And","HAdd.hAdd","LE.le","LT.lt","Nat","Nat.instAddSemigroup","Nat.instPreorder","OfNat.ofNat","Preorder.toLE","Preorder.toLT","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":556,"value_refs":["AddSemigroup.toAdd","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instAddSemigroup","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_true","false_or","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Count","name":"_private.Mathlib.Data.Nat.Count.0.Nat.exists_of_count_lt_count._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Count.0.Nat.exists_of_count_lt_count","reducibility":null,"statement_dag_size":52,"type_refs":["And","Eq","LE.le","LT.lt","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","Set","Set.Ico","Set.instMembership"],"value_dag_size":57,"value_refs":["And","LE.le","LT.lt","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","Set","Set.Ico","Set.instMembership","Set.mem_Ico","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.digits.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.digits.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1","reducibility":null,"statement_dag_size":96,"type_refs":["Eq","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":221,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.digitsAux0.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.digitsAux0.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_def'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_def'","reducibility":"abbrev","statement_dag_size":66,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":102,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_lt_base'._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_lt_base'","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_lt_base'._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_lt_base'","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_zero_of_eq_zero.match_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_zero_of_eq_zero","reducibility":"abbrev","statement_dag_size":109,"type_refs":["Eq","List","List.Mem","List.Mem.head","List.Mem.tail","List.cons","List.instMembership","Membership.mem","Nat","Nat.instSemiring","Nat.ofDigits","OfNat.ofNat","instOfNatNat"],"value_dag_size":613,"value_refs":["Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","HEq","HEq.refl","List","List.Mem","List.Mem.casesOn","List.Mem.head","List.Mem.tail","List.casesOn","List.cons","List.cons.noConfusion","List.ctorIdx","List.instMembership","List.nil","Membership.mem","Nat","Nat.instSemiring","Nat.ofDigits","OfNat.ofNat","eq_of_heq","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_zero_succ'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digits_zero_succ'","reducibility":"abbrev","statement_dag_size":56,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":76,"value_refs":["HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.lt_base_pow_length_digits._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.lt_base_pow_length_digits","reducibility":null,"statement_dag_size":59,"type_refs":["Eq","HAdd.hAdd","HPow.hPow","LT.lt","List.length","Monoid.toNPow","NPow.toPow","Nat","Nat.digits","Nat.instMonoid","OfNat.ofNat","True","instAddNat","instHAdd","instHPow","instLTNat","instOfNatNat"],"value_dag_size":59,"value_refs":["HAdd.hAdd","HPow.hPow","LT.lt","List.length","Monoid.toNPow","NPow.toPow","Nat","Nat.digits","Nat.instMonoid","Nat.lt_base_pow_length_digits'","OfNat.ofNat","eq_true","instAddNat","instHAdd","instHPow","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","List","List.cons","List.nil","Nat","Nat.ofDigits.match_1","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Nat.ofDigits.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","List","List.cons","List.nil","Nat","Nat.ofDigits.match_1","Unit"],"value_dag_size":39,"value_refs":["Eq.refl","List","List.cons","List.nil","Nat","Nat.ofDigits.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits.match_1","reducibility":"abbrev","statement_dag_size":27,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":1,"value_refs":["Nat.ofDigits.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.length","List.nil","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["Eq","List","List.length","List.length_eq_zero_iff","List.nil","Nat","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_add_ofDigits_eq_ofDigits_zipWith_of_length_eq","reducibility":null,"statement_dag_size":41,"type_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","instHAdd"],"value_dag_size":47,"value_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","add_left_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_inj_of_len_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_inj_of_len_eq","reducibility":null,"statement_dag_size":41,"type_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","instHAdd"],"value_dag_size":47,"value_refs":["Add","Eq","HAdd.hAdd","IsRightCancelAdd","add_left_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_inj_of_len_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_inj_of_len_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","instHAdd"],"value_dag_size":46,"value_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","add_right_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_lt_base_pow_length'._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_lt_base_pow_length'","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","True","instLENat","instOfNatNat"],"value_dag_size":21,"value_refs":["LE.le","Nat","Nat.zero_le","OfNat.ofNat","eq_true","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_lt_base_pow_length._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_lt_base_pow_length","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","HAdd.hAdd","HPow.hPow","LT.lt","List","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.instSemiring","Nat.ofDigits","OfNat.ofNat","True","instAddNat","instHAdd","instHPow","instLTNat","instOfNatNat"],"value_dag_size":82,"value_refs":["HAdd.hAdd","HPow.hPow","LT.lt","List","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.instSemiring","Nat.ofDigits","Nat.ofDigits_lt_base_pow_length'","OfNat.ofNat","eq_true","instAddNat","instHAdd","instHPow","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_monotone._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.ofDigits_monotone","reducibility":null,"statement_dag_size":52,"type_refs":["Add","AddLeftMono","AddLeftReflectLE","Eq","HAdd.hAdd","LE","LE.le","instHAdd"],"value_dag_size":60,"value_refs":["Add","AddLeftMono","AddLeftReflectLE","HAdd.hAdd","LE","LE.le","add_le_add_iff_left","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.repr.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.repr","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Nat","Nat.repr","Nat.toDigits","OfNat.ofNat","String","String.ofList","instOfNatNat"],"value_dag_size":9,"value_refs":["Eq.refl","Nat","Nat.repr","String"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore","reducibility":null,"statement_dag_size":26,"type_refs":["Char","Eq","List","Nat","Nat.toDigitsCore","OfNat.ofNat","instOfNatNat"],"value_dag_size":25,"value_refs":["Char","Eq.refl","List","Nat","Nat.toDigitsCore","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore","reducibility":null,"statement_dag_size":73,"type_refs":["Char","Eq","HDiv.hDiv","HMod.hMod","List","List.cons","Nat","Nat.digitChar","Nat.instDiv","Nat.instMod","Nat.succ","Nat.toDigitsCore","OfNat.ofNat","instDecidableEqNat","instHDiv","instHMod","instOfNatNat","ite"],"value_dag_size":22,"value_refs":["Char","Eq.refl","List","Nat","Nat.succ","Nat.toDigitsCore"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.eq_def","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore","reducibility":null,"statement_dag_size":93,"type_refs":["Char","Eq","HDiv.hDiv","HMod.hMod","List","List.cons","Nat","Nat.digitChar","Nat.instDiv","Nat.instMod","Nat.toDigitsCore","OfNat.ofNat","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","instDecidableEqNat","instHDiv","instHMod","instOfNatNat","ite"],"value_dag_size":583,"value_refs":["Char","Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","HDiv.hDiv","HMod.hMod","List","List.cons","Nat","Nat.below","Nat.brecOn","Nat.brecOn.eq","Nat.brecOn.go","Nat.digitChar","Nat.instDiv","Nat.instMod","Nat.rec","Nat.succ","Nat.toDigitsCore","Nat.toDigitsCore._f","OfNat.ofNat","PProd","PUnit","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1.splitter","congrArg","id","instDecidableEqNat","instHDiv","instHMod","instOfNatNat","ite"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Char","Eq","List","Nat","Nat.succ","OfNat.ofNat","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","instOfNatNat"],"value_dag_size":51,"value_refs":["Char","Eq.refl","List","Nat","Nat.succ","OfNat.ofNat","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1","reducibility":null,"statement_dag_size":59,"type_refs":["Char","Eq","List","Nat","Nat.succ","OfNat.ofNat","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","instOfNatNat"],"value_dag_size":55,"value_refs":["Char","Eq.refl","List","Nat","Nat.succ","OfNat.ofNat","_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1","reducibility":"abbrev","statement_dag_size":44,"type_refs":["Char","List","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_length._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_length","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","True","instLENat","instOfNatNat"],"value_dag_size":21,"value_refs":["LE.le","Nat","Nat.zero_le","OfNat.ofNat","eq_true","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_length._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_length","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Defs","name":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_lens_eq._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_lens_eq","reducibility":null,"statement_dag_size":110,"type_refs":["Char","Eq","HAdd.hAdd","HDiv.hDiv","HMod.hMod","List","List.cons","List.length","Nat","Nat.digitChar","Nat.instDiv","Nat.instMod","Nat.toDigitsCore","OfNat.ofNat","instAddNat","instDecidableEqNat","instHAdd","instHDiv","instHMod","instOfNatNat","ite"],"value_dag_size":663,"value_refs":["Bool","Bool.true","Char","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.length","List.length_cons","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.digitChar","Nat.instDiv","Nat.instMod","Nat.toDigitsCore","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableEqNat","instHAdd","instHDiv","instHMod","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","List","List.alternatingSum.match_1","List.cons","List.nil","Unit","Unit.unit"],"value_dag_size":51,"value_refs":["Eq.refl","List","List.alternatingSum.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","List","List.alternatingSum.match_1","List.cons","List.nil","Unit"],"value_dag_size":56,"value_refs":["Eq.refl","List","List.alternatingSum.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","List","List.alternatingSum.match_1","List.cons","List.nil","Unit"],"value_dag_size":62,"value_refs":["Eq.refl","List","List.alternatingSum.match_1","List.cons","List.nil","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.alternatingSum.match_1","reducibility":"abbrev","statement_dag_size":43,"type_refs":["List","List.cons","List.nil","Unit"],"value_dag_size":1,"value_refs":["List.alternatingSum.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.consFixedLengthDigits.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.consFixedLengthDigits","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","Finset","Finset.image","LT.lt","List","List.cons","List.consFixedLengthDigits","List.fixedLengthDigits","Nat","OfNat.ofNat","instDecidableEqList","instDecidableEqNat","instLTNat","instOfNatNat"],"value_dag_size":34,"value_refs":["Eq.refl","Finset","LT.lt","List","List.consFixedLengthDigits","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits._proof_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits","reducibility":null,"statement_dag_size":98,"type_refs":["And","Eq","Function.Injective","HPow.hPow","LT.lt","List","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.instSemiring","Nat.mapsTo_ofDigits","Nat.ofDigits","OfNat.ofNat","Set.Elem","Set.MapsTo.restrict","Set.ofPred","instHPow","instLTNat","instOfNatNat"],"value_dag_size":119,"value_refs":["And","Eq","Function.Injective","HPow.hPow","Iff.mpr","LT.lt","List","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.injOn_ofDigits","Nat.instMonoid","Nat.instSemiring","Nat.mapsTo_ofDigits","Nat.ofDigits","OfNat.ofNat","Set.Elem","Set.InjOn","Set.MapsTo.restrict","Set.MapsTo.restrict_inj","Set.ofPred","instHPow","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits","reducibility":null,"statement_dag_size":121,"type_refs":["And","Eq","Finset","Fintype.ofInjective","HPow.hPow","LT.lt","List","List.fixedLengthDigits","List.instMembership","List.length","Membership.mem","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.instSemiring","Nat.mapsTo_ofDigits","Nat.ofDigits","OfNat.ofNat","Set.Elem","Set.MapsTo.restrict","Set.fintypeLTNat","Set.ofPred","Set.toFinset","_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits._proof_1","instHPow","instLTNat","instOfNatNat"],"value_dag_size":31,"value_refs":["Eq.refl","Finset","LT.lt","List","List.fixedLengthDigits","Nat","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_one","reducibility":null,"statement_dag_size":74,"type_refs":["And","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.range","Iff","LT.lt","List","List.cons","List.instMembership","List.nil","Membership.mem","Nat","SetLike.instMembership","instDecidableEqList","instDecidableEqNat","instLTNat"],"value_dag_size":1322,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Finset.mem_range","Finset.range","HAdd.hAdd","Iff","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.of_nat_eq","Lean.Grind._simp_1","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.forall_forall_or","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_exists","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.or_of_and_eq_false","Lean.RArray.branch","Lean.RArray.leaf","List","List.cons","List.instMembership","List.mem_cons","List.nil","List.not_mem_nil","Membership.mem","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","Std.IsLinearOrder.toIsLinearPreorder","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_self","eq_true","false_or","forall_congr","forall_not_of_not_exists","id","implies_congr","instAddNat","instDecidableEqList","instDecidableEqNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true","true_or"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion","reducibility":null,"statement_dag_size":77,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":83,"value_refs":["And","DecidableEq","Exists","Finset","Finset.biUnion","Finset.instSetLike","Finset.mem_biUnion","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_succ_eq_disjiUnion","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LT.lt","List","List.length","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":38,"value_refs":["LT.lt","List","List.length","List.ne_nil_iff_length_pos","List.nil","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_zero._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_zero","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","LT.lt","List","List.instMembership","List.nil","Membership.mem","Nat","instLTNat"],"value_dag_size":207,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","List","List.instMembership","List.nil","List.not_mem_nil","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.pairwiseDisjoint_consFixedLengthDigits.match_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.pairwiseDisjoint_consFixedLengthDigits","reducibility":"abbrev","statement_dag_size":109,"type_refs":["Exists.intro","Finset","Finset.Nonempty","Finset.instInter","Finset.instSetLike","Inter.inter","LT.lt","List","List.consFixedLengthDigits","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instDecidableEqList","instDecidableEqNat","instLTNat","instOfNatNat"],"value_dag_size":131,"value_refs":["Exists.casesOn","Exists.intro","Finset","Finset.Nonempty","Finset.instInter","Finset.instSetLike","Inter.inter","LT.lt","List","List.consFixedLengthDigits","Membership.mem","Nat","OfNat.ofNat","SetLike.instMembership","instDecidableEqList","instDecidableEqNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.sum_fixedLengthDigits_sum._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.sum_fixedLengthDigits_sum","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Iff","Set","Set.InjOn","True"],"value_dag_size":45,"value_refs":["Eq","Iff","Set","Set.InjOn","Set.injOn_of_eq_iff_eq","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.base_pow_length_digits_le._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.base_pow_length_digits_le","reducibility":null,"statement_dag_size":80,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","List.length","Monoid.toNPow","NPow.toPow","Nat","Nat.digits","Nat.instMonoid","Ne","OfNat.ofNat","True","instAddNat","instHAdd","instHMul","instHPow","instLENat","instMulNat","instOfNatNat"],"value_dag_size":81,"value_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","List.length","Monoid.toNPow","NPow.toPow","Nat","Nat.base_pow_length_digits_le'","Nat.digits","Nat.instMonoid","Ne","OfNat.ofNat","eq_true","instAddNat","instHAdd","instHMul","instHPow","instLENat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digitsAppend.eq_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digitsAppend","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAppend.hAppend","HSub.hSub","List","List.instAppend","List.length","List.replicate","Nat","Nat.digits","Nat.digitsAppend","OfNat.ofNat","instHAppendOfAppend","instHSub","instOfNatNat","instSubNat"],"value_dag_size":16,"value_refs":["Eq.refl","List","Nat","Nat.digitsAppend"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_append_zeroes_append_digits._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_append_zeroes_append_digits","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","List","Nat","Nat.digits"],"value_dag_size":28,"value_refs":["Eq","List","Nat","Nat.digits","Nat.digits_inj_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_append_zeroes_append_digits._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_append_zeroes_append_digits","reducibility":null,"statement_dag_size":40,"type_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","instHAdd"],"value_dag_size":46,"value_refs":["Add","Eq","HAdd.hAdd","IsLeftCancelAdd","add_right_inj","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_two_eq_bits._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.digits_two_eq_bits","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.getD_digits._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.getD_digits","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","HAdd.hAdd","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":80,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LT.lt","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.head!_digits._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.head!_digits","reducibility":null,"statement_dag_size":34,"type_refs":["Eq","LT.lt","Nat","Ne","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":278,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.ofDigits_neg_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.ofDigits_neg_one","reducibility":"abbrev","statement_dag_size":36,"type_refs":["List","List.cons","List.nil","Nat","Unit"],"value_dag_size":62,"value_refs":["List","List.casesOn","List.cons","List.nil","Nat","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Digits.Lemmas","name":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digits._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Digits.Lemmas.0.Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digits","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq.symm","HAdd.hAdd","Nat","Nat.one_add","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist.triangle_inequality._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist.triangle_inequality","reducibility":null,"statement_dag_size":48,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":12737,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_add_add_left._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_add_add_left","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":755,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_add_add_right._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_add_add_right","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":828,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_intro._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_intro","reducibility":null,"statement_dag_size":51,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":2840,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_sub_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_sub_of_le","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":672,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_sub_of_le_right._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_sub_of_le_right","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":641,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_eq_zero","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":665,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_pos_of_ne._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_pos_of_ne","reducibility":null,"statement_dag_size":48,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":919,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_succ_succ._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_succ_succ","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","Nat.succ","instAddNat","instHAdd","instHSub","instSubNat"],"value_dag_size":200,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.add_sub_add_le","Nat.decLe","Nat.succ","Nat.succ_eq_add_one","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eq_self","instAddNat","instHAdd","instHSub","instLENat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_left'._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_left'","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":759,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_left._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_left","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":864,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_right'._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_right'","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":757,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_right._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_tri_right","reducibility":null,"statement_dag_size":37,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","Nat","instAddNat","instHAdd","instHSub","instLENat","instSubNat"],"value_dag_size":862,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_zero_left._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_zero_left","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":150,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_zero","Nat.zero_sub","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_zero_right._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.dist_zero_right","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":150,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HSub.hSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.sub_zero","Nat.zero_sub","Not","OfNat.ofNat","True","congr","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Dist","name":"_private.Mathlib.Data.Nat.Dist.0.Nat.eq_of_dist_eq_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Dist.0.Nat.eq_of_dist_eq_zero","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instOfNatNat","instSubNat"],"value_dag_size":842,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.DvdSequence","name":"_private.Mathlib.Data.Nat.DvdSequence.0.Nat.IsStrongDvdSequence.isDvdSequence._simp_1_1","namespace":"_private.Mathlib.Data.Nat.DvdSequence.0.Nat.IsStrongDvdSequence.isDvdSequence","reducibility":null,"statement_dag_size":23,"type_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.instDvd"],"value_dag_size":26,"value_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.gcd_eq_left_iff_dvd","Nat.instDvd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_descFactorial_eq_ascFactorial'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_descFactorial_eq_ascFactorial'","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_descFactorial_eq_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_descFactorial_eq_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_le_factorial_add_succ.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_le_factorial_add_succ","reducibility":"abbrev","statement_dag_size":69,"type_refs":["LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","Nat.succ","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instOfNatNat"],"value_dag_size":105,"value_refs":["LT.lt","LinearOrder.toPartialOrder","Nat","Nat.casesOn","Nat.instLinearOrder","Nat.succ","Nat.zero","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ","reducibility":null,"statement_dag_size":22,"type_refs":["HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":111,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ","reducibility":null,"statement_dag_size":40,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":322,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Nat.factorial","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":341,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.factorial","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ","reducibility":null,"statement_dag_size":38,"type_refs":["HAdd.hAdd","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":274,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1","reducibility":null,"statement_dag_size":151,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat","namedPattern"],"value_dag_size":328,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1.splitter","id","instAddNat","instHAdd","instOfNatNat","namedPattern"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":64,"value_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":64,"value_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1","reducibility":null,"statement_dag_size":77,"type_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.ascFactorialBinary.match_1","Nat.succ","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorialBinary.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_eq_ascFactorialBinary._proof_1_6","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_eq_ascFactorialBinary","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Nat","Nat.ascFactorial","Nat.ascFactorialBinary","Nat.instDiv","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMul","instMulNat","instOfNatNat"],"value_dag_size":1449,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_neg","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_split_resolve","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ascFactorial","Nat.ascFactorialBinary","Nat.ascFactorial_mul_ascFactorial","Nat.instDiv","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":267,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le_factorial_mul_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le_factorial_mul_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le_pow_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_le_pow_add","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_lt_pow_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_lt_pow_add","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_mul_ascFactorial._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.ascFactorial_mul_ascFactorial","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HMul.hMul","Nat","instHMul","instMulNat"],"value_dag_size":32,"value_refs":["Eq.symm","HMul.hMul","Nat","Nat.mul_assoc","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_descFactorialBinary._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_descFactorialBinary","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Nat.descFactorial","Not","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":738,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_sub_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.of_diseq","Nat.decLe","Nat.descFactorial","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","False","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":20,"value_refs":["Eq","Nat","Nat.one_ne_zero","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","False","LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":21,"value_refs":["LT.lt","Nat","Nat.not_lt_zero","OfNat.ofNat","eq_false","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_eq_zero_iff_lt","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_le_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_le_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow","reducibility":null,"statement_dag_size":49,"type_refs":["HAdd.hAdd","HSub.hSub","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":1068,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.toAdd","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow","reducibility":null,"statement_dag_size":22,"type_refs":["LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":165,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.le_zero_eq","Nat.not_le_eq","Ne","Not","OfNat.ofNat","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_lt_pow","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HSub.hSub","LE.le","Nat","instHSub","instLENat","instSubNat"],"value_dag_size":1582,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.natCast_add","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.sub_sub","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial","reducibility":null,"statement_dag_size":31,"type_refs":["HSub.hSub","LE.le","Nat","instHSub","instLENat","instSubNat"],"value_dag_size":812,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial","reducibility":null,"statement_dag_size":21,"type_refs":["LE.le","LT.lt","Nat","Not","instLENat","instLTNat"],"value_dag_size":286,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_mul_descFactorial","reducibility":null,"statement_dag_size":41,"type_refs":["HSub.hSub","LE.le","LT.lt","Nat","Not","instHSub","instLENat","instLTNat","instSubNat"],"value_dag_size":852,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_pos","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":26,"value_refs":["LT.lt","Nat","Nat.pos_iff_ne_zero","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_self.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.descFactorial_self","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.dvd_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.dvd_factorial","reducibility":"abbrev","statement_dag_size":57,"type_refs":["LE.le","LT.lt","Nat","Nat.succ","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":164,"value_refs":["Eq","Eq.refl","False","False.elim","HEq","HEq.refl","LE.le","LT.lt","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instLENat","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_eq_factorialBinarySplitting._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_eq_factorialBinarySplitting","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","Nat","Nat.ascFactorial","Nat.ascFactorialBinary"],"value_dag_size":11,"value_refs":["Eq.symm","Nat","Nat.ascFactorial","Nat.ascFactorialBinary","Nat.ascFactorial_eq_ascFactorialBinary"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_le_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_le_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_descFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_descFactorial","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_pow_le_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_mul_pow_le_factorial","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":43,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_pos.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_pos","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.lt_factorial_self._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.lt_factorial_self","reducibility":null,"statement_dag_size":28,"type_refs":["LE.le","LT.lt","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":249,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.one_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.one_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_lt_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_lt_ascFactorial","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_le_descFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_le_descFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial'._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial'","reducibility":null,"statement_dag_size":55,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":645,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial'.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial'","reducibility":"abbrev","statement_dag_size":69,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":94,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_lt_descFactorial","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_succ_le_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_succ_le_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.self_le_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.self_le_factorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_descFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_descFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_descFactorial_succ.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_descFactorial_succ","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.zero_ascFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.zero_ascFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.Basic","name":"_private.Mathlib.Data.Nat.Factorial.Basic.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Factorial.Basic.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.ascFactorial_eq_prod_range.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.ascFactorial_eq_prod_range","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.descFactorial_eq_prod_range.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.descFactorial_eq_prod_range","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.BigOperators","name":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial_eq_prod_range_add_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.BigOperators.0.Nat.factorial_eq_prod_range_add_one","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial._proof_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial","reducibility":null,"statement_dag_size":63,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":63,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq.unsafeIntro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial._proof_2","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial","reducibility":null,"statement_dag_size":53,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":53,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq.unsafeIntro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial._sparseCasesOn_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial.match_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial._sparseCasesOn_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial.match_4","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Mathlib.Meta.Positivity.evalDoubleFactorial","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.doubleFactorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.doubleFactorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_eq_prod_even.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_eq_prod_even","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_eq_prod_odd.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_eq_prod_odd","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_le_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_le_factorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_pos.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_pos","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_two_mul.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.doubleFactorial_two_mul","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.DoubleFactorial","name":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial_eq_mul_doubleFactorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.DoubleFactorial.0.Nat.factorial_eq_mul_doubleFactorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.NatCast","name":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_iff_of_charP.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_iff_of_charP","reducibility":"abbrev","statement_dag_size":83,"type_refs":["And","And.intro","Dvd.dvd","HAdd.hAdd","LE.le","Nat","Nat.instDvd","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":99,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","HAdd.hAdd","LE.le","Nat","Nat.instDvd","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.NatCast","name":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_algebra._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_algebra","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","GroupWithZero","GroupWithZero.toMonoidWithZero","IsUnit","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["GroupWithZero","GroupWithZero.toMonoidWithZero","IsUnit","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","Ne","OfNat.ofNat","Zero.toOfNat0","isUnit_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.NatCast","name":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent","reducibility":null,"statement_dag_size":33,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":323,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.NatCast","name":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.NatCast","name":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.NatCast.0.IsUnit.natCast_factorial_of_isNilpotent","reducibility":null,"statement_dag_size":53,"type_refs":["And","Eq","HMul.hMul","IsDedekindFiniteMonoid","IsUnit","Monoid","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"],"value_dag_size":58,"value_refs":["And","HMul.hMul","IsDedekindFiniteMonoid","IsUnit","IsUnit.mul_iff","Monoid","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.prod_Icc_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.prod_Icc_factorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.prod_range_succ_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.prod_range_succ_factorial","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.succ","Nat.superFactorial.match_1","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.succ","Nat.superFactorial.match_1","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.succ","Nat.superFactorial.match_1","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.succ","Nat.superFactorial.match_1","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.superFactorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorial.SuperFactorial","name":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial_two_mul.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorial.SuperFactorial.0.Nat.superFactorial_two_mul","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Icc","Finset.instSetLike","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Icc_factorization_eq_pow_dvd","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","iff_and_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Finset","Finset.Icc","Finset.instSetLike","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":62,"value_refs":["And","Finset","Finset.Icc","Finset.instSetLike","Finset.mem_Icc","LE.le","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_filter_pow_dvd_eq","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","LE.le","Nat","Nat.instPreorder","Not","OfNat.ofNat","Preorder.toLE","instOfNatNat"],"value_dag_size":165,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instPreorder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Preorder.toLE","eagerReduce","id","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ioc_filter_dvd_card_eq_div._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ioc_filter_dvd_card_eq_div","reducibility":null,"statement_dag_size":153,"type_refs":["Add","DistribLattice.toLattice","Eq","Finset","Finset.Ioc","Finset.instInsert","HAdd.hAdd","Insert.insert","LE.le","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LocallyFiniteOrder","NoMaxOrder","OfNat.ofNat","One","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","instDistribLatticeOfLinearOrder","instHAdd"],"value_dag_size":165,"value_refs":["Add","DistribLattice.toLattice","Eq.symm","Finset","Finset.Ioc","Finset.insert_Ioc_right_eq_Ioc_add_one","Finset.instInsert","HAdd.hAdd","Insert.insert","LE.le","Lattice.toSemilatticeInf","LinearOrder","LinearOrder.toDecidableEq","LocallyFiniteOrder","NoMaxOrder","OfNat.ofNat","One","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","SemilatticeInf.toPartialOrder","SuccAddOrder","instDistribLatticeOfLinearOrder","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_iff_prime_pow_dvd_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_iff_prime_pow_dvd_dvd","reducibility":null,"statement_dag_size":43,"type_refs":["Dvd.dvd","Eq","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","Zero.toOfNat0","semigroupDvd"],"value_dag_size":46,"value_refs":["Dvd.dvd","Eq","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","Zero.toOfNat0","propext","semigroupDvd","zero_dvd_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_iff_prime_pow_dvd_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_iff_prime_pow_dvd_dvd","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_ordCompl_of_dvd_not_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_ordCompl_of_dvd_not_dvd","reducibility":null,"statement_dag_size":60,"type_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":63,"value_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.factorization_eq_zero_iff","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_dvd_pow_iff.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_dvd_pow_iff","reducibility":"abbrev","statement_dag_size":67,"type_refs":["Dvd.dvd","Exists","Exists.intro","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instDvd","Nat.instMonoid","instHPow"],"value_dag_size":84,"value_refs":["Dvd.dvd","Exists","Exists.casesOn","Exists.intro","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instDvd","Nat.instMonoid","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_eq_pow_mul_and_not_dvd.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_eq_pow_mul_and_not_dvd","reducibility":"abbrev","statement_dag_size":148,"type_refs":["And","And.intro","Dvd.dvd","Eq","Exists","Exists.intro","HMul.hMul","HPow.hPow","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instMonoid","Not","instHMul","instHPow","multiplicity","semigroupDvd"],"value_dag_size":210,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","Eq","Exists","Exists.casesOn","Exists.intro","HMul.hMul","HPow.hPow","Monoid.toMulOneClass","Monoid.toNPow","Monoid.toSemigroup","MulOne.toMul","MulOneClass.toMulOne","NPow.toPow","Nat","Nat.instMonoid","Not","instHMul","instHPow","multiplicity","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_eq_two_pow_mul_odd.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.exists_eq_two_pow_mul_odd","reducibility":"abbrev","statement_dag_size":124,"type_refs":["And","And.intro","Dvd.dvd","Eq","Exists","Exists.intro","HMul.hMul","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instDvd","Nat.instMonoid","Not","OfNat.ofNat","instHMul","instHPow","instMulNat","instOfNatNat"],"value_dag_size":197,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","Eq","Exists","Exists.casesOn","Exists.intro","HMul.hMul","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instDvd","Nat.instMonoid","Not","OfNat.ofNat","instHMul","instHPow","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_eq_card_pow_dvd_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_eq_card_pow_dvd_of_lt","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":177,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_eq_zero_iff'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_eq_zero_iff'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","List","List.nil","Multiset","Multiset.instZero","Multiset.ofList","OfNat.ofNat","Zero.toOfNat0"],"value_dag_size":39,"value_refs":["Eq","List","List.nil","Multiset","Multiset.coe_eq_zero","Multiset.instZero","Multiset.ofList","OfNat.ofNat","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_ordCompl._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.factorization_ordCompl","reducibility":null,"statement_dag_size":60,"type_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":63,"value_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.factorization_eq_zero_iff","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Basic","name":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.setOfPred_pow_dvd_eq_Icc_factorization._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.setOfPred_pow_dvd_eq_Icc_factorization","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.dvd_iff_exists_le_factorization.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.dvd_iff_exists_le_factorization","reducibility":"abbrev","statement_dag_size":120,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.instLE","Finsupp.prod","HPow.hPow","LE.le","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","instHPow","instLENat"],"value_dag_size":166,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.instLE","Finsupp.prod","HPow.hPow","LE.le","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","instHPow","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.eq_of_factorization_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.eq_of_factorization_eq","reducibility":null,"statement_dag_size":40,"type_refs":["BEq","Eq","LawfulBEq","List","List.Perm","List.count","Nat"],"value_dag_size":46,"value_refs":["BEq","Eq","LawfulBEq","List","List.Perm","List.count","List.perm_iff_count","Nat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization._simp_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff","reducibility":null,"statement_dag_size":71,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":82,"value_refs":["DFunLike.coe","Eq","Eq.symm","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.notMem_support_iff","Finsupp.support","Membership.mem","Not","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff","reducibility":null,"statement_dag_size":50,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.mem_primeFactors","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Ne","Not"],"value_dag_size":25,"value_refs":["Eq","Ne","Not","not_ne_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_of_not_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_of_not_dvd","reducibility":null,"statement_dag_size":60,"type_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":63,"value_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.factorization_eq_zero_iff","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_of_not_prime._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_eq_zero_of_not_prime","reducibility":null,"statement_dag_size":60,"type_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":63,"value_refs":["DFunLike.coe","Dvd.dvd","Eq","Finsupp","Finsupp.instFunLike","MulZeroClass.toZero","Nat","Nat.Prime","Nat.factorization","Nat.factorization_eq_zero_iff","Nat.instDvd","Nat.instMulZeroClass","Not","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_le_iff_dvd.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_le_iff_dvd","reducibility":"abbrev","statement_dag_size":52,"type_refs":["Dvd.dvd","Eq","Exists.intro","HMul.hMul","Nat","Nat.instDvd","instHMul","instMulNat"],"value_dag_size":70,"value_refs":["Dvd.dvd","Eq","Exists.casesOn","Exists.intro","HMul.hMul","Nat","Nat.instDvd","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_minFac_ne_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_minFac_ne_zero","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":182,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_mul","reducibility":null,"statement_dag_size":42,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","List.count","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactorsList","instBEqOfDecidableEq","instDecidableEqNat"],"value_dag_size":46,"value_refs":["DFunLike.coe","Eq.symm","Finsupp","Finsupp.instFunLike","List.count","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactorsList","Nat.primeFactorsList_count_eq","instBEqOfDecidableEq","instDecidableEqNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_mul_apply_of_coprime._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.factorization_mul_apply_of_coprime","reducibility":null,"statement_dag_size":42,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","List.count","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactorsList","instBEqOfDecidableEq","instDecidableEqNat"],"value_dag_size":46,"value_refs":["DFunLike.coe","Eq.symm","Finsupp","Finsupp.instFunLike","List.count","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactorsList","Nat.primeFactorsList_count_eq","instBEqOfDecidableEq","instDecidableEqNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.ordProj_dvd_ordProj_iff_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.ordProj_dvd_ordProj_iff_dvd","reducibility":null,"statement_dag_size":54,"type_refs":["Dvd.dvd","Eq","HPow.hPow","LE.le","LT.lt","Nat","Nat.instDvd","OfNat.ofNat","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":59,"value_refs":["Dvd.dvd","HPow.hPow","LE.le","LT.lt","Nat","Nat.instDvd","Nat.pow_dvd_pow_iff_le_right","OfNat.ofNat","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Defs","name":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.prod_factorization_pow_eq_self._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Defs.0.Nat.prod_factorization_pow_eq_self","reducibility":null,"statement_dag_size":108,"type_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","CommMonoid","CommMonoid.toMonoid","DFunLike.coe","Eq","Finsupp","Finsupp.instAddZeroClass","Finsupp.prod","Finsupp.toMultiset","HPow.hPow","Monoid.toNPow","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.prod","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","instHPow"],"value_dag_size":113,"value_refs":["AddCancelCommMonoid.toAddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddMonoidHom","AddMonoidHom.instFunLike","AddZeroClass.toAddZero","CommMonoid","CommMonoid.toMonoid","DFunLike.coe","Eq.symm","Finsupp","Finsupp.instAddZeroClass","Finsupp.prod","Finsupp.prod_toMultiset","Finsupp.toMultiset","HPow.hPow","Monoid.toNPow","MulZeroClass.toZero","Multiset","Multiset.instAddCancelCommMonoid","Multiset.prod","NPow.toPow","Nat","Nat.instAddMonoid","Nat.instMulZeroClass","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.Iic_factorization_prod_pow_injective._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.Iic_factorization_prod_pow_injective","reducibility":null,"statement_dag_size":114,"type_refs":["Finset","Finset.Iic","Finset.instSetLike","Finsupp","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","Function.Injective","HPow.hPow","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","SetLike.instMembership","Subtype","Subtype.val","instDecidableEqNat","instHPow"],"value_dag_size":662,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Iic","Finset.instSetLike","Finset.mem_Iic","Finsupp","Finsupp.instLE","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","Function.Injective","Function.Injective.eq_1","HEq.refl","HPow.hPow","Iff","LE.le","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.factorization_prod_pow_eq_self_of_le_factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Not","Preorder.toLE","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.val","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instDecidableEqNat","instHPow","instLENat","instNatPowNat","instPowNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.Iio_factorization_prod_pow_injective._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.Iio_factorization_prod_pow_injective","reducibility":null,"statement_dag_size":114,"type_refs":["Finset","Finset.Iio","Finset.instSetLike","Finsupp","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","Function.Injective","HPow.hPow","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","SetLike.instMembership","Subtype","Subtype.val","instDecidableEqNat","instHPow"],"value_dag_size":682,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Iio","Finset.instSetLike","Finset.mem_Iio","Finsupp","Finsupp.instLE","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","Function.Injective","Function.Injective.eq_1","HEq.refl","HPow.hPow","Iff","LE.le","LT.lt","Lean.Grind.Order.le_eq_true_of_lt","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.of_forall_eq_false","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.factorization_prod_pow_eq_self_of_le_factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Not","Preorder.toLT","SetLike.instMembership","Subtype","Subtype.casesOn","Subtype.mk","Subtype.mk.hcongr_4","Subtype.val","True","True.intro","congrArg","eq_false","eq_of_heq","eq_true","heq_of_eq","id","instDecidableEqNat","instHPow","instLENat","instLawfulOrderLT_mathlib","instNatPowNat","instPowNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_divisors_eq_prod_pow_le_factorization.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_divisors_eq_prod_pow_le_factorization","reducibility":"abbrev","statement_dag_size":133,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.instLE","Finsupp.prod","HPow.hPow","LE.le","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","Set","Set.instMembership","Set.ofPred","instHPow","instLENat"],"value_dag_size":186,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.instLE","Finsupp.prod","HPow.hPow","LE.le","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","Set","Set.instMembership","Set.ofPred","instHPow","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_properDivisors_eq_prod_pow_lt_factorization.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_properDivisors_eq_prod_pow_lt_factorization","reducibility":"abbrev","statement_dag_size":136,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finsupp","Finsupp.preorder","Finsupp.prod","HPow.hPow","LT.lt","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPreorder","Preorder.toLT","Set","Set.instMembership","Set.ofPred","instHPow"],"value_dag_size":189,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finsupp","Finsupp.preorder","Finsupp.prod","HPow.hPow","LT.lt","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instCommMonoid","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPreorder","Preorder.toLT","Set","Set.instMembership","Set.ofPred","instHPow"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_properDivisors_eq_prod_pow_lt_factorization.match_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.coe_properDivisors_eq_prod_pow_lt_factorization","reducibility":"abbrev","statement_dag_size":52,"type_refs":["And","And.intro","Dvd.dvd","LT.lt","Nat","Nat.instDvd","instLTNat"],"value_dag_size":67,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","LT.lt","Nat","Nat.instDvd","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.divisors_eq_image_Iic_factorization_prod_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.divisors_eq_image_Iic_factorization_prod_pow","reducibility":null,"statement_dag_size":118,"type_refs":["Eq","Finset","Finset.Iic","Finset.image","Finset.instSetLike","Finsupp","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","HPow.hPow","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.divisors","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Ne","OfNat.ofNat","Set","SetLike.coe","instDecidableEqNat","instHPow","instOfNatNat"],"value_dag_size":1272,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Iic","Finset.image","Finset.instSetLike","Finset.mem_Iic","Finset.mem_coe","Finset.mem_image","Finsupp","Finsupp.instLE","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","HPow.hPow","Iff","Inhabited.default","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_const","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_false","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.coe_divisors_eq_prod_pow_le_factorization","Nat.divisors","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Preorder.toLE","Set","Set.ext","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SetLike.instMembership","True","True.casesOn","True.intro","congrArg","congrFun","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instDecidableEqNat","instHPow","instInhabitedNat","instLENat","instNatPowNat","instNonemptyOfInhabited","instOfNatNat","instPowNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Divisors","name":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.properDivisors_eq_image_Iio_factorization_prod_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Divisors.0.Nat.properDivisors_eq_image_Iio_factorization_prod_pow","reducibility":null,"statement_dag_size":106,"type_refs":["Eq","Finset","Finset.Iio","Finset.image","Finset.instSetLike","Finsupp","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","HPow.hPow","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Nat.properDivisors","Set","SetLike.coe","instDecidableEqNat","instHPow"],"value_dag_size":1170,"value_refs":["And","And.casesOn","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset","Finset.Iio","Finset.image","Finset.instSetLike","Finset.mem_Iio","Finset.mem_coe","Finset.mem_image","Finsupp","Finsupp.instLocallyFiniteOrder","Finsupp.orderBot","Finsupp.preorder","Finsupp.prod","HPow.hPow","Iff","Inhabited.default","LT.lt","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_eq","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.exists_const","Lean.Grind.forall_forall_or","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_false","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","LinearOrderedCommMonoidWithZero.toIsBotZeroClass","LocallyFiniteOrder.toLocallyFiniteOrderBot","Membership.mem","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.coe_properDivisors_eq_prod_pow_lt_factorization","Nat.factorization","Nat.instAddCommMonoid","Nat.instCommMonoid","Nat.instLinearOrderedCommMonoidWithZero","Nat.instLocallyFiniteOrder","Nat.instMonoid","Nat.instMulZeroClass","Nat.instPartialOrder","Nat.instPreorder","Nat.properDivisors","Not","Or","Or.casesOn","Preorder.toLT","Set","Set.ext","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","SetLike.coe","SetLike.instMembership","True","True.casesOn","True.intro","congrArg","congrFun","congrFun'","eq_false","eq_true","false_or","forall_congr","forall_not_of_not_exists","funext","id","implies_congr","instDecidableEqNat","instHPow","instInhabitedNat","instNatPowNat","instNonemptyOfInhabited","instPowNat","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.LCM","name":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_dvd_left._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_dvd_left","reducibility":null,"statement_dag_size":40,"type_refs":["Dvd.dvd","Eq","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","True","Zero.toOfNat0","semigroupDvd"],"value_dag_size":41,"value_refs":["Dvd.dvd","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","Zero.toOfNat0","dvd_zero","eq_true","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.LCM","name":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_pos._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_pos","reducibility":null,"statement_dag_size":95,"type_refs":["And","Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","Nontrivial","OfNat.ofNat","Zero.toOfNat0","instHPow","instOfNatNat"],"value_dag_size":101,"value_refs":["And","Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","Nontrivial","OfNat.ofNat","Zero.toOfNat0","instHPow","instOfNatNat","pow_eq_zero_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.LCM","name":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_pos._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMLeft_pos","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","False","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0"],"value_dag_size":48,"value_refs":["Eq","NeZero","OfNat.ofNat","One","One.toOfNat1","Zero","Zero.toOfNat0","eq_false","one_ne_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.LCM","name":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMRight_dvd_right._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMRight_dvd_right","reducibility":null,"statement_dag_size":40,"type_refs":["Dvd.dvd","Eq","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","True","Zero.toOfNat0","semigroupDvd"],"value_dag_size":41,"value_refs":["Dvd.dvd","MulZeroClass.toZero","OfNat.ofNat","SemigroupWithZero","SemigroupWithZero.toMulZeroClass","SemigroupWithZero.toSemigroup","Zero.toOfNat0","dvd_zero","eq_true","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.LCM","name":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMRight_pos._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.LCM.0.Nat.factorizationLCMRight_pos","reducibility":null,"statement_dag_size":95,"type_refs":["And","Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","Nontrivial","OfNat.ofNat","Zero.toOfNat0","instHPow","instOfNatNat"],"value_dag_size":101,"value_refs":["And","Eq","HPow.hPow","IsReduced","Monoid.toNPow","MonoidWithZero","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NPow.toPow","Nat","Ne","Nontrivial","OfNat.ofNat","Zero.toOfNat0","instHPow","instOfNatNat","pow_eq_zero_iff'","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.Coprime.isPrimePow_dvd_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.Coprime.isPrimePow_dvd_mul","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Or"],"value_dag_size":23,"value_refs":["Or","imp_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Nat","Nat.Coprime","OfNat.ofNat","instOfNatNat"],"value_dag_size":27,"value_refs":["Eq","Nat","Nat.Coprime","Nat.coprime_zero_left","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_10","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Or"],"value_dag_size":12,"value_refs":["Or","or_self_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":40,"type_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Eq","False","IsPrimePow","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","OfNat.ofNat","One.toOfNat1"],"value_dag_size":40,"value_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","IsPrimePow","MonoidWithZero.toMulZeroOneClass","MulOne.toOne","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","OfNat.ofNat","One.toOfNat1","eq_false","not_isPrimePow_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Nat","Nat.Coprime","OfNat.ofNat","instOfNatNat"],"value_dag_size":27,"value_refs":["Eq","Nat","Nat.Coprime","Nat.coprime_zero_right","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","HMul.hMul","Nat","OfNat.ofNat","Or","instHMul","instMulNat","instOfNatNat"],"value_dag_size":41,"value_refs":["Eq","HMul.hMul","Nat","Nat.mul_eq_zero","OfNat.ofNat","Or","instHMul","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":23,"type_refs":["And","Eq","Iff"],"value_dag_size":27,"value_refs":["And","Iff","and_congr_left_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_8","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow._simp_1_9","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.mul_divisors_filter_prime_pow","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Nat.mem_divisors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.not_isPrimePow_iff_nontrivial_of_two_le._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.Nat.not_isPrimePow_iff_nontrivial_of_two_le","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Finset.card","Iff","LE.le","LT.lt","Nat","Nat.primeFactors","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1153,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","EmptyCollection.emptyCollection","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.card","Finset.card_ne_zero_of_mem","Finset.ext","Finset.instEmptyCollection","Finset.instSetLike","Finset.notMem_empty","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","Nat.primeFactors","Nat.primeFactors_eq_empty","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","SetLike.instMembership","True","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instNatCastNat","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one","reducibility":null,"statement_dag_size":56,"type_refs":["And","Eq","Exists","Finsupp","Finsupp.single","IsPrimePow","LT.lt","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instCommMonoidWithZero","Nat.instMulZeroClass","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":58,"value_refs":["And","Eq","Exists","Finsupp","Finsupp.single","IsPrimePow","LT.lt","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instCommMonoidWithZero","Nat.instMulZeroClass","OfNat.ofNat","instLTNat","instOfNatNat","isPrimePow_iff_factorization_eq_single","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","Finset","Finsupp.support","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactors"],"value_dag_size":25,"value_refs":["Eq.symm","Finset","Finsupp.support","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","Nat.primeFactors","Nat.support_factorization"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one","reducibility":null,"statement_dag_size":78,"type_refs":["And","Eq","Exists","Finset.card","Finsupp","Finsupp.single","Finsupp.support","Nat","Ne","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat"],"value_dag_size":83,"value_refs":["And","Eq","Exists","Finset.card","Finsupp","Finsupp.card_support_eq_one'","Finsupp.single","Finsupp.support","Nat","Ne","OfNat.ofNat","Zero","Zero.toOfNat0","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_card_primeFactors_eq_one","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_factorization_eq_single._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_factorization_eq_single","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finsupp","Finsupp.instZero","Finsupp.single","OfNat.ofNat","Zero","Zero.toOfNat0"],"value_dag_size":61,"value_refs":["Eq","Finsupp","Finsupp.instZero","Finsupp.single","Finsupp.single_eq_zero","OfNat.ofNat","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_factorization_eq_single._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_factorization_eq_single","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_unique_prime_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_iff_unique_prime_dvd","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq","reducibility":null,"statement_dag_size":69,"type_refs":["DFunLike.coe","Eq","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0"],"value_dag_size":80,"value_refs":["DFunLike.coe","Eq.symm","Finset","Finset.instSetLike","Finsupp","Finsupp.instFunLike","Finsupp.mem_support_iff","Finsupp.support","Membership.mem","Ne","OfNat.ofNat","SetLike.instMembership","Zero","Zero.toOfNat0","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_of_minFac_pow_factorization_eq","reducibility":null,"statement_dag_size":17,"type_refs":["Dvd.dvd","Eq","Nat","Nat.instDvd","Nat.minFac","True"],"value_dag_size":16,"value_refs":["Dvd.dvd","Nat","Nat.instDvd","Nat.minFac","Nat.minFac_dvd","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff","reducibility":null,"statement_dag_size":29,"type_refs":["And","Dvd.dvd","Eq","ExistsUnique","IsPrimePow","Nat","Nat.Prime","Nat.instCommMonoidWithZero","Nat.instDvd"],"value_dag_size":30,"value_refs":["And","Dvd.dvd","ExistsUnique","IsPrimePow","Nat","Nat.Prime","Nat.instCommMonoidWithZero","Nat.instDvd","isPrimePow_iff_unique_prime_dvd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Nat","Nat.Prime","Nat.instCommMonoidWithZero","Prime"],"value_dag_size":16,"value_refs":["Nat","Nat.Prime","Nat.instCommMonoidWithZero","Nat.prime_iff","Prime","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.PrimePow","name":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Factorization.PrimePow.0.isPrimePow_pow_iff","reducibility":null,"statement_dag_size":76,"type_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","Eq","HPow.hPow","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toSemigroupWithZero","NPow.toPow","Nat","Ne","OfNat.ofNat","Prime","SemigroupWithZero.toSemigroup","instHPow","instOfNatNat","semigroupDvd"],"value_dag_size":83,"value_refs":["CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","Dvd.dvd","HPow.hPow","Monoid.toNPow","MonoidWithZero.toMonoid","MonoidWithZero.toSemigroupWithZero","NPow.toPow","Nat","Ne","OfNat.ofNat","Prime","Prime.dvd_pow_iff_dvd","SemigroupWithZero.toSemigroup","instHPow","instOfNatNat","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_ne_zero","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.factorization_floorRoot._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.factorization_floorRoot","reducibility":null,"statement_dag_size":28,"type_refs":["Eq","Nat","Not","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":106,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.Grind.not_or","Nat","Not","OfNat.ofNat","Or","True","True.intro","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.factorization_floorRoot._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.factorization_floorRoot","reducibility":null,"statement_dag_size":54,"type_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","Eq","LT.lt","Nat","Nat.instAddCommMonoid","Nat.instPartialOrder","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","Zero.toOfNat0","instOfNatNat"],"value_dag_size":227,"value_refs":["AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.instAddCommMonoid","Nat.instPartialOrder","Nat.le_zero_eq","Nat.not_le_eq","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","True","True.intro","Zero.toOfNat0","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_eq_zero","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_and_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_eq_zero","reducibility":null,"statement_dag_size":10,"type_refs":["Eq","Not"],"value_dag_size":12,"value_refs":["Classical.not_not","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factorization.Root","name":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_ne_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.floorRoot_ne_zero","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.isChain_cons_primeFactorsList.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.isChain_cons_primeFactorsList","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList'","reducibility":null,"statement_dag_size":45,"type_refs":["And","Dvd.dvd","Eq","List","List.instMembership","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.primeFactorsList","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":49,"value_refs":["And","Dvd.dvd","List","List.instMembership","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.mem_primeFactorsList","Nat.primeFactorsList","Ne","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList","reducibility":"abbrev","statement_dag_size":45,"type_refs":["And","And.intro","Dvd.dvd","Nat","Nat.Prime","Nat.instDvd"],"value_dag_size":59,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","Nat","Nat.Prime","Nat.instDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList_mul","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1","reducibility":null,"statement_dag_size":119,"type_refs":["Eq","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":292,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.splitter","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":42,"value_refs":["Eq.refl","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.refl","Nat","Nat.primeFactorsList.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.primeFactorsList.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList_ne_nil._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList_ne_nil","reducibility":null,"statement_dag_size":33,"type_refs":["And","Eq","LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":34,"value_refs":["And","LT.lt","Nat","Nat.one_lt_iff_ne_zero_and_ne_one","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList_unique._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList_unique","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Nat","Nat.Prime","Nat.instCommMonoidWithZero","Prime"],"value_dag_size":22,"value_refs":["Eq.symm","Nat","Nat.Prime","Nat.instCommMonoidWithZero","Nat.prime_iff","Prime","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.prime_of_mem_primeFactorsList.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.prime_of_mem_primeFactorsList","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Factors","name":"_private.Mathlib.Data.Nat.Factors.0.Nat.prod_primeFactorsList.match_1_1","namespace":"_private.Mathlib.Data.Nat.Factors.0.Nat.prod_primeFactorsList","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fastFibAux_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fastFibAux_eq","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","Prod","Prod.mk"],"value_dag_size":50,"value_refs":["And","Eq","Prod","Prod.mk","Prod.mk_inj","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_add_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_add_one","reducibility":"abbrev","statement_dag_size":49,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":88,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","absurd","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_coprime_fib_succ._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_coprime_fib_succ","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.Coprime","instAddNat","instHAdd"],"value_dag_size":27,"value_refs":["HAdd.hAdd","Nat","Nat.Coprime","Nat.coprime_add_self_right","instAddNat","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_eq_zero.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_eq_zero","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_lt_fib.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_lt_fib","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_pos","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_strictMonoOn.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_strictMonoOn","reducibility":"abbrev","statement_dag_size":90,"type_refs":["HAdd.hAdd","LT.lt","Membership.mem","Nat","Nat.instPreorder","Nat.succ","OfNat.ofNat","Preorder.toLT","Set","Set.Ici","Set.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":339,"value_refs":["Bool","Decidable.decide","Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LT.lt","Membership.mem","Nat","Nat.casesOn","Nat.ctorIdx","Nat.decLe","Nat.instPreorder","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","Preorder.toLT","Set","Set.Ici","Set.decidableMemIci","Set.instMembership","absurd","instAddNat","instHAdd","instOfNatNat","noConfusion_of_Nat","of_decide_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_two_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.fib_two_mul","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.gcd_fib_add_mul_self.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.gcd_fib_add_mul_self","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Basic","name":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.le_fib_add_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Basic.0.Nat.le_fib_add_one","reducibility":"abbrev","statement_dag_size":61,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":104,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_10","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_11","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.IsChain","List.Pairwise","Trans"],"value_dag_size":38,"value_refs":["List","List.IsChain","List.Pairwise","List.isChain_iff_pairwise","Trans","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_8","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.IsChain","List.Pairwise","Trans"],"value_dag_size":43,"value_refs":["Eq.symm","List","List.IsChain","List.Pairwise","List.isChain_iff_pairwise","Trans","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_9","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt","reducibility":"abbrev","statement_dag_size":114,"type_refs":["HAppend.hAppend","LT.lt","List","List.IsZeckendorfRep","List.cons","List.head?","List.instAppend","List.nil","Membership.mem","Nat","OfNat.ofNat","Option","Option.instMembership","instHAppendOfAppend","instLTNat","instOfNatNat"],"value_dag_size":149,"value_refs":["HAppend.hAppend","LT.lt","List","List.IsZeckendorfRep","List.casesOn","List.cons","List.head?","List.instAppend","List.nil","Membership.mem","Nat","OfNat.ofNat","Option","Option.instMembership","instHAppendOfAppend","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_fib.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_fib","reducibility":"abbrev","statement_dag_size":61,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":122,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","absurd","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_pos","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_sub_fib_greatestFib_le_greatestFib._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_sub_fib_greatestFib_le_greatestFib","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":32,"value_refs":["Eq.symm","LE.le","LT.lt","Nat","Nat.succ","Nat.succ_le_iff","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_sub_fib_greatestFib_le_greatestFib._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_sub_fib_greatestFib_le_greatestFib","reducibility":null,"statement_dag_size":105,"type_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub"],"value_dag_size":113,"value_refs":["AddCommMagma.toAdd","AddCommMonoid","AddCommMonoid.toAddCommSemigroup","AddCommMonoid.toAddMonoid","AddCommSemigroup.toAddCommMagma","AddMonoid.toAddZeroClass","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HSub.hSub","LE.le","OfNat.ofNat","OrderedSub","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Sub","Zero.toOfNat0","instHSub","propext","tsub_eq_zero_iff_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.isZeckendorfRep_zeckendorf._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.isZeckendorfRep_zeckendorf","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.some"],"value_dag_size":32,"value_refs":["Eq","Membership.mem","Option","Option.instMembership","Option.mem_some_iff","Option.some","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.isZeckendorfRep_zeckendorf.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.isZeckendorfRep_zeckendorf","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.sum_zeckendorf_fib._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.sum_zeckendorf_fib","reducibility":null,"statement_dag_size":19,"type_refs":["Eq","LE.le","Nat","Nat.fib","Nat.greatestFib","True","instLENat"],"value_dag_size":18,"value_refs":["LE.le","Nat","Nat.fib","Nat.fib_greatestFib_le","Nat.greatestFib","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1","reducibility":null,"statement_dag_size":128,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat","namedPattern"],"value_dag_size":257,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","Unit.unit","_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1.splitter","id","instAddNat","instHAdd","instOfNatNat","namedPattern"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","Unit.unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":54,"value_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":57,"value_refs":["Eq","Eq.refl","HAdd.hAdd","Nat","Nat.succ","Nat.zeckendorf.match_1","OfNat.ofNat","Unit","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_aux","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat","reducibility":null,"statement_dag_size":35,"type_refs":["HSub.hSub","LT.lt","Nat","Nat.fib","Nat.greatestFib","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":191,"value_refs":["AddCommMagma.toAdd","AddCommMonoid.toAddCommSemigroup","AddCommSemigroup.toAddCommMagma","And","And.intro","Exists","Exists.intro","HAdd.hAdd","Iff.mpr","IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT","IsOrderedAddMonoid.toAddLeftMono","IsOrderedCancelAddMonoid.toAddLeftReflectLE","LE.le","LT.lt","MulZeroClass.toZero","Nat","Nat.decLe","Nat.fib","Nat.fib_pos","Nat.findGreatest","Nat.findGreatest_pos","Nat.greatestFib","Nat.instAddCommMonoid","Nat.instCanonicallyOrderedAdd","Nat.instIsOrderedAddMonoid","Nat.instIsOrderedCancelAddMonoid","Nat.instLinearOrder","Nat.instMulZeroClass","Nat.instNeZeroSucc","Nat.instOne","Nat.instOrderedSub","Nat.instPartialOrder","Nat.instPreorder","Nat.instZeroLEOneClass","OfNat.ofNat","contravariant_lt_of_covariant_le","instAddNat","instHAdd","instIsLeftCancelAddOfAddLeftReflectLE","instLENat","instLTNat","instOfNatNat","instSubNat","le_add_self","tsub_lt_self","zero_lt_one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_of_pos.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_of_pos","reducibility":"abbrev","statement_dag_size":50,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":142,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LT.lt","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_10","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":22,"type_refs":["Eq"],"value_dag_size":26,"value_refs":["Eq","forall_eq","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_11","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":88,"type_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","Eq","HAdd.hAdd","LT.lt","OfNat.ofNat","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","instHAdd"],"value_dag_size":94,"value_refs":["AddCommMonoid","AddCommMonoid.toAddMonoid","AddMonoid.toAddZeroClass","AddZero.toAdd","AddZero.toZero","AddZeroClass.toAddZero","CanonicallyOrderedAdd","HAdd.hAdd","LT.lt","OfNat.ofNat","Or","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero.toOfNat0","add_pos_iff","instHAdd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_13","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":64,"type_refs":["And","DecidablePred","Eq","LE.le","LT.lt","Nat","Nat.findGreatest","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":70,"value_refs":["And","DecidablePred","Eq","LE.le","LT.lt","Nat","Nat.findGreatest","Nat.findGreatest_eq_iff","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_14","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":74,"type_refs":["AddRightMono","AddRightReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","Eq","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd"],"value_dag_size":81,"value_refs":["AddRightMono","AddRightReflectLE","AddZero.toAdd","AddZero.toZero","AddZeroClass","AddZeroClass.toAddZero","HAdd.hAdd","LE","LE.le","OfNat.ofNat","Zero.toOfNat0","instHAdd","le_add_iff_nonneg_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_15","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","IsBotZeroClass","LE","LE.le","OfNat.ofNat","True","Zero","Zero.toOfNat0"],"value_dag_size":41,"value_refs":["IsBotZeroClass","LE","LE.le","OfNat.ofNat","Zero","Zero.toOfNat0","eq_true","zero_le"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_16","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","True","True.intro"],"value_dag_size":16,"value_refs":["True","True.intro","forall_true_left","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_17","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","List","List.IsChain","List.Pairwise","Trans"],"value_dag_size":38,"value_refs":["List","List.IsChain","List.Pairwise","List.isChain_iff_pairwise","Trans","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":44,"type_refs":["And","Eq","List","List.Pairwise","List.cons","List.instMembership","Membership.mem"],"value_dag_size":49,"value_refs":["And","List","List.Pairwise","List.cons","List.instMembership","List.pairwise_cons","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","HAppend.hAppend","List","List.instAppend","List.instMembership","Membership.mem","Or","instHAppendOfAppend"],"value_dag_size":49,"value_refs":["HAppend.hAppend","List","List.instAppend","List.instMembership","List.mem_append","Membership.mem","Or","instHAppendOfAppend","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","List","List.cons","List.instMembership","List.nil","Membership.mem"],"value_dag_size":35,"value_refs":["Eq","List","List.cons","List.instMembership","List.mem_singleton","List.nil","Membership.mem","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_8","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Or"],"value_dag_size":24,"value_refs":["And","Or","or_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_9","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":null,"statement_dag_size":24,"type_refs":["And","Eq"],"value_dag_size":28,"value_refs":["And","forall_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Fib.Zeckendorf","name":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib.match_1_1","namespace":"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib","reducibility":"abbrev","statement_dag_size":39,"type_refs":["List","List.IsZeckendorfRep","List.cons","List.nil","Nat"],"value_dag_size":55,"value_refs":["List","List.IsZeckendorfRep","List.casesOn","List.cons","List.nil","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.findGreatest.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.findGreatest.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.findGreatest.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.findGreatest.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.findGreatest.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq.match_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq","reducibility":"abbrev","statement_dag_size":53,"type_refs":["HAdd.hAdd","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":71,"value_refs":["HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","LT.lt","Nat","Not","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":168,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","False.elim","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":288,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff._proof_1_6","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff","reducibility":null,"statement_dag_size":82,"type_refs":["And","Eq","HAdd.hAdd","Iff","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":2081,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HEq","HEq.refl","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind._simp_1","Lean.Grind.alreadyNorm","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.em","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.not_or","Lean.Grind.of_eq_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.Grind.or_of_and_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","Nat","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":26,"value_refs":["Eq","LE.le","Nat","Nat.le_zero","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","and_iff_left_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.findGreatest_eq_zero_iff","reducibility":null,"statement_dag_size":64,"type_refs":["And","DecidablePred","Eq","LE.le","LT.lt","Nat","Nat.findGreatest","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":70,"value_refs":["And","DecidablePred","Eq","LE.le","LT.lt","Nat","Nat.findGreatest","Nat.findGreatest_eq_iff","Ne","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_iff","reducibility":null,"statement_dag_size":49,"type_refs":["And","DecidablePred","Eq","Exists","LT.lt","Lean.Grind.nestedProof","Nat","Nat.find","Not","instLTNat"],"value_dag_size":552,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","HAdd.hAdd","HEq","HEq.refl","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.eq_false_of_imp_eq_false","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_imp_eq_false","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.not_and","Lean.Grind.not_eq_of_eq_true","Lean.Grind.of_forall_eq_false","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.find","Nat.find_min","Nat.find_spec","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","eagerReduce","eq_false","eq_of_heq","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_iff._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_iff","reducibility":null,"statement_dag_size":52,"type_refs":["DecidablePred","Eq","Exists","LE.le","LT.lt","Nat","Nat.find","Not","instLENat","instLTNat"],"value_dag_size":519,"value_refs":["Bool","Bool.true","Classical.byContradiction","DecidablePred","Eq","Eq.mp","Eq.refl","Exists","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.eq_false_of_imp_eq_true","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedProof","Lean.Grind.not_eq_of_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.find","Nat.find_spec","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearOrder.toIsPartialOrder","Std.IsLinearPreorder.toIsPreorder","eagerReduce","eq_true","forall_congr","id","implies_congr","instAddNat","instHAdd","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.find_eq_zero","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Not","instLTNat"],"value_dag_size":52,"value_refs":["And","DecidablePred","Eq","Exists","LT.lt","Nat","Nat.find","Nat.find_eq_iff","Not","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.find_le_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.find_le_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":32,"value_refs":["Eq.symm","LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.find_lt_iff.match_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.find_lt_iff","reducibility":"abbrev","statement_dag_size":63,"type_refs":["And","And.intro","Exists","Exists.intro","LT.lt","Nat","instLTNat"],"value_dag_size":105,"value_refs":["And","And.casesOn","And.intro","Exists","Exists.casesOn","Exists.intro","LT.lt","Nat","instLTNat"]}
+{"definition_height":3,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.lbp","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat","reducibility":"regular","statement_dag_size":5,"type_refs":["Nat"],"value_dag_size":45,"value_refs":["And","Eq","HAdd.hAdd","LE.le","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.le_find_iff","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.lt_find_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.lt_find_iff","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":32,"value_refs":["Eq.symm","LE.le","LT.lt","Nat","Nat.succ","Nat.succ_le_iff","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.lt_find_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.lt_find_iff","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","LE.le","Nat","Nat.succ","instLENat"],"value_dag_size":23,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ_iff","instLENat","propext"]}
+{"definition_height":4,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat","reducibility":"regular","statement_dag_size":17,"type_refs":["Exists","Nat","WellFounded","_private.Mathlib.Data.Nat.Find.0.Nat.lbp"],"value_dag_size":218,"value_refs":["Acc","Acc.intro","Eq","Eq.mpr","Exists","HAdd.hAdd","LE.le","Nat","Nat.add_right_comm","Nat.le_add_left","Nat.recOn","Nat.succ","Nat.zero","Not","OfNat.ofNat","WellFounded.intro","_private.Mathlib.Data.Nat.Find.0.Nat.lbp","_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp.match_1","_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp.match_3","absurd","congrArg","id","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp.match_1","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp","reducibility":"abbrev","statement_dag_size":78,"type_refs":["And.intro","Eq","Eq.refl","HAdd.hAdd","LE.le","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Nat.Find.0.Nat.lbp","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":227,"value_refs":["And.casesOn","And.intro","Eq","Eq.casesOn","Eq.ndrec","Eq.refl","Eq.symm","HAdd.hAdd","HEq","HEq.refl","LE.le","Nat","Not","OfNat.ofNat","_private.Mathlib.Data.Nat.Find.0.Nat.lbp","eq_of_heq","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Find","name":"_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp.match_3","namespace":"_private.Mathlib.Data.Nat.Find.0.Nat.wf_lbp","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Exists","Exists.intro","Nat"],"value_dag_size":47,"value_refs":["Exists","Exists.casesOn","Exists.intro","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.Basic","name":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime._simp_1_1","namespace":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Nat","Nat.Coprime","Nat.gcd","OfNat.ofNat","instOfNatNat"],"value_dag_size":29,"value_refs":["Eq","Nat","Nat.Coprime","Nat.coprime_iff_gcd_eq_one","Nat.gcd","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.Basic","name":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime._simp_1_3","namespace":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":26,"value_refs":["And","Eq.symm","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.Basic","name":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime._simp_1_4","namespace":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime","reducibility":null,"statement_dag_size":27,"type_refs":["And","Dvd.dvd","Eq","Nat","Nat.gcd","Nat.instDvd"],"value_dag_size":36,"value_refs":["And","Dvd.dvd","Eq.symm","Nat","Nat.dvd_gcd_iff","Nat.gcd","Nat.instDvd","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.Basic","name":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime._simp_1_5","namespace":"_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime","reducibility":null,"statement_dag_size":49,"type_refs":["CommMonoid","CommMonoid.toMonoid","Dvd.dvd","Eq","IsUnit","Monoid.toMulOneClass","Monoid.toSemigroup","MulOne.toOne","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","semigroupDvd"],"value_dag_size":52,"value_refs":["CommMonoid","CommMonoid.toMonoid","Dvd.dvd","IsUnit","Monoid.toMulOneClass","Monoid.toSemigroup","MulOne.toOne","MulOneClass.toMulOne","OfNat.ofNat","One.toOfNat1","isUnit_iff_dvd_one","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.BigOperators","name":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_fintype_prod_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_fintype_prod_left_iff","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.prod","Membership.mem","Nat","Nat.Coprime","Nat.instCommMonoid","SetLike.instMembership"],"value_dag_size":53,"value_refs":["Finset","Finset.instSetLike","Finset.prod","Membership.mem","Nat","Nat.Coprime","Nat.coprime_prod_left_iff","Nat.instCommMonoid","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.BigOperators","name":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_fintype_prod_right_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_fintype_prod_right_iff","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.prod","Membership.mem","Nat","Nat.Coprime","Nat.instCommMonoid","SetLike.instMembership"],"value_dag_size":53,"value_refs":["Finset","Finset.instSetLike","Finset.prod","Membership.mem","Nat","Nat.Coprime","Nat.coprime_prod_right_iff","Nat.instCommMonoid","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.BigOperators","name":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_list_prod_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_list_prod_left_iff","reducibility":null,"statement_dag_size":33,"type_refs":["And","Eq","HMul.hMul","Nat","Nat.Coprime","instHMul","instMulNat"],"value_dag_size":36,"value_refs":["And","HMul.hMul","Nat","Nat.Coprime","Nat.coprime_mul_iff_left","instHMul","instMulNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.GCD.BigOperators","name":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_list_prod_right_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.GCD.BigOperators.0.Nat.coprime_list_prod_right_iff","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","List","List.instMembership","List.prod","Membership.mem","Nat","Nat.Coprime","Nat.instOne","instMulNat"],"value_dag_size":37,"value_refs":["List","List.instMembership","List.prod","Membership.mem","Nat","Nat.Coprime","Nat.coprime_list_prod_left_iff","Nat.instOne","instMulNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":229,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":1030,"value_refs":["Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","Nat","Nat.succ","OfNat.ofNat","_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_5","_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.splitter","congr","congrArg","congrFun","hyperoperation.match_1","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":86,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":83,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":81,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":83,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":81,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_4","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":89,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":86,"value_refs":["Eq.refl","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.eq_5","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":null,"statement_dag_size":91,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","hyperoperation.match_1","instOfNatNat"],"value_dag_size":405,"value_refs":["Eq","Eq.refl","Nat","Nat.casesOn","Nat.rec","Nat.succ","Nat.zero","OfNat.ofNat","hyperoperation.match_1","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation.match_1","reducibility":"abbrev","statement_dag_size":70,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["hyperoperation.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_four_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_four_zero","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Even","HAdd.hAdd","Nat","Nat.instDecidablePredEven","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat","ite"],"value_dag_size":259,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","HAdd.hAdd","HMod.hMod","Iff","Lean.Grind.eq_true_eq","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.even_iff","Nat.instDecidablePredEven","Nat.instMod","Not","OfNat.ofNat","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_self","eq_true","hyperoperation","hyperoperation_ge_three_eq_one","id","instAddNat","instHAdd","instHMod","instOfNatNat","ite","ite_cond_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_four_zero._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_four_zero","reducibility":null,"statement_dag_size":67,"type_refs":["Eq","Even","HAdd.hAdd","Nat","Nat.instDecidablePredEven","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat","ite"],"value_dag_size":1329,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Even","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.mod","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_false_eq","Lean.Grind.iff_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.ToInt.add_congr","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ctorIdx","Nat.even_add","Nat.even_iff","Nat.instDecidablePredEven","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_false'","eq_true","hyperoperation","hyperoperation_ge_three_eq_one","hyperoperation_ge_two_eq_self","hyperoperation_recursion","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_cond_eq_true","noConfusion_of_Nat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_eq_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_eq_one","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":208,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.succ","Nat.succ_eq_add_one","Not","OfNat.ofNat","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","hyperoperation","hyperoperation.eq_4","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_one","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":117,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HAdd.hAdd","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.one_pow","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","hyperoperation","hyperoperation_three","id","instAddNat","instHAdd","instHPow","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_one._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_three_one","reducibility":null,"statement_dag_size":47,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":421,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.casesOn","Nat.succ","Nat.succ_eq_add_one","Nat.zero","Nat.zero_eq","Not","OfNat.ofNat","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","hyperoperation","hyperoperation_ge_three_eq_one","hyperoperation_recursion","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_two_eq_self._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_two_eq_self","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":117,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.instCommSemiringNat","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","hyperoperation","hyperoperation_two","id","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_two_eq_self._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_two_eq_self","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":278,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","hyperoperation","hyperoperation_ge_three_eq_one","hyperoperation_recursion","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_one","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":142,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Not","OfNat.ofNat","True","True.intro","congrArg","eagerReduce","eq_false","eq_true","hyperoperation","hyperoperation.eq_2","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_one._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_one","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":381,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","hyperoperation","hyperoperation_recursion","hyperoperation_zero","id","instAddNat","instHAdd","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_recursion._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_recursion","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":146,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HAdd.hAdd","Nat","Nat.succ","Nat.succ_eq_add_one","Not","OfNat.ofNat","True","True.intro","congr","congrArg","congrFun'","eq_false","eq_true","hyperoperation","hyperoperation.eq_5","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_three._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_three","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","hyperoperation","instHPow","instOfNatNat"],"value_dag_size":134,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HPow.hPow","Lean.Grind.intro_with_eq","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Nat.pow_zero","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","hyperoperation","hyperoperation_ge_three_eq_one","id","instAddNat","instHAdd","instHPow","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_three._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_three","reducibility":null,"statement_dag_size":61,"type_refs":["Eq","HAdd.hAdd","HPow.hPow","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instHPow","instOfNatNat"],"value_dag_size":409,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.pow_one","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.Semiring.npow","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.ne_of_ne_of_eq_right","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Monoid.toNPow","NPow.toPow","Nat","Nat.instMonoid","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","hyperoperation","hyperoperation_recursion","hyperoperation_two","id","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatPowNat","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HMul.hMul","Nat","OfNat.ofNat","hyperoperation","instHMul","instMulNat","instOfNatNat"],"value_dag_size":114,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HMul.hMul","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_zero","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Nat","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","hyperoperation","hyperoperation.eq_3","id","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":443,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_norm","Int.Internal.Linear.diseq_norm_poly","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_norm_poly","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instMul","Int.instNegInt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.ne_of_ne_of_eq_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","hyperoperation","hyperoperation_one","hyperoperation_recursion","id","instAddNat","instHAdd","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two_two_eq_four._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two_two_eq_four","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":94,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Nat","Not","OfNat.ofNat","True","True.intro","eq_false","eq_true","hyperoperation","hyperoperation_one","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two_two_eq_four._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_two_two_eq_four","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":272,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Lean.Grind.intro_with_eq","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Not","OfNat.ofNat","True","True.intro","congr","congrArg","congrFun'","eagerReduce","eq_false","eq_true","hyperoperation","hyperoperation_ge_two_eq_self","hyperoperation_recursion","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Hyperoperation","name":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_zero","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HAdd.hAdd","Nat","OfNat.ofNat","hyperoperation","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":90,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Nat","Not","OfNat.ofNat","True","True.intro","eq_false","eq_true","hyperoperation","hyperoperation.eq_1","id","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.AtLeastTwo.neZero_sub_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.AtLeastTwo.neZero_sub_one","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HSub.hSub","LE.le","Nat","Not","OfNat.ofNat","Zero.ofOfNat0","Zero.toOfNat0","instHSub","instLENat","instOfNatNat","instSubNat"],"value_dag_size":600,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","Zero.ofOfNat0","Zero.toOfNat0","congrArg","congrFun'","eagerReduce","eq_true","id","instHAdd","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.diag_induction._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.diag_induction","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":428,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.diag_induction.match_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.diag_induction","reducibility":"abbrev","statement_dag_size":69,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":265,"value_refs":["Eq","Eq.refl","False","False.elim","HAdd.hAdd","HEq","HEq.refl","LT.lt","Nat","Nat.casesOn","Nat.ctorIdx","Nat.le","Nat.le.casesOn","Nat.le.refl","Nat.le.step","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1","reducibility":null,"statement_dag_size":70,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","Nat.leRec.match_1","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":68,"value_refs":["Eq.refl","HAdd.hAdd","LE.le","Nat","Nat.leRec.match_1","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1","reducibility":null,"statement_dag_size":75,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","Nat.leRec.match_1","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":72,"value_refs":["Eq.refl","HAdd.hAdd","LE.le","Nat","Nat.leRec.match_1","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.leRec.match_1","reducibility":"abbrev","statement_dag_size":61,"type_refs":["HAdd.hAdd","LE.le","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLENat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.leRec.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.not_two_dvd_bit1._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.not_two_dvd_bit1","reducibility":null,"statement_dag_size":44,"type_refs":["Dvd.dvd","HAdd.hAdd","HMul.hMul","Nat","Nat.instDvd","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":183,"value_refs":["Bool","Bool.true","Classical.byContradiction","Dvd.dvd","Eq","Eq.refl","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.dvd_norm_expr","Int.Internal.Linear.dvd_unsat","Int.instAdd","Int.instMul","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_dvd","Nat.instDvd","NatCast.natCast","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1","reducibility":null,"statement_dag_size":139,"type_refs":["Eq","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":560,"value_refs":["Eq","Eq.mpr","Eq.ndrec","Eq.refl","Eq.symm","False","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.eq_2","_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.splitter","congr","congrArg","congrFun","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":47,"value_refs":["Eq.refl","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","False","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":196,"value_refs":["Eq","Eq.refl","False","Nat","Nat.casesOn","Nat.pincerRecursion.match_1","Nat.rec","Nat.succ","Nat.zero","OfNat.ofNat","absurd","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.eq_3","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":51,"value_refs":["Eq.refl","Nat","Nat.pincerRecursion.match_1","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.pincerRecursion.match_1","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Eq","False","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":80,"value_refs":["Eq","False","False.elim","Nat","Nat.casesOn","Nat.ctorIdx","Nat.succ","OfNat.ofNat","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.stepInduction._proof_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.stepInduction","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","HAdd.hAdd","HSub.hSub","LT.lt","Nat","Not","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":750,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.not_eq_norm_expr","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Nat","Nat.strongSubRecursion.match_1"],"value_dag_size":120,"value_refs":["Eq","Eq.refl","Nat","Nat.strongSubRecursion.match_1","_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Nat","Nat.strongSubRecursion.match_1"],"value_dag_size":27,"value_refs":["Eq.refl","Nat","Nat.strongSubRecursion.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.strongSubRecursion.match_1","reducibility":"abbrev","statement_dag_size":19,"type_refs":["Nat"],"value_dag_size":1,"value_refs":["Nat.strongSubRecursion.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.two_le_iff.match_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.two_le_iff","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.two_lt_of_ne.match_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.two_lt_of_ne","reducibility":"abbrev","statement_dag_size":123,"type_refs":["HAdd.hAdd","Nat","Nat.succ","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":240,"value_refs":["HAdd.hAdd","Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.Nat.two_mul_odd_div_two._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Init.0.Nat.two_mul_odd_div_two","reducibility":null,"statement_dag_size":66,"type_refs":["Eq","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Nat","Nat.instDiv","Nat.instMod","OfNat.ofNat","instHDiv","instHMod","instHMul","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":1062,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_coeff","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.div","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.div_congr","Nat.ToInt.mod_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instDiv","Nat.instMod","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congrArg","congrFun'","eagerReduce","eq_false","eq_true","id","instHAdd","instHDiv","instHMod","instHMul","instHSub","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Init","name":"_private.Mathlib.Data.Nat.Init.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Init.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.add_pred_div_lt._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.add_pred_div_lt","reducibility":null,"statement_dag_size":24,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":259,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.add_pred_div_lt._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.add_pred_div_lt","reducibility":null,"statement_dag_size":40,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":364,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HMul.hMul","HPow.hPow","Nat","OfNat.ofNat","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":43,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Nat","Nat.pow_two","OfNat.ofNat","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HMul.hMul","HPow.hPow","Nat","instHMul","instHPow","instMulNat","instNatPowNat","instPowNat"],"value_dag_size":45,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Nat","Nat.pow_mul","instHMul","instHPow","instMulNat","instNatPowNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog.go_spec","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HMul.hMul","LT.lt","Nat","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":47,"value_refs":["HMul.hMul","LT.lt","Nat","Nat.mul_lt_mul_left","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_clog_succ_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_clog_succ_iff","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_clog_succ_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_clog_succ_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_one","reducibility":null,"statement_dag_size":69,"type_refs":["HAdd.hAdd","HMul.hMul","HSub.hSub","LE.le","LT.lt","Nat","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":895,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.instCommRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_one._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_eq_one","reducibility":null,"statement_dag_size":34,"type_refs":["LE.le","LT.lt","Nat","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":306,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_le_iff_le_pow._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_le_iff_le_pow","reducibility":null,"statement_dag_size":61,"type_refs":["And","HPow.hPow","Iff","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":850,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HPow.hPow","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Nonneg.natCast","Int.Nonneg.pow","Int.Nonneg.toPoly","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_left","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.pow_congr","Nat.not_le_eq","Nat.one_le_pow","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHPow","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_le_of_le_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_le_of_le_pow","reducibility":null,"statement_dag_size":29,"type_refs":["GE.ge","LE.le","Nat","Nat.clog","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":287,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.clog","Nat.clog_of_left_le_one","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","True","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_left_le_one._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_left_le_one","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","LE.le","Nat","Nat.clog","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":403,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.and_eq_of_eq_false_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.clog","Nat.clog.eq_1","Nat.clog.go","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod.snd","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableAnd","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt","reducibility":null,"statement_dag_size":85,"type_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat","instSubNat"],"value_dag_size":2272,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_def'_norm","Int.Internal.Linear.eq_def_norm","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_neg","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.Nonneg.mul","Int.Nonneg.natCast","Int.Nonneg.pow","Int.Nonneg.toPoly","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instMul","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.norm_int","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast","Lean.Grind.Semiring.natCast_add","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.Semiring.natCast_mul","Lean.Grind.Semiring.natCast_pow","Lean.Grind.Semiring.toAdd","Lean.Grind.Semiring.toMul","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.iff_eq","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.var","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.of_not_le","Nat.ToInt.pow_congr","Nat.ToInt.toNat_nonneg","Nat.cast","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HPow.hPow","LE.le","LT.lt","Nat","Nat.clog","OfNat.ofNat","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":57,"value_refs":["HPow.hPow","LE.le","LT.lt","Nat","Nat.clog","Nat.clog_le_iff_le_pow","OfNat.ofNat","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","HAdd.hAdd","LE.le","Nat","instAddNat","instHAdd","instLENat"],"value_dag_size":36,"value_refs":["HAdd.hAdd","LE.le","Nat","Nat.add_le_add_iff_right","instAddNat","instHAdd","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt","reducibility":null,"statement_dag_size":82,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","LT.lt","Nat","Nat.instDiv","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":87,"value_refs":["HAdd.hAdd","HDiv.hDiv","HMul.hMul","HSub.hSub","LE.le","LT.lt","Nat","Nat.div_le_iff_le_mul","Nat.instDiv","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_right_le_one._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_right_le_one","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","LE.le","Nat","Nat.clog","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":403,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.and_eq_of_eq_false_right","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.nestedDecidable","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.clog","Nat.clog.eq_1","Nat.clog.go","Nat.decLe","Nat.decLt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod.snd","True","True.intro","congr","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instDecidableAnd","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","ite","ite_cond_eq_false","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_pow_left._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_pow_left","reducibility":null,"statement_dag_size":98,"type_refs":["Eq","GE.ge","GT.gt","HAdd.hAdd","HDiv.hDiv","HPow.hPow","HSub.hSub","Nat","Nat.clog","Nat.instDiv","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instHPow","instHSub","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat","instSubNat"],"value_dag_size":759,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GE.ge","GT.gt","HAdd.hAdd","HDiv.hDiv","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.add","Int.Nonneg.div","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.Stepwise.core","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.d_step1","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.OfSemiring.of_eq","Lean.Grind.Ring.OfSemiring.toQ","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.eq_eq_of_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommSemiringNat","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_eq_of_eq_false","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.add_congr","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.clog","Nat.clog_of_left_le_one","Nat.instDiv","Nat.pow_le_one_iff","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","congrArg","eagerReduce","eq_false","eq_true","id","implies_congr","instAddNat","instHAdd","instHDiv","instHPow","instHSub","instLENat","instLTNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_pow_left._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.clog_pow_left","reducibility":null,"statement_dag_size":38,"type_refs":["GT.gt","HSub.hSub","LT.lt","Nat","OfNat.ofNat","instHSub","instLTNat","instOfNatNat","instSubNat"],"value_dag_size":677,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","GT.gt","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.eq_of_norm_eq","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toCommSemiring","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.Semiring.natCast_eq_ofNat","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_true","ite_congr","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Nat","Nat.log.go.match_1","Prod","Prod.mk"],"value_dag_size":33,"value_refs":["Eq.refl","Nat","Nat.log.go.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_1","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Nat","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["Nat.log.go.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3.eq_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","Nat","Nat.log.go.match_3","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":40,"value_refs":["Eq.refl","Nat","Nat.log.go.match_3","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3.eq_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","Nat","Nat.log.go.match_3","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":43,"value_refs":["Eq.refl","Nat","Nat.log.go.match_3","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3.splitter","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go.match_3","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.log.go.match_3"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log","reducibility":null,"statement_dag_size":74,"type_refs":["HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instLENat","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":243,"value_refs":["Eq","Eq.mp","Eq.mpr","Eq.ndrec","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HMul.hMul","HPow.hPow","LE.le","LT.lt","Nat","Nat.lt_of_lt_of_le","Nat.not_lt_of_le","Nat.pow_le_pow_right","Nat.pow_mul","Nat.pow_one","Nat.pow_two","Nat.zero_add","OfNat.ofNat","_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux._proof_1_1","_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux._proof_1_2","congrArg","eq_false","id","instAddNat","instHAdd","instHMul","instHPow","instLENat","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux","reducibility":null,"statement_dag_size":24,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":259,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_aux","reducibility":null,"statement_dag_size":52,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":283,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LE.le","Nat","Ne","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":30,"value_refs":["LE.le","Nat","Nat.one_le_iff_ne_zero","Ne","OfNat.ofNat","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HMul.hMul","HPow.hPow","Nat","OfNat.ofNat","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":43,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Nat","Nat.pow_two","OfNat.ofNat","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","HMul.hMul","HPow.hPow","Nat","instHMul","instHPow","instMulNat","instNatPowNat","instPowNat"],"value_dag_size":45,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Nat","Nat.pow_mul","instHMul","instHPow","instMulNat","instNatPowNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_7","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","HDiv.hDiv","HMul.hMul","LT.lt","Nat","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":57,"value_refs":["HDiv.hDiv","HMul.hMul","LT.lt","Nat","Nat.div_lt_iff_lt_mul","Nat.instDiv","OfNat.ofNat","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_8","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":58,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","Nat","Nat.pow_add_one","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_9","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec","reducibility":null,"statement_dag_size":54,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","HPow.hPow","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":58,"value_refs":["Eq.symm","HAdd.hAdd","HMul.hMul","HPow.hPow","Nat","Nat.pow_add_one'","OfNat.ofNat","instAddNat","instHAdd","instHMul","instHPow","instMulNat","instNatPowNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_div_base_pow._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_div_base_pow","reducibility":null,"statement_dag_size":57,"type_refs":["Eq","HDiv.hDiv","HPow.hPow","HSub.hSub","Nat","Nat.instDiv","Nat.log","OfNat.ofNat","instHDiv","instHPow","instHSub","instNatPowNat","instOfNatNat","instPowNat","instSubNat"],"value_dag_size":144,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","HDiv.hDiv","HPow.hPow","HSub.hSub","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.div_one","Nat.instDiv","Nat.log","Nat.pow_zero","Nat.sub_zero","Not","OfNat.ofNat","True","congr","congrArg","eq_self","instHDiv","instHPow","instHSub","instNatPowNat","instOfNatNat","instPowNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_div_mul_self._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_div_mul_self","reducibility":null,"statement_dag_size":35,"type_refs":["LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instLTNat","instOfNatNat"],"value_dag_size":270,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instLinearOrder","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_iff","reducibility":null,"statement_dag_size":71,"type_refs":["And","Eq","HAdd.hAdd","HPow.hPow","Iff","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":490,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNatPow","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Nat.pow_one","Lean.Grind.Semiring.mul_zero","Lean.Grind.Semiring.ofNat","Lean.Grind.Semiring.pow_add_congr","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.iff_eq","Lean.Grind.instCommSemiringNat","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.pow_congr","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","congr","congrArg","eagerReduce","eq_false","id","instAddNat","instHAdd","instHMul","instHPow","instHSub","instLENat","instLTNat","instMulNat","instNatCastInt","instNatPowNat","instOfNat","instOfNatNat","instPowNat","instSubNat","of_decide_eq_true","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_iff._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_iff","reducibility":null,"statement_dag_size":71,"type_refs":["And","Eq","HAdd.hAdd","HPow.hPow","Iff","LE.le","LT.lt","Nat","Ne","OfNat.ofNat","instAddNat","instHAdd","instHPow","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":346,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HPow.hPow","HSub.hSub","Iff","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.eq_congr'","Lean.Grind.eq_false_of_or_eq_false_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_and","Lean.Grind.not_eq_prop","Lean.Grind.or_eq_of_eq_false_right","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.le_zero_eq","Nat.not_le_eq","Nat.one_pow","Ne","Not","OfNat.ofNat","Or","True","True.intro","congr","congrArg","congrFun'","eq_false","id","instAddNat","instHAdd","instHPow","instHSub","instLENat","instLTNat","instNatPowNat","instOfNatNat","instPowNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_log_succ_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_log_succ_iff","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_log_succ_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_log_succ_iff","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Iff"],"value_dag_size":20,"value_refs":["And","Iff","and_iff_right_iff_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_zero_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_eq_zero_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Iff","LE.le","LT.lt","Nat","Nat.log","OfNat.ofNat","Or","instLENat","instLTNat","instOfNatNat"],"value_dag_size":560,"value_refs":["And","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.iff_eq","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.le_zero_eq","Nat.log","Nat.log_of_lt","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","True","congr","congrArg","congrFun'","eagerReduce","eq_true","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_lt_of_lt_pow'._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_lt_of_lt_pow'","reducibility":null,"statement_dag_size":27,"type_refs":["LT.lt","Nat","Nat.log","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":317,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.log","Nat.log_zero_right","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_lt_self.match_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_lt_self","reducibility":"abbrev","statement_dag_size":72,"type_refs":["LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","Or","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","instOfNatNat"],"value_dag_size":86,"value_refs":["LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","OfNat.ofNat","Or","Or.casesOn","Or.inl","Or.inr","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Nat","OfNat.ofNat","Prod.mk","Prod.snd","instOfNatNat"],"value_dag_size":60,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Not","OfNat.ofNat","Prod.mk","Prod.snd","True","congrArg","eq_self","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","Nat","Nat.succ","OfNat.ofNat","Prod.mk","Prod.snd","instOfNatNat"],"value_dag_size":63,"value_refs":["Classical.byContradiction","Eq","Eq.trans","False","False.casesOn","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.succ","Not","OfNat.ofNat","Prod.mk","Prod.snd","True","congrArg","eq_self","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt","reducibility":null,"statement_dag_size":58,"type_refs":["Eq","HMul.hMul","LT.lt","Nat","Nat.succ","Not","OfNat.ofNat","Prod.mk","Prod.snd","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":430,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod.mk","Prod.snd","True","True.intro","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt._proof_1_6","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_lt","reducibility":null,"statement_dag_size":85,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","HMul.hMul","LT.lt","Nat","Nat.instDiv","Nat.succ","Not","OfNat.ofNat","Prod.mk","Prod.snd","instAddNat","instHAdd","instHDiv","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":443,"value_refs":["Bool","Bool.false","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HDiv.hDiv","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instDiv","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Prod.mk","Prod.snd","True","True.intro","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHDiv","instHMul","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le","reducibility":null,"statement_dag_size":24,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":259,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le","reducibility":null,"statement_dag_size":19,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":325,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instLinearOrder","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","True","True.intro","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HDiv.hDiv","Nat","Nat.instDiv","Ne","Not","OfNat.ofNat","instHDiv","instOfNatNat"],"value_dag_size":213,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","HDiv.hDiv","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.div","Int.Nonneg.natCast","Int.Nonneg.toPoly","Int.instDiv","Int.instNegInt","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.div_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.instDiv","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instHDiv","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.log_of_one_lt_of_le","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","LE.le","LT.lt","Nat","Not","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":241,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Log","name":"_private.Mathlib.Data.Nat.Log.0.Nat.pow_log_le_add_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Log.0.Nat.pow_log_le_add_one","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.divMaxPow_base_pow_mul._proof_1_1","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.divMaxPow_base_pow_mul","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","Or","instLTNat","instOfNatNat"],"value_dag_size":321,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv._simp_3","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv","reducibility":null,"statement_dag_size":51,"type_refs":["And","Eq","HMul.hMul","LT.lt","Nat","OfNat.ofNat","Or","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":53,"value_refs":["And","HMul.hMul","LT.lt","Nat","Nat.one_lt_mul_iff","OfNat.ofNat","Or","instHMul","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec._simp_1_3","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":46,"value_refs":["Dvd.dvd","Eq","Eq.symm","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec._simp_1_4","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HMul.hMul","Nat","instHMul","instMulNat"],"value_dag_size":32,"value_refs":["Eq.symm","HMul.hMul","Nat","Nat.mul_assoc","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec._simp_1_6","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Nat","Nat.maxPowDvdDiv.match_1","Prod","Prod.mk"],"value_dag_size":33,"value_refs":["Eq.refl","Nat","Nat.maxPowDvdDiv.match_1","Prod","Prod.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.match_1","reducibility":"abbrev","statement_dag_size":22,"type_refs":["Nat","Prod","Prod.mk"],"value_dag_size":1,"value_refs":["Nat.maxPowDvdDiv.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv_of_pow_mul_eq._proof_1_1","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv_of_pow_mul_eq","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","LT.lt","Nat","OfNat.ofNat","Or","instLTNat","instOfNatNat"],"value_dag_size":361,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.not_dvd_divMaxPow._simp_1_3","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.not_dvd_divMaxPow","reducibility":null,"statement_dag_size":73,"type_refs":["And","Eq","HMul.hMul","HPow.hPow","LT.lt","Nat","Nat.maxPowDvdDiv.go","Ne","OfNat.ofNat","Prod.fst","Prod.snd","instHMul","instHPow","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":36,"value_refs":["And","LT.lt","Nat","Nat.maxPowDvdDiv.go_spec","Ne","OfNat.ofNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.not_dvd_divMaxPow._simp_1_4","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.not_dvd_divMaxPow","reducibility":null,"statement_dag_size":51,"type_refs":["And","Dvd.dvd","Eq","False","LT.lt","Nat","Nat.instDvd","Nat.maxPowDvdDiv.go","Ne","OfNat.ofNat","Prod.snd","instLTNat","instOfNatNat"],"value_dag_size":53,"value_refs":["And","Dvd.dvd","LT.lt","Nat","Nat.instDvd","Nat.maxPowDvdDiv.go","Nat.maxPowDvdDiv.go_spec","Ne","OfNat.ofNat","Prod.snd","eq_false","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.padicValNat_lt_self._proof_1_3","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.padicValNat_lt_self","reducibility":null,"statement_dag_size":31,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":101,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.Simproc.le_add_le","Nat.decLe","Not","OfNat.ofNat","True","congrArg","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.padicValNat_lt_self.match_1_1","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.padicValNat_lt_self","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.pow_dvd_iff_le_of_spec","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat","reducibility":null,"statement_dag_size":89,"type_refs":["Dvd.dvd","Eq","HMul.hMul","HPow.hPow","Iff","LE.le","LT.lt","Nat","Nat.instDvd","Ne","Not","OfNat.ofNat","instHMul","instHPow","instLENat","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":380,"value_refs":["Dvd.dvd","Eq","Eq.mp","Eq.ndrec","Eq.refl","Eq.symm","Exists","Exists.casesOn","False","GE.ge","HAdd.hAdd","HMul.hMul","HPow.hPow","Iff","LE.le","LT.lt","Nat","Nat.add_assoc","Nat.dvd_mul_right_of_dvd","Nat.dvd_of_pow_dvd","Nat.exists_eq_add_of_lt","Nat.instDvd","Nat.le_add_left","Nat.lt_or_ge","Nat.mul_dvd_mul_iff_left","Nat.not_le_of_lt","Nat.pow_add","Nat.pow_dvd_pow","Nat.pow_pos","Nat.zero_lt_of_lt","Ne","Not","OfNat.ofNat","Or","Or.casesOn","Or.inl","Or.inr","congrArg","iff_of_false","iff_of_true","instAddNat","instHAdd","instHMul","instHPow","instLENat","instLTNat","instMulNat","instNatPowNat","instOfNatNat","instPowNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.pow_dvd_iff_le_padicValNat._proof_1_1","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.pow_dvd_iff_le_padicValNat","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","Or","instLTNat","instOfNatNat"],"value_dag_size":321,"value_refs":["And","And.casesOn","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_or","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","Or","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.pow_dvd_iff_le_padicValNat._simp_1_2","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.pow_dvd_iff_le_padicValNat","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","False","LT.lt","Nat","instLTNat"],"value_dag_size":24,"value_refs":["Eq","LT.lt","Nat","Nat.ne_of_gt","eq_false","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.MaxPowDiv","name":"_private.Mathlib.Data.Nat.MaxPowDiv.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.MaxPowDiv.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.add_le_of_lt._proof_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.add_le_of_lt","reducibility":null,"statement_dag_size":30,"type_refs":["HAdd.hAdd","LT.lt","Nat","instAddNat","instHAdd","instLTNat"],"value_dag_size":323,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.add_left_cancel._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.add_left_cancel","reducibility":null,"statement_dag_size":41,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","instHSub","instNatCastInt"],"value_dag_size":44,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","Nat.modEq_iff_dvd","instHSub","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.cancel_left_div_gcd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.cancel_left_div_gcd","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HDiv.hDiv","Int","Int.instDiv","Nat","Nat.cast","Nat.instDiv","instHDiv","instNatCastInt"],"value_dag_size":41,"value_refs":["Eq.symm","HDiv.hDiv","Int","Int.instDiv","Int.natCast_div","Nat","Nat.cast","Nat.instDiv","instHDiv","instNatCastInt"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.dvd_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.dvd_iff","reducibility":null,"statement_dag_size":27,"type_refs":["Dvd.dvd","Eq","Nat","Nat.ModEq","Nat.instDvd","OfNat.ofNat","instOfNatNat"],"value_dag_size":35,"value_refs":["Dvd.dvd","Eq.symm","Nat","Nat.ModEq","Nat.instDvd","Nat.modEq_zero_iff_dvd","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.le_of_lt_add._proof_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.le_of_lt_add","reducibility":null,"statement_dag_size":56,"type_refs":["HAdd.hAdd","HSub.hSub","LE.le","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLE","instAddNat","instHAdd","instHSub","instLTNat","instSubNat"],"value_dag_size":719,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.Internal.Linear.natCast_sub","Int.Internal.Linear.norm_le","Int.decLe","Int.instAdd","Int.instLEInt","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.alreadyNorm","Lean.Grind.em","Lean.Grind.intro_with_eq","Lean.Grind.nestedDecidable","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLE","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","ite","ite_cond_eq_false","ite_cond_eq_true","ite_congr"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_left_cancel'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_left_cancel'","reducibility":null,"statement_dag_size":41,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","instHSub","instNatCastInt"],"value_dag_size":44,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","Nat.modEq_iff_dvd","instHSub","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_left_cancel'._simp_1_2","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_left_cancel'","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","instHMul","instHSub"],"value_dag_size":42,"value_refs":["Eq.symm","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","Int.mul_sub","instHMul","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_right_cancel'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_right_cancel'","reducibility":null,"statement_dag_size":41,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","instHSub","instNatCastInt"],"value_dag_size":44,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","Nat.modEq_iff_dvd","instHSub","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_right_cancel'._simp_1_2","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.ModEq.mul_right_cancel'","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","instHMul","instHSub"],"value_dag_size":44,"value_refs":["Eq.symm","HMul.hMul","HSub.hSub","Int","Int.instMul","Int.instSub","Int.sub_mul","instHMul","instHSub"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.add_modEq_left_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.add_modEq_left_iff","reducibility":null,"statement_dag_size":41,"type_refs":["Dvd.dvd","Eq","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","instHSub","instNatCastInt"],"value_dag_size":44,"value_refs":["Dvd.dvd","HSub.hSub","Int","Int.instDvd","Int.instSub","Nat","Nat.ModEq","Nat.cast","Nat.modEq_iff_dvd","instHSub","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.add_modEq_left_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.add_modEq_left_iff","reducibility":null,"statement_dag_size":28,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Nat","Nat.cast","Nat.instDvd","instNatCastInt"],"value_dag_size":30,"value_refs":["Dvd.dvd","Int","Int.instDvd","Int.natCast_dvd_natCast","Nat","Nat.cast","Nat.instDvd","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.le_mod_add_mod_of_dvd_add_of_not_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.le_mod_add_mod_of_dvd_add_of_not_dvd","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.modEq_iff_eq_of_div_eq._proof_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.modEq_iff_eq_of_div_eq","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","HDiv.hDiv","Iff","Nat","Nat.ModEq","Nat.instDiv","instHDiv"],"value_dag_size":139,"value_refs":["And","Classical.byContradiction","Eq","Eq.mp","Eq.symm","Eq.trans","False","HDiv.hDiv","Iff","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.false_of_not_eq_self","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Nat","Nat.ModEq","Nat.ext_div_modEq_iff","Nat.instDiv","Not","congrArg","eq_true","id","instHDiv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.odd_mod_four_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.odd_mod_four_iff","reducibility":null,"statement_dag_size":18,"type_refs":["LT.lt","Nat","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":97,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_true","Nat","Nat.decLe","Not","OfNat.ofNat","True","congrArg","eq_true_of_decide","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.ModEq","name":"_private.Mathlib.Data.Nat.ModEq.0.Nat.odd_mul_odd_div_two._proof_1_1","namespace":"_private.Mathlib.Data.Nat.ModEq.0.Nat.odd_mul_odd_div_two","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","HMod.hMod","LE.le","Nat","Nat.instMod","OfNat.ofNat","instHMod","instLENat","instOfNatNat"],"value_dag_size":391,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_unsat_coeff","Int.instAdd","Int.instDiv","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.mod_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.decLe","Nat.instMod","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity","reducibility":null,"statement_dag_size":55,"type_refs":["Disjoint","Eq","Finset","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":58,"value_refs":["Disjoint","Finset","Finset.disjoint_right","Finset.instOrderBot","Finset.instPartialOrder","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity","reducibility":null,"statement_dag_size":37,"type_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat"],"value_dag_size":40,"value_refs":["Dvd.dvd","Eq","HMod.hMod","Nat","Nat.dvd_iff_mod_eq_zero","Nat.instDvd","Nat.instMod","OfNat.ofNat","instHMod","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial","reducibility":"abbrev","statement_dag_size":78,"type_refs":["HAdd.hAdd","LT.lt","Nat","Nat.log","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":107,"value_refs":["HAdd.hAdd","LT.lt","Nat","Nat.casesOn","Nat.log","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul_succ._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul_succ","reducibility":null,"statement_dag_size":45,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":415,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.Nonneg.add","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_ge","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul_succ._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_factorial_mul_succ","reducibility":null,"statement_dag_size":43,"type_refs":["Eq","Finset.Ico","Finset.prod","HAdd.hAdd","Nat","Nat.factorial","Nat.instCommMonoid","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":46,"value_refs":["Eq.symm","Finset.Ico","Finset.prod","Finset.prod_Ico_id_eq_factorial","HAdd.hAdd","Nat","Nat.factorial","Nat.instCommMonoid","Nat.instLocallyFiniteOrder","Nat.instPreorder","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_le_emultiplicity_choose_add.match_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.emultiplicity_le_emultiplicity_choose_add","reducibility":"abbrev","statement_dag_size":38,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":58,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.sub_one_mul_multiplicity_factorial._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.Prime.sub_one_mul_multiplicity_factorial","reducibility":null,"statement_dag_size":99,"type_refs":["Eq","Finset.range","Finset.sum","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","List.sum","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.digits","Nat.instAddCommMonoid","Nat.instDiv","Nat.instMonoid","Nat.instMulZeroClass","Nat.log","Nat.succ","OfNat.ofNat","instAddNat","instHDiv","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"],"value_dag_size":103,"value_refs":["Eq.symm","Finset.range","Finset.sum","HDiv.hDiv","HMul.hMul","HPow.hPow","HSub.hSub","List.sum","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.digits","Nat.instAddCommMonoid","Nat.instDiv","Nat.instMonoid","Nat.instMulZeroClass","Nat.log","Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits","Nat.succ","OfNat.ofNat","instAddNat","instHDiv","instHMul","instHPow","instHSub","instMulNat","instOfNatNat","instSubNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":62,"type_refs":["And","Eq","Finset","Finset.Ico","Finset.instSetLike","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership"],"value_dag_size":68,"value_refs":["And","Finset","Finset.Ico","Finset.instSetLike","Finset.mem_Ico","LE.le","LT.lt","LocallyFiniteOrder","Membership.mem","Preorder","Preorder.toLE","Preorder.toLT","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","LT.lt","Nat","Nat.succ","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.lt_succ_iff","Nat.succ","instLENat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq"],"value_dag_size":23,"value_refs":["And","and_assoc","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":21,"type_refs":["And","Eq","Iff"],"value_dag_size":25,"value_refs":["And","Iff","and_congr_right_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Iff"],"value_dag_size":19,"value_refs":["And","Iff","iff_and_self","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt","reducibility":null,"statement_dag_size":33,"type_refs":["And","Bool","Bool.false","Eq","Nat","Nat.bit","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["And","Bool","Bool.false","Eq","Nat","Nat.bit","Nat.bit_eq_zero_iff","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","Nat","Nat.Prime","OfNat.ofNat","True","instOfNatNat"],"value_dag_size":14,"value_refs":["Nat","Nat.Prime","Nat.prime_two","OfNat.ofNat","eq_true","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt.match_1_2","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_two_factorial_lt","reducibility":"abbrev","statement_dag_size":28,"type_refs":["ENat","ENat.instNatCast","Eq","Nat","Nat.cast","Top.top","WithTop","WithTop.top"],"value_dag_size":100,"value_refs":["ENat","ENat.instNatCast","Eq","Eq.casesOn","Eq.refl","False","False.elim","HEq","HEq.refl","Nat","Nat.cast","Option","Option.ctorIdx","Option.none","Option.some","Top.top","WithTop","WithTop.top","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.factorial.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Multiplicity","name":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Multiplicity.0.Nat.factorial.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.factorial.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_eq_insert","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert","reducibility":null,"statement_dag_size":51,"type_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Insert.insert","Membership.mem","Or","SetLike.instMembership"],"value_dag_size":56,"value_refs":["DecidableEq","Eq","Finset","Finset.instInsert","Finset.instSetLike","Finset.mem_insert","Insert.insert","Membership.mem","Or","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.filter_range_nth_subset_insert","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card","reducibility":null,"statement_dag_size":39,"type_refs":["Eq","Exists","Fin","Fin.mk","LT.lt","Nat","instLTNat"],"value_dag_size":42,"value_refs":["Exists","Fin","Fin.exists_iff","Fin.mk","LT.lt","Nat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Iio","Set.instMembership"],"value_dag_size":42,"value_refs":["LT.lt","Membership.mem","Preorder","Preorder.toLT","Set","Set.Iio","Set.instMembership","Set.mem_Iio","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.isLeast_nth.match_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.isLeast_nth","reducibility":"abbrev","statement_dag_size":121,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset.card","LT.lt","Nat","Nat.nth","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLTNat"],"value_dag_size":185,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset.card","LT.lt","Nat","Nat.nth","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_count.match_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_count","reducibility":"abbrev","statement_dag_size":103,"type_refs":["And","And.intro","DistribLattice.toLattice","Exists","Exists.intro","LT.lt","Lattice.toSemilatticeInf","Membership.mem","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instMembership","Set.ofPred","instDistribLatticeOfLinearOrder"],"value_dag_size":150,"value_refs":["And","And.casesOn","And.intro","DistribLattice.toLattice","Exists","Exists.casesOn","Exists.intro","LT.lt","Lattice.toSemilatticeInf","Membership.mem","Nat","Nat.instLinearOrder","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set","Set.instMembership","Set.ofPred","instDistribLatticeOfLinearOrder"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn","reducibility":null,"statement_dag_size":15,"type_refs":["Nat","Set.Finite","Set.ofPred"],"value_dag_size":27,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","Nat","Set.Finite","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn","reducibility":null,"statement_dag_size":71,"type_refs":["Finset.card","HAdd.hAdd","LT.lt","Membership.mem","Nat","OfNat.ofNat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.ofPred","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":685,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset.card","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","exists_prop_congr","forall_congr","funext","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn","reducibility":null,"statement_dag_size":55,"type_refs":["Finset.card","LT.lt","Membership.mem","Nat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.ofPred","instLTNat"],"value_dag_size":217,"value_refs":["Classical.byContradiction","Eq.mp","Eq.symm","Eq.trans","False","Finset.card","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.ofPred","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn","reducibility":null,"statement_dag_size":97,"type_refs":["Finset.card","HAdd.hAdd","LE.le","LT.lt","Nat","Nat.instPreorder","Nat.nth","OfNat.ofNat","Preorder.toLT","Set.Finite","Set.Finite.toFinset","Set.ofPred","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"],"value_dag_size":1023,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset.card","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_false_right","Lean.Grind.true_imp_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.eq_true_of_isValid","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.instPreorder","Nat.not_le_eq","Nat.nth","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Set.Finite","Set.Finite.toFinset","Set.ofPred","True","_private.Mathlib.Data.Nat.Nth.0.Nat.le_nth_of_monotoneOn_of_surjOn._proof_1_1","congrArg","congrFun'","eagerReduce","eq_of_heq","eq_true","exists_prop_congr","forall_congr","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","Nat.nth_eq_zero","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.lt_card_toFinset_of_nth_ne_zero","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_add._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_add","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.range"],"value_dag_size":44,"value_refs":["Eq","Exists","Membership.mem","Set","Set.instMembership","Set.mem_range","Set.range","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_add._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_add","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_comp_of_strictMono.match_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_comp_of_strictMono","reducibility":"abbrev","statement_dag_size":98,"type_refs":["And","And.intro","Eq","Exists.intro","Membership.mem","Nat","Set","Set.image","Set.instMembership","Set.ofPred"],"value_dag_size":158,"value_refs":["And","And.casesOn","And.intro","Eq","Exists.casesOn","Exists.intro","Membership.mem","Nat","Set","Set.image","Set.instMembership","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","Not","Or"],"value_dag_size":19,"value_refs":["Classical.or_iff_not_imp_right","Not","Or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero_mono._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_eq_zero_mono","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","Nat.nth_eq_zero","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo","reducibility":null,"statement_dag_size":15,"type_refs":["Nat","Set.Finite","Set.ofPred"],"value_dag_size":27,"value_refs":["Eq.refl","Iff.mpr","Iff.of_eq","Nat","Set.Finite","Set.ofPred"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo","reducibility":null,"statement_dag_size":56,"type_refs":["Finset.card","LT.lt","Membership.mem","Nat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.ofPred","instLTNat"],"value_dag_size":704,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset.card","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_true","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_true_of_le_k","Lean.Grind.Order.le_trans_k","Lean.Grind.forall_propagator","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.of_forall_eq_false","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_1","congrArg","congrFun'","eagerReduce","eq_false","eq_true","exists_prop_congr","forall_congr","funext","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo","reducibility":null,"statement_dag_size":52,"type_refs":["Finset.card","LT.lt","Membership.mem","Nat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.ofPred","instLTNat"],"value_dag_size":222,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Finset.card","HAdd.hAdd","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Membership.mem","Nat","Not","OfNat.ofNat","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","Set.mem_ofPred_eq","Set.ofPred","True","True.intro","congrArg","congrFun'","eq_false","eq_true","forall_congr","funext","id","instAddNat","instHAdd","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo","reducibility":null,"statement_dag_size":20,"type_refs":["LT.lt","Nat","Nat.instPreorder","Preorder.toLT","instLTNat"],"value_dag_size":355,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.instPreorder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","True","True.intro","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_5","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo","reducibility":null,"statement_dag_size":74,"type_refs":["Finset.card","LE.le","LT.lt","Nat","Nat.nth","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instLTNat"],"value_dag_size":1068,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","Finset.card","HAdd.hAdd","HSub.hSub","Iff.mpr","Iff.of_eq","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.le_unsat_k","Lean.Grind.Order.of_nat_eq","Lean.Grind.forall_imp_eq_or","Lean.Grind.forall_propagator","Lean.Grind.imp_eq_of_eq_true_left","Lean.Grind.instCommRingInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.nestedProof","Lean.Grind.nestedProof_congr","Lean.Grind.or_eq_of_eq_false_right","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","Nat.not_le_eq","Nat.nth","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","PartialOrder.toPreorder","SemilatticeInf.toPartialOrder","Set.Finite","Set.Finite.toFinset","Set.ofPred","True","_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_1","congrArg","congrFun'","eagerReduce","eq_of_heq","eq_true","exists_prop_congr","forall_congr","id","implies_congr","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Classical.not_forall","Exists","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_mem_anti","reducibility":null,"statement_dag_size":58,"type_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Finset.card","LE.le","Nat","Nat.nth","Nat.nth_eq_zero","OfNat.ofNat","Or","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLENat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","GetElem?.getElem?","LT.lt","List","List.getD","List.instGetElem?NatLtLength","List.length","Nat","Option.getD","instLTNat"],"value_dag_size":54,"value_refs":["Eq.symm","GetElem?.getElem?","LT.lt","List","List.getD","List.getD_eq_getElem?_getD","List.instGetElem?NatLtLength","List.length","Nat","Option.getD","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite","reducibility":null,"statement_dag_size":68,"type_refs":["DecidableRel","Eq","Finset","Finset.instSetLike","Finset.sort","IsTrans","List","List.instMembership","Membership.mem","SetLike.instMembership","Std.Antisymm","Std.Total"],"value_dag_size":77,"value_refs":["DecidableRel","Finset","Finset.instSetLike","Finset.mem_sort","Finset.sort","IsTrans","List","List.instMembership","Membership.mem","SetLike.instMembership","Std.Antisymm","Std.Total","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.range_nth_of_finite","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instSetLike","Membership.mem","Set","Set.Finite","Set.Finite.mem_toFinset","Set.Finite.toFinset","Set.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Nth","name":"_private.Mathlib.Data.Nat.Nth.0.Nat.subset_range_nth.match_1_1","namespace":"_private.Mathlib.Data.Nat.Nth.0.Nat.subset_range_nth","reducibility":"abbrev","statement_dag_size":121,"type_refs":["And","And.intro","Eq","Exists","Exists.intro","Finset.card","LT.lt","Nat","Nat.nth","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLTNat"],"value_dag_size":185,"value_refs":["And","And.casesOn","And.intro","Eq","Exists","Exists.casesOn","Exists.intro","Finset.card","LT.lt","Nat","Nat.nth","Set.Finite","Set.Finite.toFinset","Set.ofPred","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Order.Lemmas","name":"_private.Mathlib.Data.Nat.Order.Lemmas.0.Nat.set_eq_univ.match_1_1","namespace":"_private.Mathlib.Data.Nat.Order.Lemmas.0.Nat.set_eq_univ","reducibility":"abbrev","statement_dag_size":85,"type_refs":["And","And.intro","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":99,"value_refs":["And","And.casesOn","And.intro","HAdd.hAdd","Membership.mem","Nat","OfNat.ofNat","Set","Set.instMembership","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.ppred.match_1","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq.refl","Nat","Nat.ppred.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1","reducibility":null,"statement_dag_size":37,"type_refs":["Eq","Nat","Nat.ppred.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq.refl","Nat","Nat.ppred.match_1","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":1,"value_refs":["Nat.ppred.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred_eq_none.match_1_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred_eq_none","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred_eq_some.match_1_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.ppred_eq_some","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_none._proof_1_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_none","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Iff","LT.lt","Nat","Nat.psub","Option","Option.none","Option.some","instLTNat"],"value_dag_size":478,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_prop","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.of_eq","Nat.ToInt.of_not_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","Nat.psub","Nat.psub_eq_some","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Option","Option.ctorIdx","Option.none","Option.some","True","congr","congrArg","eagerReduce","eq_false'","eq_true","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","noConfusion_of_Nat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_some._simp_1_3","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_some","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_some.match_1_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.psub_eq_some","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":42,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.PSub","name":"_private.Mathlib.Data.Nat.PSub.0.Nat.sub_eq_psub.match_1_1","namespace":"_private.Mathlib.Data.Nat.PSub.0.Nat.sub_eq_psub","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.add_le_pair._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.add_le_pair","reducibility":null,"statement_dag_size":42,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","instAddNat","instHAdd","instHMul","instLENat","instMulNat"],"value_dag_size":399,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","LE.le","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq","reducibility":null,"statement_dag_size":34,"type_refs":["HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":364,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq._proof_1_4","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq","reducibility":null,"statement_dag_size":34,"type_refs":["HAdd.hAdd","LT.lt","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":336,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.pair_lt_max_add_one_sq","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LE.le","LT.lt","Nat","True","instLENat","instLTNat"],"value_dag_size":26,"value_refs":["LE.le","LT.lt","Nat","Nat.le_of_lt","eq_true","instLENat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_left_le.match_1_1","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_left_le","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_lt._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_lt","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","GT.gt","LT","LT.lt"],"value_dag_size":30,"value_refs":["GT.gt","LT","LT.lt","gt_iff_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Pairing","name":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_lt._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Pairing.0.Nat.unpair_lt","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.even_sub_one.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.even_sub_one","reducibility":"abbrev","statement_dag_size":95,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Distrib.toAdd","Distrib.toMul","Eq","Exists.intro","HAdd.hAdd","HMul.hMul","Nat","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Odd","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHAdd","instHMul","instOfNatAtLeastTwo"],"value_dag_size":111,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","AddMonoidWithOne.toOne","Distrib.toAdd","Distrib.toMul","Eq","Exists.casesOn","Exists.intro","HAdd.hAdd","HMul.hMul","Nat","Nat.instSemiring","NonAssocSemiring.toAddCommMonoidWithOne","Odd","Odd._proof_1","OfNat.ofNat","One.toOfNat1","Semiring.toNonAssocSemiring","instDistribOfSemiring","instHAdd","instHMul","instOfNatAtLeastTwo"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.mul_eq_prime_sq_iff.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.mul_eq_prime_sq_iff","reducibility":"abbrev","statement_dag_size":46,"type_refs":["And","And.intro","Eq","Nat"],"value_dag_size":60,"value_refs":["And","And.casesOn","And.intro","Eq","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.odd_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.Prime.odd_iff","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","Iff","LT.lt","LinearOrder.toPartialOrder","Nat","Nat.Prime","Nat.instLinearOrder","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLT","instOfNatNat"],"value_dag_size":848,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","HAdd.hAdd","HSub.hSub","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lattice.toSemilatticeInf","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.eq_of_toPoly_eq","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.OfCommSemiring.ofCommSemiring","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Stepwise.d_init","Lean.Grind.CommRing.Stepwise.imp_1eq","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_mp_not","Lean.Grind.Order.eq_of_le_of_le_0","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_false'","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.int_lt","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Order.le_of_eq_1_k","Lean.Grind.Order.le_of_offset_eq_1_k","Lean.Grind.Order.le_of_offset_eq_2_k","Lean.Grind.Order.le_trans_k","Lean.Grind.Order.lt_of_not_le_k","Lean.Grind.Order.nat_eq","Lean.Grind.Order.of_nat_eq","Lean.Grind.Ring.OfSemiring.Q","Lean.Grind.Ring.OfSemiring.of_diseq","Lean.Grind.Ring.toSemiring","Lean.Grind.Semiring.natCast","Lean.Grind.iff_eq","Lean.Grind.instAddRightCancelNat","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.Grind.ne_of_ne_of_eq_left","Lean.Grind.not_eq_prop","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.Prime","Nat.Prime.two_le","Nat.Simproc.add_le_le","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.instLinearOrder","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","PartialOrder.toPreorder","Preorder.toLT","SemilatticeInf.toPartialOrder","Std.IsLinearOrder.toIsLinearPreorder","congrArg","eagerReduce","eq_false","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instIsPartialOrder_mathlib","instIsPreorder_mathlib","instLENat","instLTNat","instLatticeInt","instNatCastInt","instNatCastNat","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.coprime_of_lt_minFac._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.coprime_of_lt_minFac","reducibility":null,"statement_dag_size":22,"type_refs":["LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":253,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","False","Nat","Nat.Prime","OfNat.ofNat","instOfNatNat"],"value_dag_size":14,"value_refs":["Nat","Nat.Prime","Nat.not_prime_one","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd","reducibility":null,"statement_dag_size":9,"type_refs":["Eq","False","Not","True"],"value_dag_size":9,"value_refs":["False","Not","True","not_false_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.ne_one_iff_exists_prime_dvd","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":53,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_iff_exists_dvd_lt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_iff_exists_dvd_lt","reducibility":"abbrev","statement_dag_size":93,"type_refs":["And","And.intro","Dvd.dvd","Exists","Exists.intro","LE.le","LT.lt","Nat","Nat.instDvd","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":174,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","Exists","Exists.casesOn","Exists.intro","LE.le","LT.lt","Nat","Nat.instDvd","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_iff_exists_dvd_ne.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_iff_exists_dvd_ne","reducibility":"abbrev","statement_dag_size":87,"type_refs":["And","And.intro","Dvd.dvd","Exists","Exists.intro","Nat","Nat.instDvd","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":167,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","Exists","Exists.casesOn","Exists.intro","Nat","Nat.instDvd","Ne","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.not_prime_mul","reducibility":null,"statement_dag_size":45,"type_refs":["And","Eq","HMul.hMul","Nat","Nat.Prime","OfNat.ofNat","Or","instHMul","instMulNat","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Eq","HMul.hMul","Nat","Nat.Prime","Nat.prime_mul_iff","OfNat.ofNat","Or","instHMul","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff","reducibility":null,"statement_dag_size":54,"type_refs":["And","Eq","HMul.hMul","Irreducible","IsUnit","Monoid","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Or","instHMul"],"value_dag_size":58,"value_refs":["And","HMul.hMul","Irreducible","IsUnit","Monoid","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Or","instHMul","irreducible_mul_iff","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff","reducibility":null,"statement_dag_size":15,"type_refs":["Eq","Irreducible","Nat","Nat.Prime","Nat.instMonoid"],"value_dag_size":22,"value_refs":["Eq.symm","Irreducible","Nat","Nat.Prime","Nat.instMonoid","Nat.irreducible_iff_nat_prime","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Basic","name":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Prime.Basic.0.Nat.prime_mul_iff","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","IsUnit","Nat","Nat.instMonoid","OfNat.ofNat","instOfNatNat"],"value_dag_size":25,"value_refs":["Eq","IsUnit","Nat","Nat.instMonoid","Nat.isUnit_iff","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.Prime.two_le.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.Prime.two_le","reducibility":"abbrev","statement_dag_size":62,"type_refs":["HAdd.hAdd","Nat","Nat.Prime","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":98,"value_refs":["HAdd.hAdd","Nat","Nat.Prime","Nat.casesOn","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instOfNatNat"]}
+{"definition_height":5,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat","reducibility":"regular","statement_dag_size":4,"type_refs":["Nat"],"value_dag_size":38,"value_refs":["And","Dvd.dvd","LE.le","Nat","Nat.instDvd","OfNat.ofNat","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp.eq_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","LE.le","Nat","Nat.instDvd","OfNat.ofNat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","instLENat","instOfNatNat"],"value_dag_size":12,"value_refs":["Eq.refl","Nat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_has_prop._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_has_prop","reducibility":null,"statement_dag_size":24,"type_refs":["Eq","LE.le","Nat","Nat.succ","True","instLENat"],"value_dag_size":25,"value_refs":["LE.le","Nat","Nat.succ","Nat.succ_le_succ","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_le_div.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_le_div","reducibility":"abbrev","statement_dag_size":116,"type_refs":["Dvd.dvd","Eq","Exists.intro","HAdd.hAdd","HMul.hMul","Nat","Nat.instDvd","Nat.minFac","Nat.succ","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":204,"value_refs":["Dvd.dvd","Eq","Exists.casesOn","Exists.intro","HAdd.hAdd","HMul.hMul","Nat","Nat.casesOn","Nat.instDvd","Nat.minFac","Nat.succ","Nat.zero","OfNat.ofNat","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_prime.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_prime","reducibility":"abbrev","statement_dag_size":82,"type_refs":["And","And.intro","Dvd.dvd","LE.le","Nat","Nat.instDvd","Nat.minFac","OfNat.ofNat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","instLENat","instOfNatNat"],"value_dag_size":137,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","LE.le","Nat","Nat.instDvd","Nat.minFac","OfNat.ofNat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_prime_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFac_prime_iff","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","False","Nat","Nat.Prime","OfNat.ofNat","instOfNatNat"],"value_dag_size":14,"value_refs":["Nat","Nat.Prime","Nat.not_prime_one","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","IsUnit","Nat","Nat.instMonoid","OfNat.ofNat","instOfNatNat"],"value_dag_size":25,"value_refs":["Eq","IsUnit","Nat","Nat.instMonoid","Nat.isUnit_iff","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_le_sqrt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_le_sqrt","reducibility":"abbrev","statement_dag_size":79,"type_refs":["Dvd.dvd","Eq","Exists.intro","HMul.hMul","Nat","Nat.instDvd","instHMul","instMulNat","namedPattern"],"value_dag_size":98,"value_refs":["Dvd.dvd","Eq","Eq.refl","Exists.casesOn","Exists.intro","HMul.hMul","Nat","Nat.instDvd","instHMul","instMulNat","namedPattern"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_lt'._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_lt'","reducibility":null,"statement_dag_size":30,"type_refs":["Dvd.dvd","False","LE.le","Nat","Nat.instDvd","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":413,"value_refs":["Bool","Bool.true","Decidable.decide","Dvd.dvd","Eq","Eq.refl","Eq.symm","Eq.trans","HDiv.hDiv","HMod.hMod","HMul.hMul","HSub.hSub","Int","Int.ediv_zero","Int.emod_def","Int.instDecidableEq","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","Int.instSub","Int.natCast_emod","Int.sub_eq_zero_of_eq","Int.sub_nonneg_of_le","LE.le","Lean.Omega.Coeffs.isZero","Lean.Omega.Coeffs.ofList","Lean.Omega.Constraint.addEquality_sat","Lean.Omega.Constraint.addInequality_sat","Lean.Omega.Constraint.combine_sat'","Lean.Omega.Constraint.isImpossible","Lean.Omega.Constraint.mk","Lean.Omega.Constraint.not_sat'_of_isImpossible","Lean.Omega.Int.mul_congr","Lean.Omega.Int.ofNat_congr","Lean.Omega.Int.ofNat_le_of_le","Lean.Omega.Int.sub_congr","Lean.Omega.LinearCombo","Lean.Omega.LinearCombo.coordinate","Lean.Omega.LinearCombo.coordinate_eval_0","Lean.Omega.LinearCombo.eval","Lean.Omega.LinearCombo.instSub","Lean.Omega.LinearCombo.mk","Lean.Omega.LinearCombo.mul","Lean.Omega.LinearCombo.mul_eval","Lean.Omega.LinearCombo.sub_eval","List.cons","List.decidableBAll","List.nil","Nat","Nat.cast","Nat.instDvd","Nat.instMod","Nat.mod_eq_zero_of_dvd","Neg.neg","OfNat.ofNat","Option.none","Option.some","Or","id","instDecidableEqBool","instDecidableOr","instHDiv","instHMod","instHMul","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","le_of_le_of_eq","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_minFac.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_minFac","reducibility":"abbrev","statement_dag_size":82,"type_refs":["And","And.intro","Dvd.dvd","LE.le","Nat","Nat.instDvd","Nat.minFac","OfNat.ofNat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","instLENat","instOfNatNat"],"value_dag_size":137,"value_refs":["And","And.casesOn","And.intro","Dvd.dvd","LE.le","Nat","Nat.instDvd","Nat.minFac","OfNat.ofNat","_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.minFacProp","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_minFac.match_1_3","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_def_minFac","reducibility":"abbrev","statement_dag_size":57,"type_refs":["And","And.intro","Eq","LE.le","Nat","Nat.minFac","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":71,"value_refs":["And","And.casesOn","And.intro","Eq","LE.le","Nat","Nat.minFac","OfNat.ofNat","instLENat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._proof_1_7","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HMul.hMul","LE.le","Nat","Nat.instSemigroup","Not","OfNat.ofNat","Semigroup.toMul","instHMul","instLENat","instOfNatNat"],"value_dag_size":273,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instSemigroup","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Semigroup.toMul","eagerReduce","id","instHMul","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._proof_1_8","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":44,"type_refs":["Eq","LE.le","LinearOrder.toPartialOrder","Nat","Nat.instLinearOrder","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","instLENat","instOfNatNat"],"value_dag_size":237,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","False","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","LinearOrder.toPartialOrder","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.instLinearOrder","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PartialOrder.toPreorder","Preorder.toLE","eagerReduce","id","instLENat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._proof_1_9","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":37,"type_refs":["And","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Ne","OfNat.ofNat","Zero.toOfNat0","instLTNat","instOfNatNat"],"value_dag_size":310,"value_refs":["And","Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_false_of_not_eq_true","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","MulZeroClass.toZero","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.instMulZeroClass","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","True","Zero.toOfNat0","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":50,"type_refs":["And","Dvd.dvd","Eq","LE.le","LT.lt","Nat","Nat.Prime","Nat.instDvd","OfNat.ofNat","instLENat","instLTNat","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Dvd.dvd","Eq","LE.le","LT.lt","Nat","Nat.Prime","Nat.instDvd","Nat.prime_def_lt","OfNat.ofNat","instLENat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":46,"type_refs":["Dvd.dvd","Eq","Exists","HMul.hMul","Semigroup","Semigroup.toMul","instHMul","semigroupDvd"],"value_dag_size":50,"value_refs":["Dvd.dvd","Eq","Exists","HMul.hMul","Semigroup","Semigroup.toMul","dvd_def","instHMul","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":18,"type_refs":["Eq"],"value_dag_size":21,"value_refs":["Eq","eq_comm","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":11,"type_refs":["Eq","False","Not"],"value_dag_size":13,"value_refs":["False","Not","imp_false","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Defs","name":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_6","namespace":"_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":44,"value_refs":["LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_lt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Factorial","name":"_private.Mathlib.Data.Nat.Prime.Factorial.0.Nat.Prime.coprime_descFactorial_of_lt_of_le._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Factorial.0.Nat.Prime.coprime_descFactorial_of_lt_of_le","reducibility":null,"statement_dag_size":28,"type_refs":["Dvd.dvd","Eq","LE.le","Nat","Nat.factorial","Nat.instDvd","True","instLENat"],"value_dag_size":29,"value_refs":["Dvd.dvd","LE.le","Nat","Nat.factorial","Nat.factorial_dvd_factorial","Nat.instDvd","eq_true","instLENat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Prime.Factorial","name":"_private.Mathlib.Data.Nat.Prime.Factorial.0.Nat.Prime.dvd_factorial.match_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Factorial.0.Nat.Prime.dvd_factorial","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Nat","Nat.Prime","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":56,"value_refs":["Nat","Nat.Prime","Nat.casesOn","Nat.succ","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Prime.Int","name":"_private.Mathlib.Data.Nat.Prime.Int.0.Nat.prime_iff_prime_int._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Prime.Int.0.Nat.prime_iff_prime_int","reducibility":null,"statement_dag_size":28,"type_refs":["Dvd.dvd","Eq","Int","Int.instDvd","Nat","Nat.cast","Nat.instDvd","instNatCastInt"],"value_dag_size":30,"value_refs":["Dvd.dvd","Int","Int.instDvd","Int.natCast_dvd_natCast","Nat","Nat.cast","Nat.instDvd","instNatCastInt","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors._simp_1_1","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors","reducibility":null,"statement_dag_size":47,"type_refs":["DecidableEq","Disjoint","EmptyCollection.emptyCollection","Eq","Finset","Finset.instEmptyCollection","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Inter.inter"],"value_dag_size":51,"value_refs":["DecidableEq","Disjoint","EmptyCollection.emptyCollection","Eq","Finset","Finset.disjoint_iff_inter_eq_empty","Finset.instEmptyCollection","Finset.instInter","Finset.instOrderBot","Finset.instPartialOrder","Inter.inter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors._simp_1_2","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors","reducibility":null,"statement_dag_size":26,"type_refs":["Eq","Nat","Nat.Coprime","Nat.gcd","OfNat.ofNat","instOfNatNat"],"value_dag_size":29,"value_refs":["Eq","Nat","Nat.Coprime","Nat.coprime_iff_gcd_eq_one","Nat.gcd","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors._simp_1_3","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Finset","Finset.instInter","Inter.inter","Nat","Nat.gcd","Nat.primeFactors","Ne","OfNat.ofNat","instDecidableEqNat","instOfNatNat"],"value_dag_size":48,"value_refs":["Eq.symm","Finset","Finset.instInter","Inter.inter","Nat","Nat.gcd","Nat.primeFactors","Nat.primeFactors_gcd","Ne","OfNat.ofNat","instDecidableEqNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors._simp_1_1","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","Finset","List.toFinset","Nat","Nat.primeFactors","Nat.primeFactorsList","instDecidableEqNat"],"value_dag_size":21,"value_refs":["Eq.symm","Finset","List.toFinset","Nat","Nat.primeFactors","Nat.primeFactorsList","Nat.toFinset_factors","instDecidableEqNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors._simp_1_2","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","List","List.instMembership","List.toFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","List","List.instMembership","List.mem_toFinset","List.toFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors._simp_1_3","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","List","List.instMembership","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.primeFactorsList","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Dvd.dvd","List","List.instMembership","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.mem_primeFactorsList'","Nat.primeFactorsList","Ne","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors_iff_mem_primeFactorsList._simp_1_2","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.mem_primeFactors_iff_mem_primeFactorsList","reducibility":null,"statement_dag_size":43,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","List","List.instMembership","List.toFinset","Membership.mem","SetLike.instMembership"],"value_dag_size":47,"value_refs":["DecidableEq","Finset","Finset.instSetLike","List","List.instMembership","List.mem_toFinset","List.toFinset","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_gcd._proof_1_1","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_gcd","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Finset","Finset.instInter","Inter.inter","Nat","Nat.gcd","Nat.primeFactors","Ne","OfNat.ofNat","instDecidableEqNat","instOfNatNat"],"value_dag_size":1013,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","Dvd.dvd","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","Exists","Exists.casesOn","False","False.elim","Finset","Finset.ext","Finset.instInter","Finset.instSetLike","Finset.mem_inter","Iff","Inter.inter","Lean.Grind.AC.Context","Lean.Grind.AC.Context.mk","Lean.Grind.AC.Expr","Lean.Grind.AC.Expr.op","Lean.Grind.AC.Expr.var","Lean.Grind.AC.Seq","Lean.Grind.AC.Seq.cons","Lean.Grind.AC.Seq.var","Lean.Grind.AC.diseq_norm_aci","Lean.Grind.AC.diseq_simp_lhs_exact","Lean.Grind.AC.diseq_unsat","Lean.Grind.AC.eq_erase0","Lean.Grind.AC.eq_norm_aci","Lean.Grind.AC.eq_orient","Lean.Grind.AC.eq_simp_lhs_exact","Lean.Grind.AC.superpose_ac_idempotent","Lean.Grind.and_eq_of_eq_true_left","Lean.Grind.and_eq_of_eq_true_right","Lean.Grind.eq_true_of_and_eq_true_right","Lean.Grind.eq_true_of_not_eq_false","Lean.Grind.forall_imp_eq_or","Lean.Grind.iff_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_eq_of_eq_false","Lean.Grind.not_eq_of_eq_true","Lean.Grind.not_eq_prop","Lean.Grind.not_not","Lean.Grind.of_eq_eq_true","Lean.RArray.branch","Lean.RArray.leaf","Membership.mem","Nat","Nat.Prime","Nat.dvd_gcd_iff","Nat.gcd","Nat.instAssociativeGcd","Nat.instCommutativeGcd","Nat.instDvd","Nat.instIdempotentOpGcd","Nat.instLawfulIdentityGcdOfNat","Nat.mem_primeFactors","Nat.primeFactors","Ne","Not","OfNat.ofNat","Or","Or.casesOn","PLift","PLift.up","SetLike.instMembership","True","True.intro","congrArg","congrFun'","eagerReduce","eq_false","eq_true","forall_congr","funext","id","implies_congr","instDecidableEqNat","instOfNatNat","of_eq_true","or_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mono._simp_1_1","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mono","reducibility":null,"statement_dag_size":56,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":59,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.subset_iff","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mono._simp_1_2","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mono","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mul","reducibility":null,"statement_dag_size":49,"type_refs":["DecidableEq","Eq","Finset","Finset.instSetLike","Finset.instUnion","Membership.mem","Or","SetLike.instMembership","Union.union"],"value_dag_size":54,"value_refs":["DecidableEq","Finset","Finset.instSetLike","Finset.instUnion","Finset.mem_union","Membership.mem","Or","SetLike.instMembership","Union.union","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.PrimeFin","name":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mul._simp_1_2","namespace":"_private.Mathlib.Data.Nat.PrimeFin.0.Nat.primeFactors_mul","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","Finset","Finset.instSetLike","List","List.instMembership","Membership.mem","Nat","Nat.primeFactors","Nat.primeFactorsList","SetLike.instMembership"],"value_dag_size":38,"value_refs":["Finset","Finset.instSetLike","List","List.instMembership","Membership.mem","Nat","Nat.mem_primeFactors_iff_mem_primeFactorsList","Nat.primeFactors","Nat.primeFactorsList","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.shiftLeft'_true_eq_mul_pow.match_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.shiftLeft'_true_eq_mul_pow","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.shiftLeft'_true_ne_zero.match_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.shiftLeft'_true_ne_zero","reducibility":"abbrev","statement_dag_size":42,"type_refs":["Nat","Nat.succ","Ne","OfNat.ofNat","instOfNatNat"],"value_dag_size":59,"value_refs":["Nat","Nat.casesOn","Nat.succ","Nat.zero","Ne","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_bits_len._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_bits_len","reducibility":null,"statement_dag_size":33,"type_refs":["And","Bool","Bool.false","Eq","Nat","Nat.bit","OfNat.ofNat","instOfNatNat"],"value_dag_size":36,"value_refs":["And","Bool","Bool.false","Eq","Nat","Nat.bit","Nat.bit_eq_zero_iff","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_zero","reducibility":null,"statement_dag_size":25,"type_refs":["Eq","LT.lt","Nat","Ne","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":26,"value_refs":["LT.lt","Nat","Nat.pos_iff_ne_zero","Ne","OfNat.ofNat","instLTNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_zero._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_eq_zero","reducibility":null,"statement_dag_size":22,"type_refs":["Decidable","Eq","Iff","Not"],"value_dag_size":28,"value_refs":["Decidable","Decidable.not_iff_not","Iff","Not","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft'","reducibility":null,"statement_dag_size":46,"type_refs":["Eq","HPow.hPow","Nat","OfNat.ofNat","Or","instHPow","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":49,"value_refs":["Eq","HPow.hPow","Nat","Nat.pow_eq_one","OfNat.ofNat","Or","instHPow","instNatPowNat","instOfNatNat","instPowNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft'._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft'","reducibility":null,"statement_dag_size":14,"type_refs":["Eq","False","Nat","Nat.succ"],"value_dag_size":14,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_ne_self","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Size","name":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Size.0.Nat.size_shiftLeft","reducibility":null,"statement_dag_size":25,"type_refs":["Bool.false","Eq","HShiftLeft.hShiftLeft","Nat","Nat.instShiftLeft","Nat.shiftLeft'","instHShiftLeftOfShiftLeft"],"value_dag_size":29,"value_refs":["Bool.false","Eq.symm","HShiftLeft.hShiftLeft","Nat","Nat.instShiftLeft","Nat.shiftLeft'","Nat.shiftLeft'_false","instHShiftLeftOfShiftLeft"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.eq_sqrt.match_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.eq_sqrt","reducibility":"abbrev","statement_dag_size":101,"type_refs":["And","And.intro","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":118,"value_refs":["And","And.casesOn","And.intro","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.exists_mul_self.match_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.exists_mul_self","reducibility":"abbrev","statement_dag_size":46,"type_refs":["Eq","Exists","Exists.intro","HMul.hMul","Nat","instHMul","instMulNat"],"value_dag_size":61,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","HMul.hMul","Nat","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.le_three_of_sqrt_eq_one._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.le_three_of_sqrt_eq_one","reducibility":null,"statement_dag_size":29,"type_refs":["Eq","LT.lt","Nat","Nat.sqrt","OfNat.ofNat","instLTNat","instOfNatNat"],"value_dag_size":279,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.decLe","Nat.not_le_eq","Nat.sqrt","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","eagerReduce","id","instAddNat","instHAdd","instHSub","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.not_exists_sq._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.not_exists_sq","reducibility":null,"statement_dag_size":34,"type_refs":["False","HAdd.hAdd","LT.lt","Nat","OfNat.ofNat","instAddNat","instHAdd","instLTNat","instOfNatNat"],"value_dag_size":316,"value_refs":["Bool","Bool.true","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_add_le","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.natCast_ofNat","Nat.decLe","NatCast.natCast","Neg.neg","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","eagerReduce","eq_true","id","instAddNat","instHAdd","instHSub","instIntCastInt","instLENat","instLTNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_add_eq._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_add_eq","reducibility":null,"statement_dag_size":47,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.succ","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat"],"value_dag_size":514,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.instCommRingInt","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congr","congrArg","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instIntCastInt","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_add_eq._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_add_eq","reducibility":null,"statement_dag_size":33,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","instAddNat","instHAdd","instHMul","instLENat","instMulNat"],"value_dag_size":122,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LE.le","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_false_of_isUnsat","Nat.Internal.Linear.ExprCnstr.mk","Nat.not_le_eq","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_eq_zero._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_eq_zero","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HMul.hMul","Iff","LT.lt","Nat","Nat.sqrt","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":241,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Iff","LE.le","LT.lt","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Semiring.mul_one","Lean.Grind.iff_eq","Lean.Grind.instCommSemiringNat","Nat","Nat.Simproc.add_le_le","Nat.decLe","Nat.le_zero_eq","Nat.sqrt","Not","OfNat.ofNat","True","True.intro","congr","congrArg","eq_false","eq_true","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instLTNat","instMulNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_eq_zero._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_eq_zero","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Nat","Nat.sqrt","OfNat.ofNat","instOfNatNat"],"value_dag_size":84,"value_refs":["Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","Nat","Nat.sqrt","Nat.sqrt_zero","Not","OfNat.ofNat","True","True.intro","congrArg","eq_false","eq_true","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt'._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt'","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt'._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt'","reducibility":null,"statement_dag_size":42,"type_refs":["Eq","HPow.hPow","LE.le","Nat","Nat.sqrt","OfNat.ofNat","instHPow","instLENat","instNatPowNat","instOfNatNat","instPowNat"],"value_dag_size":44,"value_refs":["HPow.hPow","LE.le","Nat","Nat.le_sqrt'","Nat.sqrt","OfNat.ofNat","instHPow","instLENat","instNatPowNat","instOfNatNat","instPowNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt","reducibility":null,"statement_dag_size":40,"type_refs":["Eq","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":50,"value_refs":["Eq.symm","LE.le","LT.lt","LinearOrder","LinearOrder.toPartialOrder","Not","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","not_le","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","HMul.hMul","LE.le","Nat","Nat.sqrt","instHMul","instLENat","instMulNat"],"value_dag_size":33,"value_refs":["HMul.hMul","LE.le","Nat","Nat.le_sqrt","Nat.sqrt","instHMul","instLENat","instMulNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt_self._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_lt_self","reducibility":null,"statement_dag_size":35,"type_refs":["HMul.hMul","LT.lt","Nat","OfNat.ofNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":429,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.instAdd","Int.instLEInt","Int.instLTInt","Int.instMul","Int.instNatPow","Int.instNegInt","IntCast.intCast","LE.le","LT.lt","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.intCast","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.pow","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.le_norm_expr","Lean.Grind.CommRing.toRing","Lean.Grind.CommSemiring.toSemiring","Lean.Grind.Nat.lt_eq","Lean.Grind.Order.eq_mp","Lean.Grind.Order.eq_trans_false","Lean.Grind.Order.eq_trans_true'","Lean.Grind.Order.le_eq_false_of_le_k","Lean.Grind.Semiring.mul_one","Lean.Grind.instCommRingInt","Lean.Grind.instCommSemiringNat","Lean.Grind.instIsLinearOrderInt","Lean.Grind.instLawfulOrderLTInt","Lean.Grind.instOrderedRingInt","Lean.Grind.intro_with_eq","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.le_eq","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Std.IsLinearOrder.toIsLinearPreorder","Std.IsLinearPreorder.toIsPreorder","True","True.intro","congrArg","congrFun'","eagerReduce","eq_true","id","instAddNat","instHAdd","instHMul","instHPow","instIntCastInt","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instPowNat","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_one._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_one","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":64,"value_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.eq_sqrt","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_succ_le_succ_sqrt._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_succ_le_succ_sqrt","reducibility":null,"statement_dag_size":50,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.sqrt","Nat.succ","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat"],"value_dag_size":757,"value_refs":["Bool","Bool.false","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HPow.hPow","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_def'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_combine_coeff","Int.Internal.Linear.le_norm","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_norm_poly","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNatPow","Int.instNegInt","LE.le","LT.lt","Lean.Grind.CommRing.Expr","Lean.Grind.CommRing.Expr.add","Lean.Grind.CommRing.Expr.mul","Lean.Grind.CommRing.Expr.neg","Lean.Grind.CommRing.Expr.num","Lean.Grind.CommRing.Expr.var","Lean.Grind.CommRing.Mon.mult","Lean.Grind.CommRing.Mon.unit","Lean.Grind.CommRing.Poly","Lean.Grind.CommRing.Poly.add","Lean.Grind.CommRing.Poly.num","Lean.Grind.CommRing.Power.mk","Lean.Grind.CommRing.norm_int","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.num","Nat.Internal.Linear.Expr.var","Nat.Internal.Linear.ExprCnstr.eq_of_toNormPoly_eq","Nat.Internal.Linear.ExprCnstr.mk","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.not_le_eq","Nat.sqrt","Nat.succ","Nat.succ_eq_add_one","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congr","congrArg","eagerReduce","id","instAddNat","instHAdd","instHMul","instHPow","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instPowNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_two._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_two","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":64,"value_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.eq_sqrt","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Sqrt","name":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_zero._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt_zero","reducibility":null,"statement_dag_size":61,"type_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":64,"value_refs":["And","Eq","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.eq_sqrt","Nat.sqrt","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Nat","Nat.MinSqFacProp.match_1","Option","Option.none","Option.some","Unit","Unit.unit"],"value_dag_size":30,"value_refs":["Eq.refl","Nat","Nat.MinSqFacProp.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1.eq_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","Nat","Nat.MinSqFacProp.match_1","Option","Option.none","Option.some","Unit"],"value_dag_size":33,"value_refs":["Eq.refl","Nat","Nat.MinSqFacProp.match_1","Option","Option.none","Option.some","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.MinSqFacProp.match_1","reducibility":"abbrev","statement_dag_size":23,"type_refs":["Nat","Option","Option.none","Option.some","Unit"],"value_dag_size":1,"value_refs":["Nat.MinSqFacProp.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.Squarefree.ext_iff._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.Squarefree.ext_iff","reducibility":null,"statement_dag_size":79,"type_refs":["DFunLike.coe","Eq","Finsupp","Finsupp.instFunLike","Iff","LE.le","MulZeroClass.toZero","Nat","Nat.factorization","Nat.instMulZeroClass","OfNat.ofNat","instLENat","instOfNatNat"],"value_dag_size":583,"value_refs":["And","And.casesOn","Bool","Bool.true","Classical.byContradiction","DFunLike.coe","Eq","Eq.mp","Eq.refl","Eq.symm","Eq.trans","False","False.elim","Finsupp","Finsupp.instFunLike","Iff","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.diseq_unsat","Int.Internal.Linear.eq_diseq_subst","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.eq_unsat","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lean.Grind.iff_eq","Lean.Grind.of_eq_eq_true","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","MulZeroClass.toZero","Nat","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.factorization","Nat.instMulZeroClass","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","Or","Or.casesOn","True","eagerReduce","eq_false","eq_true","id","instLENat","instNatCastInt","instOfNat","instOfNatNat","of_eq_false","of_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.coprime_div_gcd_of_squarefree._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.coprime_div_gcd_of_squarefree","reducibility":null,"statement_dag_size":20,"type_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.instDvd","True"],"value_dag_size":20,"value_refs":["Dvd.dvd","Nat","Nat.gcd","Nat.gcd_dvd_left","Nat.instDvd","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.coprime_div_gcd_of_squarefree._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.coprime_div_gcd_of_squarefree","reducibility":null,"statement_dag_size":20,"type_refs":["Dvd.dvd","Eq","Nat","Nat.gcd","Nat.instDvd","True"],"value_dag_size":20,"value_refs":["Dvd.dvd","Nat","Nat.gcd","Nat.gcd_dvd_right","Nat.instDvd","eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree","reducibility":null,"statement_dag_size":42,"type_refs":["And","DecidablePred","Eq","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership"],"value_dag_size":48,"value_refs":["And","DecidablePred","Membership.mem","Multiset","Multiset.filter","Multiset.instMembership","Multiset.mem_filter","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Multiset","Multiset.instMembership","Multiset.map","Multiset.mem_map","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership"],"value_dag_size":47,"value_refs":["Eq.symm","Finset","Finset.instSetLike","Finset.mem_def","Finset.val","Membership.mem","Multiset","Multiset.instMembership","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree","reducibility":null,"statement_dag_size":46,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":48,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.divisors","Nat.instDvd","Nat.mem_divisors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.divisors_filter_squarefree","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership"],"value_dag_size":48,"value_refs":["Finset","Finset.instPartialOrder","Finset.instSetLike","Finset.mem_powerset","Finset.powerset","LE.le","Membership.mem","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1","reducibility":null,"statement_dag_size":84,"type_refs":["Eq","Nat","Nat.minSqFacAux.match_1"],"value_dag_size":120,"value_refs":["Eq","Eq.refl","Nat","Nat.minSqFacAux.match_1","_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1.splitter","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1.eq_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Nat","Nat.minSqFacAux.match_1"],"value_dag_size":27,"value_refs":["Eq.refl","Nat","Nat.minSqFacAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1.splitter","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1","reducibility":"abbrev","statement_dag_size":19,"type_refs":["Nat"],"value_dag_size":1,"value_refs":["Nat.minSqFacAux.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux_has_prop._proof_1_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux_has_prop","reducibility":null,"statement_dag_size":50,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","LE.le","Nat","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":317,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HMul.hMul","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_combine","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instAdd","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.add_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.not_le_eq","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","eagerReduce","id","instAddNat","instHAdd","instHMul","instHSub","instLENat","instMulNat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux_has_prop._proof_1_3","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux_has_prop","reducibility":null,"statement_dag_size":51,"type_refs":["HAdd.hAdd","HMul.hMul","LE.le","Nat","Not","OfNat.ofNat","instAddNat","instHAdd","instHMul","instLENat","instMulNat","instOfNatNat"],"value_dag_size":98,"value_refs":["Bool","Bool.true","Eq.mp","Eq.refl","Eq.symm","False","False.elim","HAdd.hAdd","HMul.hMul","LE.le","LT.lt","Nat","Nat.Simproc.add_le_gt","Nat.decLt","Not","OfNat.ofNat","True","True.intro","eq_true","instAddNat","instHAdd","instHMul","instLENat","instLTNat","instMulNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd","reducibility":null,"statement_dag_size":50,"type_refs":["And","Dvd.dvd","Eq","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Dvd.dvd","Finset","Finset.instSetLike","Membership.mem","Nat","Nat.Prime","Nat.instDvd","Nat.mem_primeFactors","Nat.primeFactors","Ne","OfNat.ofNat","SetLike.instMembership","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq","Not"],"value_dag_size":19,"value_refs":["And","Not","not_and","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.primeFactors_div_gcd","reducibility":null,"statement_dag_size":51,"type_refs":["And","DecidableEq","Eq","Finset","Finset.instSDiff","Finset.instSetLike","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership"],"value_dag_size":56,"value_refs":["And","DecidableEq","Finset","Finset.instSDiff","Finset.instSetLike","Finset.mem_sdiff","Membership.mem","Not","SDiff.sdiff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.sq_mul_squarefree_of_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.sq_mul_squarefree_of_pos","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.sq_mul_squarefree_of_pos._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.sq_mul_squarefree_of_pos","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.squarefree_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Nat.squarefree_mul","reducibility":null,"statement_dag_size":87,"type_refs":["And","CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","DecompositionMonoid","Eq","HMul.hMul","IsCancelMulZero","IsRelPrime","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MonoidWithZero.toSemigroupWithZero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","SemigroupWithZero.toSemigroup","Squarefree","instHMul"],"value_dag_size":93,"value_refs":["And","CommMonoidWithZero","CommMonoidWithZero.toMonoidWithZero","DecompositionMonoid","HMul.hMul","IsCancelMulZero","IsRelPrime","MonoidWithZero.toMonoid","MonoidWithZero.toMulZeroOneClass","MonoidWithZero.toSemigroupWithZero","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","SemigroupWithZero.toSemigroup","Squarefree","instHMul","propext","squarefree_mul_iff"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.PSigma.casesOn._arg_pusher","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.PSigma.casesOn","reducibility":null,"statement_dag_size":102,"type_refs":["Eq","PSigma","PSigma.casesOn","PSigma.mk"],"value_dag_size":143,"value_refs":["Eq","Eq.refl","PSigma","PSigma.casesOn","PSigma.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Squarefree","name":"_private.Mathlib.Data.Nat.Squarefree.0.Squarefree.natFactorization_le_one._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Squarefree.0.Squarefree.natFactorization_le_one","reducibility":null,"statement_dag_size":23,"type_refs":["Eq","IsUnit","Nat","Nat.instMonoid","OfNat.ofNat","instOfNatNat"],"value_dag_size":25,"value_refs":["Eq","IsUnit","Nat","Nat.instMonoid","Nat.isUnit_iff","OfNat.ofNat","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.SuccPred","name":"_private.Mathlib.Data.Nat.SuccPred.0.Nat.pred_iterate.match_1_1","namespace":"_private.Mathlib.Data.Nat.SuccPred.0.Nat.pred_iterate","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Even.eq_of_totient_eq_totient._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Even.eq_of_totient_eq_totient","reducibility":null,"statement_dag_size":18,"type_refs":["Eq","False","Nat","OfNat.ofNat","instOfNatNat"],"value_dag_size":54,"value_refs":["Bool","Bool.false","Eq","Eq.mp","Eq.refl","Eq.symm","False","Nat","OfNat.ofNat","True","True.intro","eq_false_of_decide","eq_true","id","instDecidableEqNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._proof_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":null,"statement_dag_size":63,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":63,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq.unsafeIntro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._proof_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":null,"statement_dag_size":53,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq"],"value_dag_size":53,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","OfNat.ofNat","Qq.Quoted","Qq.QuotedDefEq.unsafeIntro"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._sparseCasesOn_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":"abbrev","statement_dag_size":177,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","Option","Option.some","Qq.Quoted"],"value_dag_size":415,"value_refs":["Bool","Bool.false","Eq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.none","Mathlib.Meta.Positivity.Strictness.nonnegative","Mathlib.Meta.Positivity.Strictness.nonzero","Mathlib.Meta.Positivity.Strictness.positive","Mathlib.Meta.Positivity.Strictness.rec","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","Option","Option.some","Qq.Quoted","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._sparseCasesOn_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Lean.Level","Lean.Level.ctorIdx","Lean.Level.zero","Nat.hasNotBit"],"value_dag_size":161,"value_refs":["Bool","Bool.false","Eq.refl","Lean.LMVarId","Lean.Level","Lean.Level.ctorIdx","Lean.Level.imax","Lean.Level.max","Lean.Level.mvar","Lean.Level.param","Lean.Level.rec","Lean.Level.succ","Lean.Level.zero","Lean.Name","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient.match_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":"abbrev","statement_dag_size":159,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.positive","OfNat.ofNat","Option.some","Qq.Quoted"],"value_dag_size":489,"value_refs":["Eq","Eq.ndrec","Eq.refl","Eq.symm","HEq","HEq.refl","Lean.Expr.app","Lean.Expr.const","Lean.Expr.lit","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Literal.natVal","Lean.Name.mkStr1","Lean.Name.mkStr2","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Mathlib.Meta.Positivity.Strictness.ctorIdx","Mathlib.Meta.Positivity.Strictness.positive","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Option.some.noConfusion","Qq.Quoted","_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._sparseCasesOn_1","eq_of_heq"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient.match_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":"abbrev","statement_dag_size":187,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","OfNat.ofNat","Option","Option.some","Qq.Quoted"],"value_dag_size":333,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.ctorIdx","Lean.Level.instOfNat","Lean.Level.succ","Lean.Level.zero","Lean.Meta.MetaM","Lean.Name.mkStr1","List.cons","List.nil","Mathlib.Meta.Positivity.Strictness","Nat.hasNotBit","OfNat.ofNat","Option","Option.some","Qq.Quoted","_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient._sparseCasesOn_4"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient.match_7","namespace":"_private.Mathlib.Data.Nat.Totient.0.Mathlib.Meta.Positivity.evalNatTotient","reducibility":"abbrev","statement_dag_size":69,"type_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.none","Option.some","Qq.Quoted","Unit"],"value_dag_size":81,"value_refs":["Lean.Expr.app","Lean.Expr.const","Lean.Expr.sort","Lean.Level","Lean.Level.succ","Lean.Name.mkStr1","List.cons","List.nil","Option","Option.casesOn","Option.none","Option.some","Qq.Quoted","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.Ico_filter_coprime_le._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.Ico_filter_coprime_le","reducibility":null,"statement_dag_size":35,"type_refs":["AddSemigroup","AddSemigroup.toAdd","Eq","HAdd.hAdd","instHAdd"],"value_dag_size":42,"value_refs":["AddSemigroup","AddSemigroup.toAdd","Eq.symm","HAdd.hAdd","add_assoc","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","Even","LT.lt","Nat","Nat.totient","OfNat.ofNat","True","instAddNat","instLTNat","instOfNatNat"],"value_dag_size":31,"value_refs":["Even","LT.lt","Nat","Nat.totient","Nat.totient_even","OfNat.ofNat","eq_true","instAddNat","instLTNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff_eq_one._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff_eq_one","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Nat","Nat.instSemiring","Nat.totient","Odd","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":35,"value_refs":["Eq","Nat","Nat.instSemiring","Nat.odd_totient_iff","Nat.totient","Odd","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff_eq_one._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.odd_totient_iff_eq_one","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Nat","Nat.totient","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":32,"value_refs":["Eq","Nat","Nat.totient","Nat.totient_eq_one_iff","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.prime_iff_card_units._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.prime_iff_card_units","reducibility":null,"statement_dag_size":16,"type_refs":["Eq","False","Nat","Nat.Prime","OfNat.ofNat","instOfNatNat"],"value_dag_size":14,"value_refs":["Nat","Nat.Prime","Nat.not_prime_zero","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.prime_pow_pow_totient_ediv_prod._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.prime_pow_pow_totient_ediv_prod","reducibility":null,"statement_dag_size":49,"type_refs":["Eq","HMul.hMul","HPow.hPow","Monoid","Monoid.toNPow","NPow.toPow","Nat","instHMul","instHPow","instMulNat"],"value_dag_size":56,"value_refs":["Eq.symm","HMul.hMul","HPow.hPow","Monoid","Monoid.toNPow","NPow.toPow","Nat","instHMul","instHPow","instMulNat","pow_mul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff","reducibility":null,"statement_dag_size":33,"type_refs":["Eq","Nat","Nat.instSemiring","Nat.totient","Odd","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":41,"value_refs":["Eq","Eq.symm","Nat","Nat.instSemiring","Nat.odd_totient_iff","Nat.totient","Odd","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff","reducibility":null,"statement_dag_size":19,"type_refs":["And","Eq","Not","Or"],"value_dag_size":22,"value_refs":["And","Not","Or","not_or","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Even","Nat","Nat.instSemiring","Not","Odd","instAddNat"],"value_dag_size":21,"value_refs":["Even","Nat","Nat.instSemiring","Nat.not_odd_iff_even","Not","Odd","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff","reducibility":null,"statement_dag_size":80,"type_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Dvd.dvd","Eq","Even","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSemiring.toSemigroupWithZero","OfNat.ofNat","SemigroupWithZero.toSemigroup","Semiring","Semiring.toNonAssocSemiring","Semiring.toNonUnitalSemiring","instDistribOfSemiring","instOfNatAtLeastTwo","instOfNatNat","semigroupDvd"],"value_dag_size":83,"value_refs":["AddCommMonoidWithOne.toAddMonoidWithOne","AddMonoidWithOne.toNatCast","Distrib.toAdd","Dvd.dvd","Even","Nat","Nat.instAtLeastTwoHAddOfNat","Nat.instNeZeroSucc","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalSemiring.toSemigroupWithZero","OfNat.ofNat","SemigroupWithZero.toSemigroup","Semiring","Semiring.toNonAssocSemiring","Semiring.toNonUnitalSemiring","even_iff_two_dvd","instDistribOfSemiring","instOfNatAtLeastTwo","instOfNatNat","propext","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff._simp_1_5","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_coprime_totient_iff","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","Nat","Nat.totient","OfNat.ofNat","Or","instOfNatNat"],"value_dag_size":38,"value_refs":["Eq","Eq.symm","Nat","Nat.totient","Nat.totient_eq_one_iff","OfNat.ofNat","Or","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd","reducibility":null,"statement_dag_size":16,"type_refs":["And","Eq"],"value_dag_size":21,"value_refs":["And","and_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_div_of_dvd","reducibility":null,"statement_dag_size":17,"type_refs":["And","Eq","Exists"],"value_dag_size":20,"value_refs":["And","Exists","exists_prop","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_card_lt_and_coprime._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_card_lt_and_coprime","reducibility":null,"statement_dag_size":46,"type_refs":["And","DecidablePred","Eq","Finset","Finset.filter","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":52,"value_refs":["And","DecidablePred","Finset","Finset.filter","Finset.instSetLike","Finset.mem_filter","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_card_lt_and_coprime._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_card_lt_and_coprime","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_iff_prime._proof_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_iff_prime","reducibility":null,"statement_dag_size":58,"type_refs":["DistribLattice.toLattice","HAdd.hAdd","LE.le","Lattice.toSemilatticeInf","Nat","Nat.instLinearOrder","Nat.instOne","Ne","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instOfNatNat"],"value_dag_size":261,"value_refs":["Bool","Bool.true","Classical.byContradiction","DistribLattice.toLattice","Eq","Eq.refl","Eq.trans","False","HAdd.hAdd","HSub.hSub","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.not_eq_norm_expr","Int.instNegInt","LE.le","Lattice.toSemilatticeInf","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.leaf","Nat","Nat.Simproc.add_le_le","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.ToInt.of_eq","Nat.ToInt.toNat_nonneg","Nat.decLe","Nat.instLinearOrder","Nat.instOne","Nat.le_zero_eq","Nat.not_le_eq","NatCast.natCast","Ne","Neg.neg","Not","OfNat.ofNat","One.toOfNat1","PartialOrder.toPreorder","Preorder.toLE","SemilatticeInf.toPartialOrder","eagerReduce","id","instAddNat","instDistribLatticeOfLinearOrder","instHAdd","instHSub","instLENat","instNatCastInt","instOfNat","instOfNatNat","instSubNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_mul_prod_factors._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_mul_prod_factors","reducibility":null,"statement_dag_size":75,"type_refs":["CommMonoid","CommMonoid.toMonoid","Eq","Finset","Finset.prod","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"],"value_dag_size":83,"value_refs":["CommMonoid","CommMonoid.toMonoid","Eq.symm","Finset","Finset.prod","Finset.prod_mul_distrib","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_one_iff._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_one_iff","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","False","Nat","Nat.succ","OfNat.ofNat","instOfNatNat"],"value_dag_size":22,"value_refs":["Eq","Nat","Nat.succ","Nat.succ_succ_ne_one","OfNat.ofNat","eq_false","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_one_iff.match_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_one_iff","reducibility":"abbrev","statement_dag_size":43,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":70,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_zero._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_zero","reducibility":null,"statement_dag_size":54,"type_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership"],"value_dag_size":59,"value_refs":["DecidablePred","EmptyCollection.emptyCollection","Eq","Finset","Finset.filter","Finset.filter_eq_empty_iff","Finset.instEmptyCollection","Finset.instSetLike","Membership.mem","Not","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_zero.match_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_eq_zero","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_mul._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_mul","reducibility":null,"statement_dag_size":52,"type_refs":["CommRing.toCommSemiring","CommSemiring.toSemiring","Eq","Fintype","Fintype.card","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.totient","NeZero","Semiring.toMonoid","Units","ZMod","ZMod.commRing"],"value_dag_size":57,"value_refs":["CommRing.toCommSemiring","CommSemiring.toSemiring","Eq.symm","Fintype","Fintype.card","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.totient","NeZero","Semiring.toMonoid","Units","ZMod","ZMod.card_units_eq_totient","ZMod.commRing"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_mul_prod_primeFactors._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_mul_prod_primeFactors","reducibility":null,"statement_dag_size":89,"type_refs":["CommMonoid","CommMonoid.toMonoid","Eq","Finsupp","Finsupp.prod","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Zero","instHMul"],"value_dag_size":99,"value_refs":["CommMonoid","CommMonoid.toMonoid","Eq.symm","Finsupp","Finsupp.prod","Finsupp.prod_mul","HMul.hMul","Monoid.toMulOneClass","MulOne.toMul","MulOneClass.toMulOne","Zero","instHMul"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_pos._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_pos","reducibility":null,"statement_dag_size":52,"type_refs":["Eq","IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0"],"value_dag_size":57,"value_refs":["IsBotZeroClass","LT.lt","Ne","OfNat.ofNat","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","Preorder.toLT","Zero","Zero.toOfNat0","pos_iff_ne_zero","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ._simp_1_1","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ","reducibility":null,"statement_dag_size":32,"type_refs":["Eq","Finset","Finset.instSetLike","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat"],"value_dag_size":34,"value_refs":["Finset","Finset.instSetLike","Finset.mem_range","Finset.range","LT.lt","Membership.mem","Nat","SetLike.instMembership","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ","reducibility":null,"statement_dag_size":70,"type_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Membership.mem","SetLike.instMembership"],"value_dag_size":76,"value_refs":["And","DecidableEq","Eq","Exists","Finset","Finset.image","Finset.instSetLike","Finset.mem_image","Membership.mem","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ._simp_1_3","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","Exists","Not"],"value_dag_size":23,"value_refs":["Exists","Not","not_exists","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ._simp_1_4","namespace":"_private.Mathlib.Data.Nat.Totient.0.Nat.totient_prime_pow_succ","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","Exists"],"value_dag_size":25,"value_refs":["Exists","exists_imp","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.Totient","name":"_private.Mathlib.Data.Nat.Totient.0.ZMod.card_units_eq_totient._simp_1_2","namespace":"_private.Mathlib.Data.Nat.Totient.0.ZMod.card_units_eq_totient","reducibility":null,"statement_dag_size":44,"type_refs":["AddCommMonoid","Eq","Fin","Fin.fintype","Fin.val","Finset.range","Finset.sum","Finset.univ","Nat"],"value_dag_size":50,"value_refs":["AddCommMonoid","Eq.symm","Fin","Fin.fintype","Fin.sum_univ_eq_sum_range","Fin.val","Finset.range","Finset.sum","Finset.univ","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Nat.Upto","name":"_private.Mathlib.Data.Nat.Upto.0.Nat.Upto.wf.match_1_1","namespace":"_private.Mathlib.Data.Nat.Upto.0.Nat.Upto.wf","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Exists","Exists.intro","Nat"],"value_dag_size":47,"value_refs":["Exists","Exists.casesOn","Exists.intro","Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_one_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_one_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Add","Eq","HAdd.hAdd","WithBot","WithBot.add","WithBot.some","instHAdd"],"value_dag_size":49,"value_refs":["Add","Eq.symm","HAdd.hAdd","WithBot","WithBot.add","WithBot.coe_add","WithBot.some","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_one_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_one_iff","reducibility":null,"statement_dag_size":49,"type_refs":["And","Eq","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":52,"value_refs":["And","Eq","HAdd.hAdd","Nat","Nat.add_eq_one_iff","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_three_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_three_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Add","Eq","HAdd.hAdd","WithBot","WithBot.add","WithBot.some","instHAdd"],"value_dag_size":49,"value_refs":["Add","Eq.symm","HAdd.hAdd","WithBot","WithBot.add","WithBot.coe_add","WithBot.some","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_three_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_three_iff","reducibility":null,"statement_dag_size":69,"type_refs":["And","Eq","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":72,"value_refs":["And","Eq","HAdd.hAdd","Nat","Nat.add_eq_three_iff","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_two_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_two_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Add","Eq","HAdd.hAdd","WithBot","WithBot.add","WithBot.some","instHAdd"],"value_dag_size":49,"value_refs":["Add","Eq.symm","HAdd.hAdd","WithBot","WithBot.add","WithBot.coe_add","WithBot.some","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_two_iff._simp_1_2","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_two_iff","reducibility":null,"statement_dag_size":59,"type_refs":["And","Eq","HAdd.hAdd","Nat","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat"],"value_dag_size":62,"value_refs":["And","Eq","HAdd.hAdd","Nat","Nat.add_eq_two_iff","OfNat.ofNat","Or","instAddNat","instHAdd","instOfNatNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_zero_iff._simp_1_1","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_zero_iff","reducibility":null,"statement_dag_size":43,"type_refs":["Add","Eq","HAdd.hAdd","WithBot","WithBot.add","WithBot.some","instHAdd"],"value_dag_size":49,"value_refs":["Add","Eq.symm","HAdd.hAdd","WithBot","WithBot.add","WithBot.coe_add","WithBot.some","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Nat.WithBot","name":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_one_le_of_lt._simp_1_1","namespace":"_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_one_le_of_lt","reducibility":null,"statement_dag_size":32,"type_refs":["Bot.bot","Eq","LE","LE.le","OrderBot","OrderBot.toBot","True"],"value_dag_size":34,"value_refs":["Bot.bot","LE","LE.le","OrderBot","OrderBot.toBot","bot_le","eq_true"]}
+{"definition_height":7,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum","reducibility":"regular","statement_dag_size":5,"type_refs":["Num","PosNum"],"value_dag_size":12,"value_refs":["Num","PosNum","PosNum.brecOn","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux._f"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux._f","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","reducibility":"abbrev","statement_dag_size":11,"type_refs":["Num","PosNum","PosNum.below"],"value_dag_size":94,"value_refs":["Eq","Num","OfNat.ofNat","One.toOfNat1","PosNum","PosNum.below","PosNum.bit0","PosNum.bit1","PosNum.divMod.match_1","PosNum.one","Prod","Prod.fst","Unit","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux.match_1","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux1","instOnePosNum","namedPattern"]}
+{"definition_height":8,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux._sunfold","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","reducibility":"regular","statement_dag_size":5,"type_refs":["Num","PosNum"],"value_dag_size":74,"value_refs":["Eq","Num","OfNat.ofNat","One.toOfNat1","PosNum","PosNum.bit0","PosNum.bit1","PosNum.divMod.match_1","Prod","Prod.fst","Unit","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux.match_1","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux1","instOnePosNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux._unsafe_rec","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","reducibility":"opaque","statement_dag_size":5,"type_refs":["Num","PosNum"],"value_dag_size":71,"value_refs":["Eq","Num","OfNat.ofNat","One.toOfNat1","PosNum","PosNum.bit0","PosNum.bit1","PosNum.divMod.match_1","Prod","Prod.fst","Unit","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux._unsafe_rec","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux.match_1","_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux1","instOnePosNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux.match_1","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux","reducibility":"abbrev","statement_dag_size":45,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit","namedPattern"],"value_dag_size":66,"value_refs":["Eq","Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit","namedPattern"]}
+{"definition_height":6,"is_auto_or_private":true,"is_internal_name":true,"kind":"definition","module":"Mathlib.Data.Num.Basic","name":"_private.Mathlib.Data.Num.Basic.0.PosNum.sqrtAux1","namespace":"_private.Mathlib.Data.Num.Basic.0.PosNum","reducibility":"regular","statement_dag_size":8,"type_refs":["Num","PosNum","Prod"],"value_dag_size":53,"value_refs":["HAdd.hAdd","Num","Num.div2","Num.instAdd","Num.ofZNum'","Num.pos","Num.sub'","Option","PosNum","PosNum.divModAux.match_1","Prod","Prod.mk","Unit","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Bitwise","name":"_private.Mathlib.Data.Num.Bitwise.0.PosNum.shiftl_succ_eq_bit0_shiftl.match_1_1","namespace":"_private.Mathlib.Data.Num.Bitwise.0.PosNum.shiftl_succ_eq_bit0_shiftl","reducibility":"abbrev","statement_dag_size":34,"type_refs":["Nat","Nat.succ","OfNat.ofNat","PosNum","instOfNatNat"],"value_dag_size":44,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","PosNum","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_one.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_one","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_succ.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_succ","reducibility":"abbrev","statement_dag_size":33,"type_refs":["Num","Num.pos","Num.zero","PosNum"],"value_dag_size":53,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.add_to_nat","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":69,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit0_of_bit0.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit0_of_bit0","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit1_of_bit1.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit1_of_bit1","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit1_succ.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.bit1_succ","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftLeft._simp_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftLeft","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","HShiftLeft.hShiftLeft","Nat","Num","Num.instHShiftLeftNat","Num.shiftl"],"value_dag_size":25,"value_refs":["Eq.symm","HShiftLeft.hShiftLeft","Nat","Num","Num.instHShiftLeftNat","Num.shiftl","Num.shiftl_eq_shiftLeft"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight._proof_1_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","HAdd.hAdd","HDiv.hDiv","Nat","Nat.instDiv","OfNat.ofNat","instAddNat","instHAdd","instHDiv","instOfNatNat"],"value_dag_size":552,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HAdd.hAdd","HDiv.hDiv","HMod.hMod","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.add","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.neg","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.ediv_emod","Int.Internal.Linear.emod_le","Int.Internal.Linear.emod_nonneg","Int.Internal.Linear.eq_def","Int.Internal.Linear.eq_eq_subst'","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_le_subst_nonpos","Int.Internal.Linear.eq_norm","Int.Internal.Linear.eq_of_core","Int.Internal.Linear.eq_of_le_ge","Int.Internal.Linear.le_coeff","Int.Internal.Linear.le_of_le_diseq","Int.Internal.Linear.le_unsat","Int.Internal.Linear.norm_eq","Int.Internal.Linear.norm_le","Int.Internal.Linear.not_eq_norm_expr","Int.Nonneg.mod","Int.Nonneg.mul","Int.Nonneg.natCast","Int.Nonneg.num","Int.Nonneg.toPoly","Int.instAdd","Int.instDiv","Int.instLEInt","Int.instMod","Int.instMul","Int.instNegInt","LE.le","Lean.Grind.intro_with_eq","Lean.RArray","Lean.RArray.branch","Lean.RArray.leaf","Nat","Nat.Internal.Linear.Expr.add","Nat.Internal.Linear.Expr.eq_of_toNormPoly_eq","Nat.Internal.Linear.Expr.mulL","Nat.Internal.Linear.Expr.var","Nat.ToInt.div_congr","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_diseq","Nat.instDiv","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","congrArg","congrFun'","eagerReduce","id","instAddNat","instHAdd","instHDiv","instHMod","instHMul","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight._simp_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight","reducibility":null,"statement_dag_size":21,"type_refs":["Eq","HShiftRight.hShiftRight","Nat","Num","Num.instHShiftRightNat","Num.shiftr"],"value_dag_size":25,"value_refs":["Eq.symm","HShiftRight.hShiftRight","Nat","Num","Num.instHShiftRightNat","Num.shiftr","Num.shiftr_eq_shiftRight"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight._simp_1_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight","reducibility":null,"statement_dag_size":22,"type_refs":["Eq","HShiftRight.hShiftRight","Nat","Num","PosNum","PosNum.instHShiftRightNatNum","PosNum.shiftr"],"value_dag_size":26,"value_refs":["Eq.symm","HShiftRight.hShiftRight","Nat","Num","PosNum","PosNum.instHShiftRightNatNum","PosNum.shiftr","PosNum.shiftr_eq_shiftRight"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight._simp_1_4","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftRight","reducibility":null,"statement_dag_size":27,"type_refs":["Eq","HDiv.hDiv","Nat","Nat.div2","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"],"value_dag_size":30,"value_refs":["Eq.symm","HDiv.hDiv","Nat","Nat.div2","Nat.div2_val","Nat.instDiv","OfNat.ofNat","instHDiv","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_mul.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_mul","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":69,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_toZNum.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_toZNum","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_toZNumNeg.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_toZNumNeg","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cast_to_nat","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_eq._simp_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","LT.lt.ne","Preorder","Preorder.toLT","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_eq._simp_1_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","LT.lt.ne'","Preorder","Preorder.toLT","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.cmp_to_nat","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":69,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.commSemiring._simp_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.commSemiring","reducibility":null,"statement_dag_size":30,"type_refs":["Eq","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","castNum","instAddNat"],"value_dag_size":39,"value_refs":["Eq","Eq.symm","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Num.to_nat_inj","castNum","instAddNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.dvd_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.dvd_to_nat","reducibility":"abbrev","statement_dag_size":71,"type_refs":["Dvd.dvd","Eq","Exists.intro","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instDvd","Nat.instMulZeroClass","Nat.instOne","Num","castNum","instAddNat","instHMul","instMulNat"],"value_dag_size":89,"value_refs":["Dvd.dvd","Eq","Exists.casesOn","Exists.intro","HMul.hMul","MulZeroClass.toZero","Nat","Nat.instDvd","Nat.instMulZeroClass","Nat.instOne","Num","castNum","instAddNat","instHMul","instMulNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.dvd_to_nat.match_1_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.dvd_to_nat","reducibility":"abbrev","statement_dag_size":69,"type_refs":["CommSemiring.toNonUnitalCommSemiring","Dvd.dvd","Eq","Exists.intro","HMul.hMul","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSemiring.toSemigroupWithZero","Num","Num.commSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","instHMul","semigroupDvd"],"value_dag_size":87,"value_refs":["CommSemiring.toNonUnitalCommSemiring","Dvd.dvd","Eq","Exists.casesOn","Exists.intro","HMul.hMul","NonUnitalCommSemiring.toNonUnitalSemiring","NonUnitalSemiring.toSemigroupWithZero","Num","Num.commSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","instHMul","semigroupDvd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.lt_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.lt_to_nat","reducibility":"abbrev","statement_dag_size":106,"type_refs":["Eq","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Ordering","Ordering.casesOn","Ordering.eq","Ordering.gt","Ordering.lt","castNum","instAddNat","instLTNat"],"value_dag_size":147,"value_refs":["Eq","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Ordering","Ordering.casesOn","Ordering.eq","Ordering.gt","Ordering.lt","castNum","instAddNat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.mul_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.mul_to_nat","reducibility":"abbrev","statement_dag_size":39,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":69,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.ofNat'_succ._simp_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.ofNat'_succ","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","HAdd.hAdd","Num","Num.bit1","Num.instAdd","OfNat.ofNat","One.toOfNat1","instHAdd","instOneNum"],"value_dag_size":34,"value_refs":["Eq.symm","HAdd.hAdd","Num","Num.bit1","Num.bit1_of_bit1","Num.instAdd","OfNat.ofNat","One.toOfNat1","instHAdd","instOneNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.ofNat'_succ._simp_1_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.ofNat'_succ","reducibility":null,"statement_dag_size":20,"type_refs":["Eq","HAdd.hAdd","Num","Num.bit0","Num.instAdd","instHAdd"],"value_dag_size":23,"value_refs":["Eq.symm","HAdd.hAdd","Num","Num.bit0","Num.bit0_of_bit0","Num.instAdd","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.of_to_nat'.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.of_to_nat'","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder._simp_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Num.instLT","castNum","instAddNat","instLTNat"],"value_dag_size":43,"value_refs":["Eq.symm","LT.lt","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Num.instLT","Num.lt_to_nat","castNum","instAddNat","instLTNat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder._simp_4","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder","reducibility":null,"statement_dag_size":35,"type_refs":["Eq","LE.le","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Num.instLE","castNum","instAddNat","instLENat"],"value_dag_size":43,"value_refs":["Eq.symm","LE.le","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Num","Num.instLE","Num.le_to_nat","castNum","instAddNat","instLENat","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder._simp_5","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.partialOrder","reducibility":null,"statement_dag_size":39,"type_refs":["And","Eq","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT"],"value_dag_size":43,"value_refs":["And","LE.le","LT.lt","Not","Preorder","Preorder.toLE","Preorder.toLT","lt_iff_le_not_ge","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.ppred_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.ppred_to_nat","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.pred_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.pred_to_nat","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.size_eq_natSize.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.size_eq_natSize","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.size_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.size_to_nat","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.succ'_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.succ'_to_nat","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Num","Num.pos","Num.zero","PosNum","Unit"],"value_dag_size":32,"value_refs":["Num","Num.casesOn","Num.pos","Num.zero","PosNum","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.Num.to_of_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.Num.to_of_nat","reducibility":"abbrev","statement_dag_size":25,"type_refs":["Nat","Nat.succ","OfNat.ofNat","Unit","instOfNatNat"],"value_dag_size":37,"value_refs":["Nat","Nat.casesOn","Nat.succ","OfNat.ofNat","Unit","Unit.unit","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.add_succ.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.add_succ","reducibility":"abbrev","statement_dag_size":57,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one"],"value_dag_size":100,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.add_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.add_to_nat","reducibility":"abbrev","statement_dag_size":52,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one"],"value_dag_size":95,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.bit0_of_bit0.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.bit0_of_bit0","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cast_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cast_to_nat","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":73,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit","Unit.unit"],"value_dag_size":70,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","False","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":326,"value_refs":["Eq","Eq.refl","False","Nat.hasNotBit","PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.cmp.match_1","PosNum.ctorIdx","PosNum.isOne._sparseCasesOn_1","PosNum.one","PosNum.rec","Unit","Unit.unit","absurd","id"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":81,"type_refs":["Eq","False","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":341,"value_refs":["Bool","Bool.false","Eq","Eq.mpr","Eq.refl","False","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.cmp.match_1","PosNum.ctorIdx","PosNum.isOne._sparseCasesOn_1","PosNum.isOne._sparseCasesOn_1.else_eq","PosNum.one","PosNum.rec","Unit","Unit.unit","_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.splitter._sparseCasesOn_3","absurd","congrArg","id","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_4","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":76,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_5","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":76,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_6","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":76,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.eq_7","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":null,"statement_dag_size":79,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"],"value_dag_size":76,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.cmp.match_1","PosNum.one","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.splitter","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1","reducibility":"abbrev","statement_dag_size":66,"type_refs":["Eq","False","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":205,"value_refs":["Bool","Bool.true","Eq","Eq.ndrec","Eq.refl","Eq.symm","False","False.elim","Nat","Nat.eq_of_beq_eq_true","Nat.hasNotBit","Nat.land","Nat.shiftRight","OfNat.ofNat","PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.ctorIdx","PosNum.one","Unit","Unit.unit","_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.splitter._sparseCasesOn_3","absurd","instOfNatNat","noConfusion_of_Nat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.splitter._sparseCasesOn_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp.match_1.splitter","reducibility":"abbrev","statement_dag_size":20,"type_refs":["Nat.hasNotBit","PosNum","PosNum.ctorIdx","PosNum.one"],"value_dag_size":89,"value_refs":["Bool","Bool.false","Eq.refl","Nat","Nat.hasNotBit","Nat.land","Nat.ne_of_beq_eq_false","Nat.shiftRight","OfNat.ofNat","PosNum","PosNum.bit0","PosNum.bit1","PosNum.ctorIdx","PosNum.one","PosNum.rec","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_eq._simp_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","LT.lt.ne","Preorder","Preorder.toLT","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_eq._simp_1_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_eq","reducibility":null,"statement_dag_size":31,"type_refs":["Eq","False","LT.lt","Preorder","Preorder.toLT"],"value_dag_size":34,"value_refs":["Eq","LT.lt","LT.lt.ne'","Preorder","Preorder.toLT","eq_false"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.cmp_to_nat","reducibility":"abbrev","statement_dag_size":68,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":124,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.lt_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.lt_to_nat","reducibility":"abbrev","statement_dag_size":101,"type_refs":["Eq","LT.lt","Nat","Nat.instOne","Ordering","Ordering.casesOn","Ordering.eq","Ordering.gt","Ordering.lt","PosNum","castPosNum","instAddNat","instLTNat"],"value_dag_size":142,"value_refs":["Eq","LT.lt","Nat","Nat.instOne","Ordering","Ordering.casesOn","Ordering.eq","Ordering.gt","Ordering.lt","PosNum","castPosNum","instAddNat","instLTNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.mul_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.mul_to_nat","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.of_to_nat'.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.of_to_nat'","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1.eq_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1.eq_2","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1.eq_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1","reducibility":null,"statement_dag_size":38,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit"],"value_dag_size":36,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.pred'.match_1","Unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1.splitter","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'.match_1","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":1,"value_refs":["PosNum.pred'.match_1"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'_to_nat","reducibility":"abbrev","statement_dag_size":73,"type_refs":["Eq","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Nat.succ","Num","Num.pos","Num.zero","OfNat.ofNat","One.toOfNat1","PosNum","castNum","castPosNum","instAddNat","instOneNum"],"value_dag_size":98,"value_refs":["Eq","MulZeroClass.toZero","Nat","Nat.instMulZeroClass","Nat.instOne","Nat.succ","Num","Num.casesOn","Num.pos","Num.zero","OfNat.ofNat","One.toOfNat1","PosNum","castNum","castPosNum","instAddNat","instOneNum"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'_to_nat.match_1_3","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.pred'_to_nat","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_eq_natSize.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_eq_natSize","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat._proof_1_7","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat","reducibility":null,"statement_dag_size":48,"type_refs":["Eq","HMul.hMul","LT.lt","Nat","Nat.instOne","Not","OfNat.ofNat","PosNum","castPosNum","instAddNat","instHMul","instLTNat","instMulNat","instOfNatNat"],"value_dag_size":241,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.mp","Eq.refl","False","HMul.hMul","Int","Int.Internal.Linear.Expr","Int.Internal.Linear.Expr.mulL","Int.Internal.Linear.Expr.num","Int.Internal.Linear.Expr.var","Int.Internal.Linear.Poly","Int.Internal.Linear.Poly.add","Int.Internal.Linear.Poly.num","Int.Internal.Linear.eq_coeff","Int.Internal.Linear.eq_le_subst_nonneg","Int.Internal.Linear.eq_norm_expr","Int.Internal.Linear.le_norm_expr","Int.Internal.Linear.le_unsat","Int.instMul","Int.instNegInt","LE.le","LT.lt","Lean.Grind.Nat.lt_eq","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Lean.RArray","Lean.RArray.leaf","Nat","Nat.ToInt.mul_congr","Nat.ToInt.natCast_ofNat","Nat.ToInt.of_eq","Nat.ToInt.of_le","Nat.instOne","NatCast.natCast","Neg.neg","Not","OfNat.ofNat","PosNum","castPosNum","eagerReduce","id","instAddNat","instHMul","instLENat","instLTNat","instMulNat","instNatCastInt","instOfNat","instOfNatNat"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat._proof_1_8","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat","reducibility":null,"statement_dag_size":53,"type_refs":["Eq","HAdd.hAdd","HMul.hMul","Nat","Nat.instOne","Not","OfNat.ofNat","PosNum","castPosNum","instAddNat","instHAdd","instHMul","instMulNat","instOfNatNat"],"value_dag_size":102,"value_refs":["Bool","Bool.true","Classical.byContradiction","Eq","Eq.refl","Eq.trans","False","False.casesOn","HAdd.hAdd","HMul.hMul","LT.lt","Lean.Grind.intro_with_eq","Lean.Grind.not_not","Nat","Nat.Simproc.add_eq_gt","Nat.decLt","Nat.instOne","Not","OfNat.ofNat","PosNum","castPosNum","instAddNat","instHAdd","instHMul","instLTNat","instMulNat","instOfNatNat","of_decide_eq_true"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat.match_1_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.size_to_nat","reducibility":"abbrev","statement_dag_size":25,"type_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","Unit"],"value_dag_size":40,"value_refs":["PosNum","PosNum.bit0","PosNum.bit1","PosNum.casesOn","PosNum.one","Unit","Unit.unit"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Data.Num.Lemmas","name":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.succ.match_1.eq_1","namespace":"_private.Mathlib.Data.Num.Lemmas.0.PosNum.succ.match_1","reducibility":null,"statement_dag_size":36,"type_refs":["Eq","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.succ.match_1","Unit","Unit.unit"],"value_dag_size":33,"value_refs":["Eq.refl","PosNum","PosNum.bit0","PosNum.bit1","PosNum.one","PosNum.succ.match_1","Unit"]}